Academic literature on the topic 'Trajectory convergence'

This paper analyzes the convergence properties and convergence region of a class of trajectory-based power flow methods. The convergence region of the trajectory-based method is a connected set and possesses the near-by property. The convergence region of Newton method and trajectory-based method in solving power flow problems are numerically investigated. Since the convergence region of trajectory-based method corresponds to the stability region of the nonlinear dynamic system, the stability regions of two dynamic systems are computed. The numerical results indicate that the stability region of the dynamic system possesses better geometry features than the convergence region of Newton method. These properties make the trajectory-based power flow method robust, especially on heavy loading conditions.

A mathematical model is established for self-twist spinning process by applying laws of fluid mechanics (i.e. mass conservation and momentum conservation). The motion curve of the convergent point was determined and the convergence point was decided by densities and velocities of two fed-in strands and the resultant self-twist yarn, independent of their mechanical properties. The experimental verification proves that the motion trajectory of the convergence point reaches a better agreement with the theoretical trajectory. The results provide general way to study the self-twist yarn spinning process and optimize the process parameters.

The output trajectory convergence of an extended projection neural network was developed under the positive definiteness condition of the Jacobian matrix of nonlinear mapping. This note offers several new convergence results. The state trajectory convergence and the output trajectory convergence of the extended projection neural network are obtained under the positive semidefiniteness condition of the Jacobian matrix. Comparison and illustrative examples demonstrate applied significance of these new results.

Purpose The purpose of this study is to investigate sequences of event and the resulting innovation paths and trajectories followed by a university spin-off organization. Design/methodology/approach A single longitudinal case study methodology was applied to analyze innovation events and paths along the trajectory. Narrative methods were used to analyze actor perceptions on innovation processes/events. Findings The study categorizes events and paths in two categories, technical and commercialization, and finds that lock-in events matter for convergence of an innovation trajectory. The results indicate that understanding critical events may assist timely interventions in the innovation paths, thus potentially avoiding disruptions of the development of an innovation trajectory. The temporal processes reveal contrasting convergence–divergence patterns in the trajectory, depending on the types of events that occur. Research limitations/implications Using a single case data may limit the applicability of the findings, which calls for future research. Practical implications Industries could monitor the technical and commercialization paths as a strategy to reduce “vulnerability” of the innovation trajectory and possible negative impacts. Knowledge about the role of the CEO is key for a university spin-off organization. Originality/value This study presents a new typology of events and paths, identifies and characterizes lock-in events and shows the relatively fragile dexterity between convergent and divergent paths along an innovation trajectory.

The Optimal trajectory design for hypersonic cruise missile is an optimal control problem with strict terminal constraints and variable final time. The classical algorithms always encounter the problems of high sensitivity to initial guess and local convergence in solving this problem. Aiming at these problems, genetic algorithm (GA) which is of good global convergence is applied to designing the optimal trajectory for hypersonic cruise missile. In order to improve the convergence rate of GA and overcome its premature problems, this text introduces a predatory search (PS) strategy to speed the convergence of genetic algorithms, robust and closer to the optimal solution. This text compares the original genetic algorithm (GA) and improved genetic algorithm by the emulate experiments, and the results show that the PSGA is a more effective method to design the Optimal trajectory for hypersonic cruise missile than the original genetic algorithm.

The dynamics model of the unmanned underwater vehicle (UUV) system is highly nonlinear, multi-degree-of-freedom, strongly coupled, and time-varying. Its motion control has been a complex problem due to the unknown information about and the uncertainty of the working environment. To improve the performance and reliability of UUV trajectory tracking control, a trajectory tracking method based on nonlinear model predictive control is designed, and an improved gray wolf optimization (IGWO) is proposed for the optimization of nonlinear model predictive control. The convergence factor of IGWO is designed as a nonlinear attenuation function, and the memory function is added to the position update equation to enhance the effect of trajectory tracking control. Through the simulation in the ROS environment, the influence of the convergence factor on the convergence rate of trajectory tracking error and tracking control performance is obtained. By comparing the tracking effects of several groups of reference trajectories, it is shown that the proposed method is universally applicable and effective to the trajectory tracking control of UUV. Compared with traditional gray wolf optimization (GWO), SQP, and other optimization algorithms, the reliability of the proposed method for UUV trajectory tracking control is demonstrated.

Abstract In this article, the implementation of the method of parallel convergence in space in a computer mathematics system is considered and discussed. In this method, the pursuer’s velocity vector is directed arbitrarily. The pursuer’s trajectory gradually approaches movement in the plane formed by the line connecting the initial positions of the pursuer and the target, and the velocity vector. In this task, the target moves uniformly and rectilinearly. The pursuer moves evenly. The points of the pursuer’s trajectory are calculated sequentially. They are being the result of the intersection of the plane containing the line of sight, sphere and cone. As we approach the plane where the target is moving, the algorithm for calculating the trajectory points changes. Now the point of the pursuer’s trajectory is the result of the intersection of the sphere, the plane of movement of the target and the plane containing the line of sight.

The heating load forecast provides a basis for saving heating energy. Considering the nonstationary, nonlinear, and large time-delay characteristics of thermal load, this paper introduces the trajectory tracking stability theory into the field of load forecasting and proposes a heuristic correction that can ensure the convergence of forecast errors and does not depend on the system prediction model algorithm. The Lyapunov method is used to derive an error convergence criterion that has nothing to do with the prediction model, and a heuristic correction algorithm is designed for the predicted value with error divergence trend to ensure the error convergence of the load forecast sequence.

In this paper, a new open-loop PD2D? type a fractional order iterative learning control (ILC) is studied for joint space trajectory tracking control of a linearized uncertain robotic arm. The robust convergent analysis of the tracking errors has been done in time domain where it is theoretically proven that the boundednesses of the tracking error are guaranteed in the presence of model uncertainty. The convergence of the proposed open-loop ILC law is proven mathematically using Gronwall integral inequality for a linearized robotic system and sufficient conditions for convergence and robustness are obtained.

Consider the problem of developing an algorithm that computes optimal preprogrammed evasive maneuvers for a Maneuvering Reentry Vehicle (MaRV) attacking a target defended with Anti-Ballistic Missiles (ABMs). The problem is large in terms of the number of optimization parameters, and perhaps in terms of the number of nonlinear constraints. Since both MaRV and ABM trajectories are expensive to compute, rapid convergence of the optimization algorithm is of prime concern. This paper examines a discontinuity in the cost function that degrades both the speed and the reliability of optimizer convergence. A solution is offered, proposing that the optimization algorithm be operated in a new parameter space, in which the discontinuity occurs at infinity. Effectively, the mapping prevents the optimization algorithm from crossing the discontinuity thereby improving optimizer convergence. Results comparing convergence with and without the parameter mapping demonstrate the effectiveness of the procedure.
Master of Science

China is a large country characterized by remarkable growth and distinct regional diversity. Spatial disparity has always been a hot issue since China has been struggling to follow a balanced growth path but still confronting with unprecedented pressures and challenges. To better understand the inequality level benchmarking spatial distributions of Chinese provinces and municipalities and estimate dynamic trajectory of sustainable development in China, I constructed the Composite Index of Regional Development (CIRD) with five sub pillars/dimensions involving Macroeconomic Index (MEI), Science and Innovation Index (SCI), Environmental Sustainability Index (ESI), Human Capital Index (HCI) and Public Facilities Index (PFI), endeavoring to cover various fields of regional socioeconomic development. Ranking reports on the five sub dimensions and aggregated CIRD were provided in order to better measure the developmental degrees of 31 or 30 Chinese provinces and municipalities over 13 years from 1998 to 2010 as the time interval of three “Five-year Plans”. Further empirical applications of this CIRD focused on clustering and convergence estimation, attempting to fill up the gap in quantifying the developmental levels of regional comprehensive socioeconomics and estimating the dynamic convergence trajectory of regional sustainable development in a long run. Four clusters were benchmarked geographically-oriented in the map on the basis of cluster analysis, and club-convergence was observed in the Chinese provinces and municipalities based on stochastic kernel density estimation.

