Academic literature on the topic 'Relaxed control'

This thesis presents and extrapolates on the research works concerning the stability analysis of fuzzy-model-based (FMB) control systems. In this study, two types of FMB control systems are considered: 1) Takagi-Sugeno (T-S) FMB control systems; and 2) polynomial fuzzy-model-based (PFMB) control systems. The control scheme illustrated in this thesis has great design flexibility because it allows the number and/or shape of membership functions of fuzzy controllers to be designed independently from the fuzzy models. However, in wake of the imperfectly matched membership functions, the stability conditions of the FMB control systems are typically very conservative given the fact that they are con-gruent with traditional stability analysis methods. In this thesis, based on Lya-punov stability theory, membership-function-dependent (MFD) stability analysis methods are proposed to relax the stability conditions. Firstly, piecewise mem-bership functions (PMFs) are utilised as approximate membership functions to carry out a relaxed stability analysis of T-S FMB control system. Subsequently, PMF-based stability analysis is improved with the consideration of membership function boundary information. Based on the PMF method, we propose a lower-upper-PFM-based stability analysis method. Relaxed stability conditions are obtained in the form of linear matrix inequalities (LMIs) in consideration of the approximation accuracy of the membership function. For the purpose of stability analysis of PFMB control system, the other MFD method proposed is to extract the regional membership function information via operating domain partition. Two types of membership information are consid-ered in each sub-domain: 1) the numerical relationship between all membership function overlap terms; and 2) the bounds of every single membership function overlap term. Thereafter, relaxed sum of squares (SOS)-based stability conditions are derived. In conjunction with these proposed MFD methods, sub-domain fuzzy controllers are utilised to enhance the capability of feedback compensation. In this thesis, all the LMI/SOS-based stability conditions obtained can be solved nu-merically using existing computational tools. Furthermore, simulation examples are provided to illustrate the validity and applicability of the proposed methods.

Los problemas de optimización de desigualdades matriciales lineales en control borroso se han convertido en la herramienta más utilizada en dicha área desde los años 90. Muchos sistemas no lineales pueden ser modelados como sistemas borrosos de modo que el control borroso puede considerarse como una técnica de control no lineal. Aunque se han obtenido muchos y buenos resultados, quedan algunas fuentes de conservadurismo cuando se comparan con otros enfoques de control no lineal. Esta tesis discute dichas cuestiones de conservadurismo y plantea nuevos enfoques para resolverlas. La principal ventaja de la formulación mediante desigualdades matriciales lineales es la posibilidad de asegurar estabilidad y prestaciones de un sistema no lineal modelado como un sistema borroso Takagi-Sugeno. Estos modelos están formados por un conjunto de modelos lineales eligiendo el sistema a aplicar mediante el uso de unas reglas borrosas. Estas reglas se traducen en funciones de interpolación o de pertenecía que nos indican el grado de validez de un modelo lineal respecto del resto. El mayor problema que presentan estas técnicas basadas en desigualdades matriciales lineales es que las funciones de pertenencia no están incluidas en las condiciones de estabilidad del sistema, lo que significa que se prueba la estabilidad y prestaciones para cualquier forma de interpolación entre los diferentes modelos lineales. Esto genera una fuente de conservadurismo que sería conveniente limitar. En la tesis doctoral se presentan varias metodologías capaces de trasladar la información de las funciones de pertenencia del sistema al problema basado en desigualdades matriciales lineales de estabilidad y prestaciones. Las dos principales aportaciones propuestas se basan, respectivamente, en introducir una serie de matrices de relajación que permitan incorporar esta información y en aprovechar la descripción de una amplia clase de sistemas borrosos en productos tensoriales de...<br>Ariño Latorre, CV. (2008). Relaxed LMI conditions for control of nonlinear Takagi-Sugeno models [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8301<br>Palancia

Fuzzy-model-based (FMB) control scheme is an efficient approach to conduct stability analysis for nonlinear systems. Both Takagi-Sugeno (T-S) FMB and polynomial fuzzy-model-based (PFMB) control systems have been widely investigated. In this thesis, the stability analysis of FMB control systems is conducted via Lyapunov stability theory. The main contribution of the thesis is improving the applicability of T-S FMB and PFMB control strategies by relaxing stability conditions and designing fuzzy observer-controller, which is presented in the following three parts: 1) The stability conditions of FMB control systems are relaxed such that the FMB control strategy can be applied to a wider range of nonlinear systems. For T-S FMB control systems, higher order derivatives of Lyapunov function (HODLF) are employed, which generalizes the commonly used first order derivative. For PFMB control systems, Taylor series membership functions (TSMF) are brought into stability conditions such that the relation between membership grades and system states is expressed. 2) Two types of T-S fuzzy observer-controller are designed such that the T-S FMB control strategy can be applied to systems with unmeasurable states. For the first type, the T-S fuzzy observer with unmeasurable premise variables is designed to estimate the system states and then the estimated states are employed for state-feedback control of nonlinear systems. Convex stability conditions are obtained through matrix decoupling technique. For the second type, the T-S fuzzy functional observer is designed to directly estimate the control input instead of the system states, which can reduce the order of the observer. A new form of fuzzy functional observer is proposed to facilitate the stability analysis such that the observer gains can be numerically obtained and the stability can be guaranteed simultaneously. 3) The polynomial fuzzy observer-controller with unmeasurable premise variables is designed for systems with unmeasurable states. Although the consideration of the polynomial fuzzy model and unmeasurable premise variables enhances the applicability of the FMB control strategy, it leads to non-convex stability conditions. Therefore, two methods are applied to derive convex stability conditions: refined completing square approach and matrix decoupling technique. Additionally, the designed polynomial fuzzy observer-controller is extended for systems where only sampled-output measurements are available. Furthermore, the membership functions of the designed polynomial observer-controller are optimized by the improved gradient descent method. Simulation examples are provided to demonstrate and verify the theoretical analysis.