China is a large country characterized by remarkable growth and distinct regional diversity. Spatial disparity has always been a hot issue since China has been struggling to follow a balanced growth path but still confronting with unprecedented pressures and challenges. To better understand the inequality level benchmarking spatial distributions of Chinese provinces and municipalities and estimate dynamic trajectory of sustainable development in China, I constructed the Composite Index of Regional Development (CIRD) with five sub pillars/dimensions involving Macroeconomic Index (MEI), Science and Innovation Index (SCI), Environmental Sustainability Index (ESI), Human Capital Index (HCI) and Public Facilities Index (PFI), endeavoring to cover various fields of regional socioeconomic development. Ranking reports on the five sub dimensions and aggregated CIRD were provided in order to better measure the developmental degrees of 31 or 30 Chinese provinces and municipalities over 13 years from 1998 to 2010 as the time interval of three “Five-year Plans”. Further empirical applications of this CIRD focused on clustering and convergence estimation, attempting to fill up the gap in quantifying the developmental levels of regional comprehensive socioeconomics and estimating the dynamic convergence trajectory of regional sustainable development in a long run. Four clusters were benchmarked geographically-oriented in the map on the basis of cluster analysis, and club-convergence was observed in the Chinese provinces and municipalities based on stochastic kernel density estimation.

Motivé par l'omniprésence de l'optimisation dans de nombreux domaines de la science et de l'ingénierie, en particulier dans la science des données, ce manuscrit de thèse exploite le lien étroit entre les systèmes dynamiques dissipatifs à temps continu et les algorithmes d'optimisation pour fournir une analyse systématique du comportement global et local de plusieurs systèmes du premier et du second ordre, en se concentrant sur le cadre convexe, stochastique et en dimension infinie d'une part, et le cadre non convexe, déterministe et en dimension finie d'autre part. Pour les problèmes de minimisation convexe stochastique dans des espaces de Hilbert réels séparables de dimension infinie, notre proposition clé est de les analyser à travers le prisme des équations différentielles stochastiques (EDS) et des inclusions différentielles stochastiques (IDS), ainsi que de leurs variantes inertielles. Nous considérons d'abord les problèmes convexes différentiables lisses et les EDS du premier ordre, en démontrant une convergence faible presque sûre vers les minimiseurs sous hypothèse d'intégrabilité du bruit et en fournissant une analyse globale et locale complète de la complexité. Nous étudions également des problèmes convexes non lisses composites utilisant des IDS du premier ordre et montrons que, sous des conditions d'intégrabilité du bruit, la convergence faible presque sûre des trajectoires vers les minimiseurs, et avec la régularisation de Tikhonov la convergence forte presque sûre des trajectoires vers la solution de norme minimale. Nous développons ensuite un cadre mathématique unifié pour analyser la dynamique inertielle stochastique du second ordre via la reparamétrisation temporelle et le moyennage de la dynamique stochastique du premier ordre, ce qui permet d'obtenir une convergence faible presque sûre des trajectoires vers les minimiseurs et une convergence rapide des valeurs et des gradients. Ces résultats sont étendus à des EDS plus générales du second ordre avec un amortissement visqueux et Hessien, en utilisant une analyse de Lyapunov spécifique pour prouver la convergence et établir de nouveaux taux de convergence. Enfin, nous étudions des problèmes d'optimisation déterministes non convexes et proposons plusieurs algorithmes inertiels pour les résoudre, dérivés d'équations différentielles ordinaires (EDO) du second ordre combinant à la fois un amortissement visqueux sans vanité et un amortissement géométrique piloté par le Hessien, sous des formes explicites et implicites. Nous prouvons d'abord la convergence des trajectoires en temps continu des EDO vers un point critique pour des objectives vérifiant la propriété de Kurdyka-Lojasiewicz (KL) avec des taux explicites, et génériquement vers un minimum local si l'objective est Morse. De plus, nous proposons des schémas algorithmiques par une discrétisation appropriée de ces EDO et montrons que toutes les propriétés précédentes des trajectoires en temps continu sont toujours valables dans le cadre discret sous réserve d'un choix approprié de la taille du pas
Motivated by the ubiquity of optimization in many areas of science and engineering, particularly in data science, this thesis exploits the close link between continuous-time dissipative dynamical systems and optimization algorithms to provide a systematic analysis of the global and local behavior of several first- and second-order systems, focusing on convex, stochastic, and infinite-dimensional settings on the one hand, and non-convex, deterministic, and finite-dimensional settings on the other hand. For stochastic convex minimization problems in infinite-dimensional separable real Hilbert spaces, our key proposal is to analyze them through the lens of stochastic differential equations (SDEs) and inclusions (SDIs), as well as their inertial variants. We first consider smooth differentiable convex problems and first-order SDEs, demonstrating almost sure weak convergence towards minimizers under integrability of the noise and providing a comprehensive global and local complexity analysis. We also study composite non-smooth convex problems using first-order SDIs, and show under integrability conditions on the noise, almost sure weak convergence of the trajectory towards a minimizer, with Tikhonov regularization almost sure strong convergence of trajectory to the minimal norm solution. We then turn to developing a unified mathematical framework for analyzing second-order stochastic inertial dynamics via time scaling and averaging of stochastic first-order dynamics, achieving almost sure weak convergence of trajectories towards minimizers and fast convergence of values and gradients. These results are extended to more general second-order SDEs with viscous and Hessian-driven damping, utilizing a dedicated Lyapunov analysis to prove convergence and establish new convergence rates. Finally, we study deterministic non-convex optimization problems and propose several inertial algorithms to solve them derived from second-order ordinary differential equations (ODEs) combining both non-vanishing viscous damping and geometric Hessian-driven damping in explicit and implicit forms. We first prove convergence of the continuous-time trajectories of the ODEs to a critical point under the Kurdyka-Lojasiewicz (KL) property with explicit rates, and generically to a local minimum under a Morse condition. Moreover, we propose algorithmic schemes by appropriate discretization of these ODEs and show that all previous properties of the continuous-time trajectories still hold in the discrete setting under a proper choice of the stepsize

This article seeks to present the principal stages of the prehistory and history of the Quechuan language family in its interaction with the Aimaran family. It reconstructs a plausible scenario for a unique, intensive process of linguistic convergence that underlies the protolanguages of both families. From there on, it traces the principal developments that characterize the history of the Quechuan linguistic family, such as the initial split in two main branches, Quechua I and Quechua II (following Torero 1964), as well as further divisions that subsequently affected the Quechua II branch (Cajamarca, Laraos and Lincha Quechua, Quechua IIB and IIC). It is argued that the state of Huari (AD 500-900) may have acted as a driving force (cf. Beresford-Jones and Heggarty 2011) for the initial diffusion of Quechua II and, later on, for the expansion of southern Aimara and Quechua IIC into the Andes of southern Perú.
Este trabajo pretende presentar las principales etapas de la prehistoria e historia de la familia lingüística quechua en su interacción con la familia aimara. Se reconstruye el escenario más plausible de un proceso intensivo y excepcional de convergencia lingüística subyacente a las protolenguas de ambas familias. Desde allí, se trazan los desarrollos más marcados ocurridos en la historia de la familia lingüística quechua, tales como su bifurcación inicial en dos ramas dialectales, quechua I y II (según Torero 1964), así como las particiones posteriores del quechua II (quechua de Cajamarca, Laraos y Lincha Quechua, quechua IIB y IIC). Se defiende la hipótesis de que el Estado huari (500-900 d.n.e.) operó como fuerza motriz (cf. Beresford-Jones y Heggarty 2011) para la difusión inicial del quechua II y, posteriormente, para la expansión del aimara sureño y del quechua IIC en los Andes meridionales del Perú.

La famille a un parametre d'applications de l'intervalle que nous etudions a l'avantage de se preter facilement a des calculs combinatoires. Ceux-ci en retour, permettent de faire le calcul de tout le diagramme de bifurcation, de demontrer quelques belles proprietes de la famille et de mieux comprendre ce qu'est le chaos

A new method of adaptive impulse control is developed to precisely and quickly control the position of machine components subject to friction. Friction dominates the forces affecting fine positioning dynamics. Friction can depend on payload, velocity, step size, path, initial position, temperature, and other variables. Control problems such as steady-state error and limit cycles often arise when applying conventional control techniques to the position control problem. Studies in the last few decades have shown that impulsive control can produce repeatable displacements as small as ten nanometers without limit cycles or steady-state error in machines subject to dry sliding friction. These displacements are achieved through the application of short duration, high intensity pulses. The relationship between pulse duration and displacement is seldom a simple function. The most dependable practical methods for control are self-tuning; they learn from online experience by adapting an internal control parameter until precise position control is achieved. To date, the best known adaptive pulse control methods adapt a single control parameter. While effective, the single parameter methods suffer from sub-optimal settling times and poor parameter convergence. To improve performance while maintaining the capacity for ultimate precision, a new control method referred to as Adaptive Impulse Control (AIC) has been developed. To better fit the nonlinear relationship between pulses and displacements, AIC adaptively tunes a set of parameters. Each parameter affects a different range of displacements. Online updates depend on the residual control error following each pulse, an estimate of pulse sensitivity, and a learning gain. After an update is calculated, it is distributed among the parameters that were used to calculate the most recent pulse. As the stored relationship converges to the actual relationship of the machine, pulses become more accurate and fewer pulses are needed to reach each desired destination. When fewer pulses are needed, settling time improves and efficiency increases. AIC is experimentally compared to conventional PID control and other adaptive pulse control methods on a rotary system with a position measurement resolution of 16000 encoder counts per revolution of the load wheel. The friction in the test system is nonlinear and irregular with a position dependent break-away torque that varies by a factor of more than 1.8 to 1. AIC is shown to improve settling times by as much as a factor of two when compared to other adaptive pulse control methods while maintaining precise control tolerances.

Applications such as urban surveillance, search and rescue, agricultural applications, military applications, etc., require miniature air vehicles (MAVs) to fly for a long time. But they have restricted flight duration due to their dependence on battery life, which necessitates optimal path planning. The generated optimal path should obey the curvature limits prescribed by the minimum turn radius/ maximum turn rate of the MAV. Further, in a dynamically changing environment, the final configuration that the MAV has to achieve may change en route, which demands the path to be replanned by an airborne processor in real-time. As MAVs are small in size and light in weight, wind has a very significant effect on the flight of MAVs and the computation of the minimum-time path in the presence of wind plays an important role. The thesis develops feasible trajectory generation algorithms which are fast, efficient, optimal and implementable in an onboard computer for rectilinear and circular path convergence problems and waypoint following problems both in the absence and in the presence of wind. The first part of the thesis addresses the problem of computation of optimal trajectories when MAVs fly on a two-dimensional (2D) plane maintaining a constant altitude. The shortest path is computed for MAVs from a given initial position and orientation to a given final path with a specified direction as required for a given mission. Unlike the classical Dubins problem where the shortest path was computed between two given configurations (position and orientation), the final point in this case is not specified. However, the final path, which can either be a rectilinear path or a circular path, and the direction to which the MAV should converge, is specified. The time-optimal path of MAVs is developed in the presence of wind mainly using the geometric approach although a few important properties are also obtained using optimal control theory, specifically, Pontryagin’s minimum principle (which provides only the necessary condition for optimality) for control-constrained systems. The complete optima l solution to this problem in all its generality is a major contribution of this thesis as existing methods in the literature that address this problem are either not optimal or do not give a complete solution. Further, the time-optimal path for specified initial and final configurations is generated in reasonably short time without computing all the path lengths of possible candidate paths, which is the method that exists in the literature for similar problems. Simulation results illustrate path generation for various cases, including the presence of steady and time-varying wind. Another problem in MAV path planning in 2D addressed in this thesis computes an extremal path that transitions between two consecutive waypoint segments (obtained by joining two way points in sequence) in a time-optimal fashion. This designed trajectory, named as γ-trajectory, is also used to track the maximum portion of waypoint segments in minimum time and the shortest distance between this trajectory and the associated waypoint can be set to a desired value. Another optimal path, called the loop trajectory, that goes through the way points as well as through the entire waypoint segments, is also proposed. Subsequently, the thesis proposes algorithms to generate trajectories in the presence of steady wind and compares these with the optimal trajectory generated using nonlinear programming based multiple shooting method to show that the generated paths are optimal in most cases. In three-dimensional (3D) space, if the initial and final configurations – in terms of (X,Y,Z) position, heading angle and flight path angle- of the vehicle are specified then shortest path computation is an interesting problem in literature. The proposed method in this thesis is based on 3D geometry and, unlike the existing iterative methods which yield suboptimal paths and are computationally more intensive, this method generates the shortest path in much less time. Due to its simplicity and low computational requirements, this approach can be implemented on a MAV in real-time. But, If the path demands very high pitch angle (as in the case of steep climbs), the generated path may not be flyable for an aerial vehicle with limited range of flight path angles. In such cases numerical methods, such as multiple shooting, coupled with nonlinear programming, are used to obtain the optimal solution. The time-optimal 3D path is also developed in the presence of wind which has a magnitude comparable to the speed of MAVs. The simulation results show path generation for a few sample cases to show the efficacy of the proposed approach as compared to the available approach in the literature. Next, the path convergence problem is studied in 3D for MAVs. The shortest path is generated to converge to a rectilinear path and a circular path starting from a known initial position and orientation. The method is also extended to compute the time-optimal path in the presence of wind. In simulation, optimal paths are generated for a variety of cases to show the efficacy of the algorithm. The other problem discussed in this thesis considers curvature-constrained trajectory generation technique for following a series of way points in 3D space. Extending the idea used in 2D, a γ-trajectory in 3D is generated to track the maximum portion of waypoint segments with a desired shortest distance between the trajectory and the associated waypoint. Considering the flyability issue of the plane a loop-trajectory is generated which is flyable by a MAV with constrained flight path angle. Simulation results are given for illustrative purposes. The path generation algorithms are all based on a kinematic model, considering the vehicle as a point in space. Implementing these results in a real MAV will require the dynamics of the MAV to be considered. So, a 6-DOF SIMULINK model of a MAV is used to demonstrate the tracking of the computed paths both in 2D plane and in 3D space using autopilots consisting of proportional-integral-derivative (PID )controllers .Achieving terminal condition accurately in real-time, if there is noisy measurement of wind data, is also addressed.

Applications such as urban surveillance, search and rescue, agricultural applications, military applications, etc., require miniature air vehicles (MAVs) to fly for a long time. But they have restricted flight duration due to their dependence on battery life, which necessitates optimal path planning. The generated optimal path should obey the curvature limits prescribed by the minimum turn radius/ maximum turn rate of the MAV. Further, in a dynamically changing environment, the final configuration that the MAV has to achieve may change en route, which demands the path to be replanned by an airborne processor in real-time. As MAVs are small in size and light in weight, wind has a very significant effect on the flight of MAVs and the computation of the minimum-time path in the presence of wind plays an important role. The thesis develops feasible trajectory generation algorithms which are fast, efficient, optimal and implementable in an onboard computer for rectilinear and circular path convergence problems and waypoint following problems both in the absence and in the presence of wind. The first part of the thesis addresses the problem of computation of optimal trajectories when MAVs fly on a two-dimensional (2D) plane maintaining a constant altitude. The shortest path is computed for MAVs from a given initial position and orientation to a given final path with a specified direction as required for a given mission. Unlike the classical Dubins problem where the shortest path was computed between two given configurations (position and orientation), the final point in this case is not specified. However, the final path, which can either be a rectilinear path or a circular path, and the direction to which the MAV should converge, is specified. The time-optimal path of MAVs is developed in the presence of wind mainly using the geometric approach although a few important properties are also obtained using optimal control theory, specifically, Pontryagin’s minimum principle (which provides only the necessary condition for optimality) for control-constrained systems. The complete optima l solution to this problem in all its generality is a major contribution of this thesis as existing methods in the literature that address this problem are either not optimal or do not give a complete solution. Further, the time-optimal path for specified initial and final configurations is generated in reasonably short time without computing all the path lengths of possible candidate paths, which is the method that exists in the literature for similar problems. Simulation results illustrate path generation for various cases, including the presence of steady and time-varying wind. Another problem in MAV path planning in 2D addressed in this thesis computes an extremal path that transitions between two consecutive waypoint segments (obtained by joining two way points in sequence) in a time-optimal fashion. This designed trajectory, named as γ-trajectory, is also used to track the maximum portion of waypoint segments in minimum time and the shortest distance between this trajectory and the associated waypoint can be set to a desired value. Another optimal path, called the loop trajectory, that goes through the way points as well as through the entire waypoint segments, is also proposed. Subsequently, the thesis proposes algorithms to generate trajectories in the presence of steady wind and compares these with the optimal trajectory generated using nonlinear programming based multiple shooting method to show that the generated paths are optimal in most cases. In three-dimensional (3D) space, if the initial and final configurations – in terms of (X,Y,Z) position, heading angle and flight path angle- of the vehicle are specified then shortest path computation is an interesting problem in literature. The proposed method in this thesis is based on 3D geometry and, unlike the existing iterative methods which yield suboptimal paths and are computationally more intensive, this method generates the shortest path in much less time. Due to its simplicity and low computational requirements, this approach can be implemented on a MAV in real-time. But, If the path demands very high pitch angle (as in the case of steep climbs), the generated path may not be flyable for an aerial vehicle with limited range of flight path angles. In such cases numerical methods, such as multiple shooting, coupled with nonlinear programming, are used to obtain the optimal solution. The time-optimal 3D path is also developed in the presence of wind which has a magnitude comparable to the speed of MAVs. The simulation results show path generation for a few sample cases to show the efficacy of the proposed approach as compared to the available approach in the literature. Next, the path convergence problem is studied in 3D for MAVs. The shortest path is generated to converge to a rectilinear path and a circular path starting from a known initial position and orientation. The method is also extended to compute the time-optimal path in the presence of wind. In simulation, optimal paths are generated for a variety of cases to show the efficacy of the algorithm. The other problem discussed in this thesis considers curvature-constrained trajectory generation technique for following a series of way points in 3D space. Extending the idea used in 2D, a γ-trajectory in 3D is generated to track the maximum portion of waypoint segments with a desired shortest distance between the trajectory and the associated waypoint. Considering the flyability issue of the plane a loop-trajectory is generated which is flyable by a MAV with constrained flight path angle. Simulation results are given for illustrative purposes. The path generation algorithms are all based on a kinematic model, considering the vehicle as a point in space. Implementing these results in a real MAV will require the dynamics of the MAV to be considered. So, a 6-DOF SIMULINK model of a MAV is used to demonstrate the tracking of the computed paths both in 2D plane and in 3D space using autopilots consisting of proportional-integral-derivative (PID )controllers .Achieving terminal condition accurately in real-time, if there is noisy measurement of wind data, is also addressed.

Although India’s foreign trade policy has undergone drastic changes over the years, its recognition of the international trading system as the vehicle for trade negotiations has remained unwavering. As India’s economy has begun to grow due to the use of open policies, so has its influence in championing the ambitions of developing countries. India’s history tells a story of the convergence of its foreign trade policy with the underlying principles of the multilateral trading system. However, looking forward, to maximize fully the benefits to it of the international trading system, India’s attention must now turn to facilitating convergence between its domestic policy and its foreign policy. This chapter discusses India’s trajectory in the international trading system over the years and the domestic issues India must now confront in order to fully garner its benefits.

One of the most puzzling pieces of evidence surrounding Brazil’s economic performance is that, despite the country’s ability to grow at high rates, its long-term growth has been disappointing. Behind this deficient long-term outcome, Brazil shows a high degree of growth volatility. It has experienced substantial growth booms and busts as measured by international standards. This chapter provides an analysis of growth volatility and its impact on Brazil’s growth performance and long-term trajectory. Particular attention is given to its long-term underperformance, its macroeconomic regularities, and the possible causes and implications of its limited growth potential and degree of international convergence.

This article discusses Internet research ethics, which promises to become an ever-more robust and significant field within information ethics, on the one hand, and research ethics more broadly, on the other. As new venues emerge for human–human and human–machine interaction, it seems certain that new ethical conundrums will emerge. But the overall history of Internet research ethics includes at least some convergence on key values and rights, while at the same time preserving important local differences with regard to approaches to ethical decision making and implementation of basic rights and principles – even across East–West divides. This trajectory suggests not the certainty of finding resolutions to every ethical problem that comes along, but rather the sense of finding such resolutions in the face of new difficulties, with sufficient frequency and success to encourage further efforts to do so.

Abstract The Unforgotten Women of the Islamic State explores the governance of the Islamic State (IS) terrorist organization through the lives and words of local Iraqi, Syrian, and Kurdish women. While the roles and activities of foreign (predominantly Western), pro-IS women have garnered significant attention, the experiences and insights of local civilian populations have been largely overlooked. Drawing on the testimonies of sixty-three local Sunni Muslim and Yazidi women, The Unforgotten Women of the Islamic State exposes the group’s intra-gender stratified system of governance. Eligibility for the group’s protection, security, ‘citizenship’, and entrance into the (semi-)public sphere was not universal, but required convergence with IS’s gender norms, through permanent erasure or at least temporary disguise of certain markers of difference. In some cases, this was directed by a premeditated ‘divide and conquer’ strategy; in others, this manifested as unregulated violences at the hands of individual group members, including women. The structure follows the trajectory of IS’s increasing control of its ‘citizens’ and captive populations, from its militarization of society; imposition of law and order; provision of goods and services; and intervention in civilians’ private lives. Through analysis of diverse first-hand accounts and the group’s documentation, Vale argues that the presence, exclusion, and victimization of local civilian women were necessary to the functioning and legitimation of IS’s ‘caliphate’ project, and the supremacy of affiliated men—and women. As a fledgling proto-state, IS needed local Iraqi, Syrian, and Kurdish women. Though far from represented or protected, they were by no means forgotten.

Presbyterians and Congregationalists arrived in colonial America as Dissenters; however, they soon exercised a religious and cultural dominance that extended well into the first half of the nineteenth century. The multi-faceted Second Great Awakening led within the Reformed camp by the Presbyterian James McGready in Kentucky, a host of New Divinity ministers in New England, and Congregationalist Charles Finney in New York energized Christians to improve society (Congregational and Presbyterian women were crucial to the three most important reform movements of the nineteenth century—antislavery, temperance, and missions) and extend the evangelical message around the world. Although outnumbered by other Protestant denominations by mid-century, Presbyterians and Congregationalists nevertheless expanded geographically, increased in absolute numbers, spread the Gospel at home and abroad, created enduring institutions, and continued to dominate formal religious thought. The overall trajectory of nineteenth-century Presbyterianism and Congregationalism in the United States is one that tracks from convergence to divergence, from cooperative endeavours and mutual interests in the first half the nineteenth century to an increasingly self-conscious denominational awareness that became firmly established in both denominations by the 1850s. With regional distribution of Congregationalists in the North and Presbyterians in the mid-Atlantic region and South, the Civil War intensified their differences (and also divided Presbyterians into antislavery northern and pro-slavery southern parties). By the post-Civil War period these denominations had for the most part gone their separate ways. However, apart from the southern Presbyterians, who remained consciously committed to conservatism, they faced a similar host of social and intellectual challenges, including higher criticism of the Bible and Darwinian evolutionary theory, to which they responded in varying ways. In general, Presbyterians maintained a conservative theological posture whereas Congregationalists accommodated to the challenges of modernity. At the turn of the century Congregationalists and Presbyterians continued to influence sectors of American life but their days of cultural hegemony were long past. In contrast to the nineteenth-century history of Presbyterian and Congregational churches in the United States, the Canadian story witnessed divergence evolving towards convergence and self-conscious denominationalism to ecclesiastical cooperation. During the very years when American Presbyterians were fragmenting over first theology, then slavery, and finally sectional conflict, political leaders in all regions of Canada entered negotiations aimed at establishing the Dominion of Canada, which were finalized in 1867. The new Dominion enjoyed the strong support of leading Canadian Presbyterians who saw in political confederation a model for uniting the many Presbyterian churches that Scotland’s fractious history had bequeathed to British North America. In 1875, the four largest Presbyterian denominations joined together as the Presbyterian Church in Canada. The unifying and mediating instincts of nineteenth-century Canadian Presbyterianism contributed to forces that in 1925 led two-thirds of Canadian Presbyterians (and almost 90 per cent of their ministers) into the United Church, Canada’s grand experiment in institutional ecumenism. By the end of the nineteenth century, Congregationalism had only a slight presence, whereas Presbyterians, by contrast, became increasingly more important until they stood at the centre of Canada’s Protestant history.

Evolutionary demography applies models and theories from evolutionary biology to understand variability in fertility and mortality patterns. Many important ecological influences derive from the natural environment, such as the burden of infectious disease, or the availability of energy and other nutrients. However, human society is itself a source of diverse stimuli and stresses that may generate profound impacts on demographic traits. On this issue, much attention to date has focused on the benefits of social interaction, in particular ‘cooperative breeding’ through which the costs of reproduction are shared among kin or others. In contrast, this chapter will use a simple model of social inequality, based on the ecological ‘producer-scrounger’ game, to shed light on how social hierarchy, through the key medium of nutrition, can shape diversity in life history trajectories. Life history trade-offs shape both physiological and behavioural characteristics of individuals, which in turn affect both fertility and mortality profiles. In every society, it is ultimately through relationships embedded in the context of nutrition that different groups within social hierarchies interact. The key insight from the producer-scrounger game is that in social hierarchies, the life history strategies of producers and scroungers are structurally inter-related. This results in contrasting phenotypes and demographic outcomes between the two groups. Those lower in social hierarchies have higher risks, and fewer opportunities to acquire resources, and may adapt through trade-offs that favour immediate survival and reproduction over growth and long-term health maintenance. In contrast, those with priority access to resources may demonstrate trade-offs that favour growth and long-term health maintenance, leading to greater longevity, a lengthier reproductive career and higher quality offspring. These contrasting life history strategies may emerge through the direct control of subordinates by high-ranked individuals, or through indirect control over the resources that subordinates struggle to access. This simple conceptual approach can help understand both contemporary variability within and between populations in demographic traits, and also their historical divergence or convergence over time.

AbstractDistributed stochastic gradient descent techniques have gained significant attention in recent years as a prevalent approach for reinforcement learning. Current distributed learning predominantly employs synchronous or asynchronous training strategies. While the asynchronous scheme avoids idle computing resources present in synchronous methods, it grapples with the stale gradient issue. This paper introduces a novel gradient correction algorithm aimed at alleviating the stale gradient problem. By leveraging second-order information within the worker node and incorporating current parameters from both the worker and server nodes, the gradient correction algorithm yields a refined gradient closer to the desired value. Initially, we outline the challenges associated with asynchronous update schemes and derive a gradient correction algorithm employing local second-order approximations. Subsequently, we propose an asynchronous training scheme incorporating gradient correction within the generalized policy iteration framework. Lastly, in the context of trajectory tracking tasks, we compare the impact of employing gradient correction versus its absence in an asynchronous update scheme. Simulation results underscore the superiority of our proposed training scheme, demonstrating notably faster convergence and higher policy performance compared to the existing asynchronous update methods.

The relationship between the Horthy era (1920–1944) and the communist era shows continuities if it is examined from a social historical perspective. The paper contributes to the reinterpretation of these relations by looking at Hungarian health care in the 1930s and 1940s with a focus on the relationship between international transfers and path dependency in forging health care reforms. I argue that the achievements communists regarded as inventions of socialism in health care and the welfare state had already been developed thoroughly in the 1930s and 1940s. It was only because of the strict wartime budget of the early 1940s that these welfare reforms had not been realised. With the help of internal affairs documents, essays on health care, and official statistics records in the National Archives of Hungary and the Semmelweis Library and Archives of Medical History in Budapest as well as press material, I demonstrate that, even if communists depicted the interwar period as “fascist and imperialist”, the health care system of the so-called “productive social policy” showed continuities. Moreover, social policy makers of the 1930s and early 1940s, such as Béla Johan, Ferenc Keresztes-Fischer and Béla Kovrig, also designed welfare and health care reforms for the post-war period by both developing already existing Hungarian programmes and selectively adapting foreign welfare models (American management principles, the Alsace scheme, and the Beveridge Plan). The study investigates Hungarian health care in view of the theory of path dependency and the macrohistorical convergence thesis developed by Béla Tomka (on the question of East-West convergence). It is within this framework that the paper addresses the issue of health care transfers to better understand the development of 20th -century European health care systems by identifying similarities and differences in their development as well as to speculate on the trajectory of various political solutions to social challenges, including health care.

Abstract The aim of this work is to propose a data-driven ILC algorithm that features fast convergence for nonlinear dynamic systems. This idea utilizes adaptive filtering that implicitly identifies the time-varying system inverse along the trajectory being tracked. By feeding the error signal through the copied inverse filter, it results in a rapidly convergent inversion-based ILC. This approach is compared to a nonlinear extension of the data-driven ILC that uses system adjoint as the learning filter. The developed algorithm is validated through simulation on a fully actuated 2 DOF Furuta pendulum.

Banco de la República is celebrating its 100th anniversary in 2023. This is a very significant anniversary and one that provides an opportunity to highlight the contribution the Bank has made to the country’s development. Its track record as guarantor of monetary stability has established it as the one independent state institution that generates the greatest confidence among Colombians due to its transparency, management capabilities, and effective compliance with the central banking and cultural responsibilities entrusted to it by the Constitution and the Law. On a date as important as this, the Board of Directors of Banco de la República (BDBR) pays tribute to the generations of governors and officers whose commitment and dedication have contributed to the growth of this institution.1 Banco de la República’s mandate was confirmed in the National Constitutional Assembly of 1991 where the citizens had the opportunity to elect the seventy people who would have the task of drafting a new constitution. The leaders of the three political movements with the most votes were elected as chairs to the Assembly, and this tripartite presidency reflected the plurality and the need for consensus among the different political groups to move the reform forward. Among the issues considered, the National Constitutional Assembly gave special importance to monetary stability. That is why they decided to include central banking and to provide Banco de la República with the necessary autonomy to use the instruments for which they are responsible without interference from other authorities. The constituent members understood that ensuring price stability is a state duty and that the entity responsible for this task must be enshrined in the Constitution and have the technical capability and institutional autonomy necessary to adopt the decisions they deem appropriate to achieve this fundamental objective in coordination with the general economic policy. In particular, Article 373 established that “the State, through Banco de la República, shall ensure the maintenance of the purchasing power of the currency,” a provision that coincided with the central banking system adopted by countries that have been successful in controlling inflation. In 1999, in Ruling 481, the Constitutional Court stated that “the duty to maintain the purchasing power of the currency applies to not only the monetary, credit, and exchange authority, i.e., the Board of Banco de la República, but also those who have responsibilities in the formulation and implementation of the general economic policy of the country” and that “the basic constitutional purpose of Banco de la República is the protection of a sound currency. However, this authority must take the other economic objectives of state intervention such as full employment into consideration in their decisions since these functions must be coordinated with the general economic policy.” The reforms to Banco de la República agreed upon in the Constitutional Assembly of 1991 and in Act 31/1992 can be summarized in the following aspects: i) the Bank was assigned a specific mandate: to maintain the purchasing power of the currency in coordination with the general economic policy; ii) the BDBR was designatedas the monetary, foreign exchange, and credit authority; iii) the Bank and its Board of Directors were granted a significant degree of independence from the government; iv) the Bank was prohibited from granting credit to the private sector except in the case of the financial sector; v) established that in order to grant credit to the government, the unanimous vote of its Board of Directors was required except in the case of open market transactions; vi) determined that the legislature may, in no case, order credit quotas in favor of the State or individuals; vii) Congress was appointed, on behalf of society, as the main addressee of the Bank’s reporting exercise; and viii) the responsibility for inspection, surveillance, and control over Banco de la República was delegated to the President of the Republic. The members of the National Constitutional Assembly clearly understood that the benefits of low and stable inflation extend to the whole of society and contribute mto the smooth functioning of the economic system. Among the most important of these is that low inflation promotes the efficient use of productive resources by allowing relative prices to better guide the allocation of resources since this promotes economic growth and increases the welfare of the population. Likewise, low inflation reduces uncertainty about the expected return on investment and future asset prices. This increases the confidence of economic agents, facilitates long-term financing, and stimulates investment. Since the low-income population is unable to protect itself from inflation by diversifying its assets, and a high proportion of its income is concentrated in the purchase of food and other basic goods that are generally the most affected by inflationary shocks, low inflation avoids arbitrary redistribution of income and wealth.2 Moreover, low inflation facilitates wage negotiations, creates a good labor climate, and reduces the volatility of employment levels. Finally, low inflation helps to make the tax system more transparent and equitable by avoiding the distortions that inflation introduces into the value of assets and income that make up the tax base. From the monetary authority’s point of view, one of the most relevant benefits of low inflation is the credibility that economic agents acquire in inflation targeting, which turns it into an effective nominal anchor on price levels. Upon receiving its mandate, and using its autonomy, Banco de la República began to announce specific annual inflation targets as of 1992. Although the proposed inflation targets were not met precisely during this first stage, a downward trend in inflation was achieved that took it from 32.4% in 1990 to 16.7% in 1998. At that time, the exchange rate was kept within a band. This limited the effectiveness of monetary policy, which simultaneously sought to meet an inflation target and an exchange rate target. The Asian crisis spread to emerging economies and significantly affected the Colombian economy. The exchange rate came under strong pressure to depreciate as access to foreign financing was cut off under conditions of a high foreign imbalance. This, together with the lack of exchange rate flexibility, prevented a countercyclical monetary policy and led to a 4.2% contraction in GDP that year. In this context of economic slowdown, annual inflation fell to 9.2% at the end of 1999, thus falling below the 15% target set for that year. This episode fully revealed how costly it could be, in terms of economic activity, to have inflation and exchange rate targets simultaneously. Towards the end of 1999, Banco de la República announced the adoption of a new monetary policy regime called the Inflation Targeting Plan. This regime, known internationally as ‘Inflation Targeting,’ has been gaining increasing acceptance in developed countries, having been adopted in 1991 by New Zealand, Canada, and England, among others, and has achieved significant advances in the management of inflation without incurring costs in terms of economic activity. In Latin America, Brazil and Chile also adopted it in 1999. In the case of Colombia, the last remaining requirement to be fulfilled in order to adopt said policy was exchange rate flexibility. This was realized around September 1999, when the BDBR decided to abandon the exchange-rate bands to allow the exchange rate to be freely determined in the market.Consistent with the constitutional mandate, the fundamental objective of this new policy approach was “the achievement of an inflation target that contributes to maintaining output growth around its potential.”3 This potential capacity was understood as the GDP growth that the economy can obtain if it fully utilizes its productive resources. To meet this objective, monetary policy must of necessity play a countercyclical role in the economy. This is because when economic activity is below its potential and there are idle resources, the monetary authority can reduce the interest rate in the absence of inflationary pressure to stimulate the economy and, when output exceeds its potential capacity, raise it. This policy principle, which is immersed in the models for guiding the monetary policy stance, makes the following two objectives fully compatible in the medium term: meeting the inflation target and achieving a level of economic activity that is consistent with its productive capacity. To achieve this purpose, the inflation targeting system uses the money market interest rate (at which the central bank supplies primary liquidity to commercial banks) as the primary policy instrument. This replaced the quantity of money as an intermediate monetary policy target that Banco de la República, like several other central banks, had used for a long time. In the case of Colombia, the objective of the new monetary policy approach implied, in practical terms, that the recovery of the economy after the 1999 contraction should be achieved while complying with the decreasing inflation targets established by the BDBR. The accomplishment of this purpose was remarkable. In the first half of the first decade of the 2000s, economic activity recovered significantly and reached a growth rate of 6.8% in 2006. Meanwhile, inflation gradually declined in line with inflation targets. That was how the inflation rate went from 9.2% in 1999 to 4.5% in 2006, thus meeting the inflation target established for that year while GDP reached its potential level. After this balance was achieved in 2006, inflation rebounded to 5.7% in 2007, above the 4.0% target for that year due to the fact that the 7.5% GDP growth exceeded the potential capacity of the economy.4 After proving the effectiveness of the inflation targeting system in its first years of operation, this policy regime continued to consolidate as the BDBR and the technical staff gained experience in its management and state-of-the-art economic models were incorporated to diagnose the present and future state of the economy and to assess the persistence of inflation deviations and expectations with respect to the inflation target. Beginning in 2010, the BDBR established the long-term 3.0% annual inflation target, which remains in effect today. Lower inflation has contributed to making the macroeconomic environment more stable, and this has favored sustained economic growth, financial stability, capital market development, and the functioning of payment systems. As a result, reductions in the inflationary risk premia and lower TES and credit interest rates were achieved. At the same time, the duration of public domestic debt increased significantly going from 2.27 years in December 2002 to 5.86 years in December 2022, and financial deepening, measured as the level of the portfolio as a percentage of GDP, went from around 20% in the mid-1990s to values above 45% in recent years in a healthy context for credit institutions.Having been granted autonomy by the Constitution to fulfill the mandate of preserving the purchasing power of the currency, the tangible achievements made by Banco de la República in managing inflation together with the significant benefits derived from the process of bringing inflation to its long-term target, make the BDBR’s current challenge to return inflation to the 3.0% target even more demanding and pressing. As is well known, starting in 2021, and especially in 2022, inflation in Colombia once again became a serious economic problem with high welfare costs. The inflationary phenomenon has not been exclusive to Colombia and many other developed and emerging countries have seen their inflation rates move away from the targets proposed by their central banks.5 The reasons for this phenomenon have been analyzed in recent Reports to Congress, and this new edition delves deeper into the subject with updated information. The solid institutional and technical base that supports the inflation targeting approach under which the monetary policy strategy operates gives the BDBR the necessary elements to face this difficult challenge with confidence. In this regard, the BDBR reiterated its commitment to the 3.0% inflation target in its November 25 communiqué and expects it to be reached by the end of 2024.6 Monetary policy will continue to focus on meeting this objective while ensuring the sustainability of economic activity, as mandated by the Constitution. Analyst surveys done in March showed a significant increase (from 32.3% in January to 48.5% in March) in the percentage of responses placing inflation expectations two years or more ahead in a range between 3.0% and 4.0%. This is a clear indication of the recovery of credibility in the medium-term inflation target and is consistent with the BDBR’s announcement made in November 2022. The moderation of the upward trend in inflation seen in January, and especially in February, will help to reinforce this revision of inflation expectations and will help to meet the proposed targets. After reaching 5.6% at the end of 2021, inflation maintained an upward trend throughout 2022 due to inflationary pressures from both external sources, associated with the aftermath of the pandemic and the consequences of the war in Ukraine, and domestic sources, resulting from: strengthening of local demand; price indexation processes stimulated by the increase in inflation expectations; the impact on food production caused by the mid-2021 strike; and the pass-through of depreciation to prices. The 10% increase in the minimum wage in 2021 and the 16% increase in 2022, both of which exceeded the actual inflation and the increase in productivity, accentuated the indexation processes by establishing a high nominal adjustment benchmark. Thus, total inflation went to 13.1% by the end of 2022. The annual change in food prices, which went from 17.2% to 27.8% between those two years, was the most influential factor in the surge in the Consumer Price Index (CPI). Another segment that contributed significantly to price increases was regulated products, which saw the annual change go from 7.1% in December 2021 to 11.8% by the end of 2022. The measure of core inflation excluding food and regulated items, in turn, went from 2.5% to 9.5% between the end of 2021 and the end of 2022. The substantial increase in core inflation shows that inflationary pressure has spread to most of the items in the household basket, which is characteristic of inflationary processes with generalized price indexation as is the case in Colombia. Monetary policy began to react early to this inflationary pressure. Thus, starting with its September 2021 session, the BDBR began a progressive change in the monetary policy stance moving away from the historical low of a 1.75% policy rate that had intended to stimulate the recovery of the economy. This adjustment process continued without interruption throughout 2022 and into the beginning of 2023 when the monetary policy rate reached 12.75% last January, thus accumulating an increase of 11 percentage points (pp). The public and the markets have been surprised that inflation continued to rise despite significant interest rate increases. However, as the BDBR has explained in its various communiqués, monetary policy works with a lag. Just as in 2022 economic activity recovered to a level above the pre-pandemic level, driven, along with other factors, by the monetary stimulus granted during the pandemic period and subsequent months, so too the effects of the current restrictive monetary policy will gradually take effect. This will allow us to expect the inflation rate to converge to 3.0% by the end of 2024 as is the BDBR’s purpose.Inflation results for January and February of this year showed declining marginal increases (13 bp and 3 bp respectively) compared to the change seen in December (59 bp). This suggests that a turning point in the inflation trend is approaching. In other Latin American countries such as Chile, Brazil, Perú, and Mexico, inflation has peaked and has begun to decline slowly, albeit with some ups and downs. It is to be expected that a similar process will take place in Colombia in the coming months. The expected decline in inflation in 2023 will be due, along with other factors, to lower cost pressure from abroad as a result of the gradual normalization of supply chains, the overcoming of supply shocks caused by the weather, and road blockades in previous years. This will be reflected in lower adjustments in food prices, as has already been seen in the first two months of the year and, of course, the lagged effect of monetary policy. The process of inflation convergence to the target will be gradual and will extend beyond 2023. This process will be facilitated if devaluation pressure is reversed. To this end, it is essential to continue consolidating fiscal sustainability and avoid messages on different public policy fronts that generate uncertainty and distrust. 1 This Report to Congress includes Box 1, which summarizes the trajectory of Banco de la República over the past 100 years. In addition, under the Bank’s auspices, several books that delve into various aspects of the history of this institution have been published in recent years. See, for example: Historia del Banco de la República 1923-2015; Tres banqueros centrales; Junta Directiva del Banco de la República: grandes episodios en 30 años de historia; Banco de la República: 90 años de la banca central en Colombia. 2 This is why lower inflation has been reflected in a reduction of income inequality as measured by the Gini coefficient that went from 58.7 in 1998 to 51.3 in the year prior to the pandemic. 3 See Gómez Javier, Uribe José Darío, Vargas Hernando (2002). “The Implementation of Inflation Targeting in Colombia”. Borradores de Economía, No. 202, March, available at: https://repositorio.banrep.gov.co/handle/20.500.12134/5220 4 See López-Enciso Enrique A.; Vargas-Herrera Hernando and Rodríguez-Niño Norberto (2016). “The inflation targeting strategy in Colombia. An historical view.” Borradores de Economía, No. 952. https://repositorio.banrep.gov.co/handle/20.500.12134/6263 5 According to the IMF, the percentage change in consumer prices between 2021 and 2022 went from 3.1% to 7.3% for advanced economies, and from 5.9% to 9.9% for emerging market and developing economies. 6 https://www.banrep.gov.co/es/noticias/junta-directiva-banco-republica-reitera-meta-inflacion-3

1.1 Macroeconomic summary In September, headline inflation (11.4% annually) and the average of core inflation indicators (8.6% annually) continued on a rising trend, and higher increases than expected were recorded. Forecasts increased again, and inflation expectations remained above 3%. Inflationary surprises in the third quarter were significant and widespread, and they are the result of several shocks. On the one hand, international cost and price shocks, which have mainly affected goods and foods, continue to exert upwards pressure on national inflation. In addition to these external supply shocks, domestic supply shocks have also affected foods. On the other hand, the strong recovery of aggregate demand, especially for private consumption and for machinery and equipment, as well as a higher accumulated depreciation of the Colombian peso and its pass-through to domestic prices also explain the rise in inflation. Indexation also contributes, both through the Consumer Price Index (CPI) and through the Producer Price Index (PPI), which continues to have a significant impact on electricity prices and, to a lesser degree, on other public utilities and rent. In comparison with July’s report, the new forecast trajectory for headline and core inflation (excluding food and regulated items) is higher in the forecast horizon, mainly due to exchange rate pressures, higher excess demand, and indexation at higher inflation rates, but it maintains a trend of convergence towards the target. In the case of food, a good domestic supply of perishable foods and some moderation in international processed food prices are still expected. However, the technical staff estimates higher pressures on this group’s prices from labor costs, raw material prices, and exchange rates. In terms of the CPI for regulated items, the new forecast supposes reductions in electricity prices at the end of the year, but the effects of indexation at higher inflation rates and the expected rises in fuel prices would continue to push this CPI group. Therefore, the new projection suggests that, in December, inflation would reach 11.3% and would decrease throughout 2023 and 2024, closing the year at 7.1% and 3.5%, respectively. These forecasts have a high level of uncertainty, due especially to the future behavior of international financial conditions, external price and cost shocks, the persistence of depreciation of the Colombian peso, the pace of adjustment of domestic demand, the indexation degree of nominal contracts, and the decisions that would be made regarding domestic fuel and electricity prices. Economic activity continues to surprise on the upside, and the projection of growth for 2022 rose from 6.9% to 7.9% but lowered for 2023 from 1.1% to 0.5%. Thus, excess demand is higher than estimated in the previous report, and it would diminish in 2023. Economic growth in the second quarterwas higher than estimated in July due to stronger domestic demand, mainly because of private consumption. Economic activity indicators for the third quarter suggest that the GDP would stay at a high level, above its potential, with an annual change of 6.4%, and 0.6% higher than observed in the second quarter. Nevertheless, these numbers reflect deceleration in its quarterly and annual growth. Domestic demand would show similar behavior, with a high value, higher than that of output. This can be explained partly by the strong behavior of private consumption and investment in machinery and equipment. In the third quarter, investment in construction would have continued with mediocre performance, which would still place it at levels lower than those observed before the pandemic. The trade deficit would have widened due to high imports with a stronger trend than that for exports. It is expected that, in the forecast horizon, consumption would decrease from its current high levels, partly as a consequence of tighter domestic financial conditions, lower repressed demand, higher exchange rate pressures on imported goods prices, and the deterioration of actual income due to the rise in inflation. Investment would continue to lag behind, without reaching the levels observed before the pandemic, in a context of high financing costs and high uncertainty. A lower projected behavior in domestic demand and the high levels of prices for oil and other basic goods that the country exports would be reflected in a reduction in the trade deficit. Due to all of this, economic growth for all of 2022, 2023, and 2024 would be 7.9%, 0.5%, and 1.3%, respectively. Expected excess demand (measured via the output gap) is estimated to be higher than contemplated in the previous report; it would diminish in 2023 and could turn negative in 2024. These estimates remain subject to a high degree of uncertainty related to global political tension, a rise in international interest rates, and the effects of this rise on demand and financial conditions abroad. In the domestic context, the evolution of fiscal policy as well as future measures regarding economic policy and their possible effects on macroeconomic imbalances in the country, among others, are factors that generate uncertainty and affect risk premia, the exchange rate, investment, and the country’s economic activity. Interest rates at several of the world’s main central banks continue to rise, some at a pace higher than expected by the market. This is in response to the high levels of inflation and their inflation expectations, which continue to exceed the targets. Thus, global growth projections are still being moderated, risk premia have risen, and the dollar continues to gain strength against other main currencies. International pressures on global inflation have heightened. In the United States, core inflation has not receded, pressured by the behavior of the CPI for services and a tight labor market. Consequently, the U.S. Federal Reserve continued to increase the policy interest rate at a strong pace. This rate is expected to now reach higher levels than projected in the previous quarter. Other developed and emerging economies have also increased their policy interest rates. Thus, international financial conditions have tightened significantly, which reflects in a widespread strengthening of the dollar, increases in worldwide risk premia, and the devaluation of risky assets. Recently, these effects have been stronger in Colombia than in the majority of its peers in the region. Considering all of the aforementioned, the technical staff of the bank increased its assumption regarding the U.S. Federal Reserve’s interest rate, reduced the country’s external demand growth forecast, and raised the projected trajectory for the risk premium. The latter remains elevated at higher levels than its historical average, within a context of high local uncertainty and of extensive financing needs from the foreign sector and the public sector. All of this results in higher inflationary pressures associated to the depreciation of the Colombian peso. The uncertainty regarding external forecasts and its impact on the country remain elevated, given the unforeseeable evolution of the conflict between Russia and Ukraine, of geopolitical tensions, and of the tightening of external financial conditions, among others. A macroeconomic context of high inflation, inflation expectations and forecasts above 3%, and a positive output gap suggests the need for contractionary monetary policy, compatible with the macroeconomic adjustment necessary to eliminate excess demand, mitigate the risk of unanchoring in inflation expectations, and guarantee convergence of inflation at the target. In comparison with the July report forecasts, domestic demand has been more dynamic, with a higher observed output level that surpasses the economy’s productive capacity. Headline and core inflation have registered surprising rises, associated with the effects of domestic and external price shocks that were more persistent than anticipated, with excess demand and indexation processes in some CPI groups. The country’s risk premium and the observed and expected international interest rates increased. As a consequence of this, inflationary pressures from the exchange rate rose, and in this report, the probability of the neutral real interest rate being higher than estimated increased. In general, inflation expectations for all terms and the bank’s technical staff inflation forecast for 2023 increased again and continue to stray from 3%. All of the aforementioned elevated the risk of unanchoring inflation expectations and could heighten widespread indexation processes that push inflation away from the target for a longer time. In this context, it is necessary to consolidate a contractionary monetary policy that tends towards convergence of inflation at the target in the forecast horizon and towards the reduction of excess demand in order to guarantee a sustainable output level trajectory. 1.2 Monetary policy decision In its September and October of 2022 meetings, Banco de la República’s Board of Directors (BDBR) decided to continue adjusting its monetary policy. In September, the BDBR decided by a majority vote to raise the monetary policy interest rate by 100 basis points (bps), and in its October meeting, unanimously, by 100bps. Therefore, the rate is at 11.0%. Boxes 1 Food inflation: a comparison with other countries

Inflation continues to decline but remains well above 3%. It is anticipated to decrease significantly in 2024 and draw closer to the established target in the first half of 2025. The ongoing moderation in the economy's price levels is evidenced by the decline in headline inflation from 11% to 9.3% between September and December 2023. A noteworthy contributor to the decrease in inflation has been the reduction of food prices adjustments throughout 2023, complemented by favorable trends in the price of goods. The decrease in inflation has, however, been constrained by the behavior of the price of services, which continue to exhibit high consumption levels, acerbated by the indexation of prices to recent elevated inflation rates. Additionally, necessary adjustments in fuel prices have curbed the inflation’s decline. Going forward, the outlook is for inflation to continue its downward trajectory, converging toward the 3% target by the first half of 2025. Factors supporting the prospect of a gradual inflation reduction include the absence of significant appreciations in the exchange rate, together with lower external inflation, reduced pressure on spending over prices due to the economic deceleration, and the cumulative impact of Banco de la República’s monetary policy measures. However, persistent risks remain that could slow down the anticipated fall in inflation, such as an unforeseen increase in the exchange rate or heightened impacts of the El Niño (ENSO) phenomenon on food and energy prices. The decrease in inflation would occur against a backdrop of slow economic growth for 2024 and a recovery thereof in 2025. Towards the close of 2023, economic activity persisted in its deceleration, reflecting the low levels of investment and, to a lesser extent, a moderation in consumption. The unemployment rate, while still relatively low, has witnessed a recent uptick in the past months. The economy is poised to sustain modest growth rates for 2024, further consolidating the ongoing convergence of inflation toward the established target. An acceleration in economic activity should begin in the latter half of 2024, attaining sustainable levels in 2025 in line with the economy's productive capacity. The monetary policy stance has contributed towards mitigating inflation and addressing broader macroeconomic imbalances within the country. Notably, inflation rates and associated expectations have declined, albeit persisting above the 3% target, concurrent with an overall deceleration of economic activity. Against this backdrop, the Board of Directors of Banco de la República adjusted its monetary policy interest rate, lowering it from 13.25% to 12.75%. The monetary policy decisions enacted by Banco de la República have contributed to rectifying prevailing macroeconomic imbalances accumulated in recent years, including elevated inflation, excessive spending and credit levels, and a pronounced external deficit. Consequently, the macroeconomic landscape has undergone requisite adjustments characterized by: A realignment of economic activity towards levels more consistent with the economy’s productive capacity. Attainment of a more sustainable balance in foreign transactions. A reduction in both inflation rates and associated expectations. Considering these outcomes and amid diminishing inflationary pressures and subdued economic growth, the Board of Directors of Banco de la República opted to decrease the monetary policy interest rate by 25 basis points during its meetings of December 2023 and January 2024, bringing it down to 12.75%. This interest rate adjustment acknowledges the reduction in inflation and its associated expectations, in alignment with the overarching goal of steering inflation towards the 3% target by mid-2025 while fostering sustained economic growth over time. Box 1 - Regional Economic Pulse: High-Frequency, Short-Lag Indicators to Understand Local Economies Autor: Dora Alicia Mora Pérez, Diana María Cortázar Gómez, Carolina Ramírez Rodríguez and Antonio José Orozco Gallo