Ingeniero Civil en Computación<br>La protección de la confidencialidad de la información manipulada por los programas computacionales es abordada a nivel del código fuente con distintas técnicas. Una de ellas es tipado de seguridad para el control de flujo, que controla el nivel de seguridad donde fluye la información agregando anotaciones a las variables tipadas. La propiedad de seguridad fundamental de control de flujo es conocida como no-interferencia (noninterference), que establece que un observador público no puede obtener conocimiento desde datos confidenciales. A pesar de ser una propiedad muy atractiva, los sistemas reales la vulneran fácilmente, y necesitan mecanismos para desclasificar selectivamente alguna información. En esta dirección, Cruz et al. proponen una forma de desclasificación basada en tipos (type-based declassification), en donde se utilizan las relaciones de subtipos del lenguaje para expresar las políticas de desclasificación de los datos que maneja el programa, en una forma simple y expresiva. A pesar de que el fundamento teórico de la desclasificación basada en tipos está bien descrito, carece de una implementación que permita comprobar la utilidad práctica de la propuesta. En este trabajo, se implementa el análisis de la desclasificación basada en tipos para un subconjunto del lenguaje Dart, un lenguaje de programación de propósito general orientado a objetos desarrollado por Google. Además, se implementó un sistema de inferencia de políticas de desclasificación y una extensión para ambientes de desarrollo, con el objetivo de facilitar el trabajo al programador y mejorar su experiencia.

Researchers have studied nicotine’s ability to attenuate stress and negative affect for decades, but there has been limited research into the cortical regions most responsible for these effects. Recent paradigms have emerged that define large-scale neural networks that operate in conjunction to elicit complex effects: the Default Mode Network (DMN), the Executive Control Network (ECN), and the Salience Network (SN). The current study utilized archival topographic (surface) EEG recordings to analyze the tomographic (3-dimensional) cortical differences in three major large-scale neural networks during relaxing and task-induced anticipatory stress resting states while nicotine-satiated and nicotine-deprived, and as a function of trait negative affect (NA). Various interaction and main effects of nicotine use, stress, and NA occurred in the connectivity between regions of interest (ROIs) of all three networks. Total current source density (CSD) analyses demonstrated an interaction between smoking and stress, such that the effects of smoking and stress were highest during the combination of deprivation and stress, and lowest when individuals were in nicotine satiated and in the low stress condition. A whole-brain exploratory analysis also identified a significant interaction between smoking and NA in the postcentral gyrus.

Nous considérons les équations différentielles stochastiques (EDS) de Mc Kean-Vlasov, qui sont des EDS dont les coefficients de dérive et de diffusion dépendent non seulement de l'état du processus inconnu, mais également de sa loi de probabilité. Ces EDS, également appelées EDS à champ moyen, ont d'abord été étudiées en physique statistique et représentent en quelque sorte le comportement moyen d'un nombre infini de particules. Récemment, ce type d'équations a suscité un regain d'intérêt dans le contexte de la théorie des jeux à champ moyen. Cette théorie a été inventée par P.L. Lions et J.M. Lasry en 2006, pour résoudre le problème de l'existence d'un équilibre de Nash approximatif pour les jeux différentiels, avec un grand nombre de joueurs. Ces équations ont trouvé des applications dans divers domaines tels que la théorie des jeux, la finance mathématique, les réseaux de communication et la gestion des ressources pétrolières. Dans cette thèse, nous avons étudié les questions de stabilité par rapport aux données initiales, aux coefficients et aux processus directeurs des équations de McKean-Vlasov. Les propriétés génériques de ce type d'équations stochastiques, telles que l'existence et l'unicité, la stabilité par rapport aux paramètres, ont été examinées. En théorie du contrôle, notre attention s'est portée sur l'existence et l'approximation de contrôles relaxés pour les systèmes gouvernés par des EDS de Mc Kean-Vlasov<br>We consider Mc Kean-Vlasov stochastic differential equations (SDEs), which are SDEs where the drift and diffusion coefficients depend not only on the state of the unknown process but also on its probability distribution. These SDEs called also mean- field SDEs were first studied in statistical physics and represent in some sense the average behavior of an infinite number of particles. Recently there has been a renewed interest for this kind of equations in the context of mean-field game theory. Since the pioneering papers by P.L. Lions and J.M. Lasry, mean-field games and mean-field control theory has raised a lot of interest, motivated by applications to various fields such as game theory, mathematical finance, communications networks and management of oil resources. In this thesis, we studied questions of stability with respect to initial data, coefficients and driving processes of Mc Kean-Vlasov equations. Generic properties for this type of SDEs, such as existence and uniqueness, stability with respect to parameters, have been investigated. In control theory, our attention were focused on existence, approximation of relaxed controls for controlled Mc Kean-Vlasov SDEs

This doctoral thesis addresses topology optimization problems at a single scale. Based on this purpose, a new topology optimization approach is developed in order to improve existing and widespread techniques in the research community on the topic. The proposed technique presents several characteristics that overcome some of the well-known difficulties in topological optimization while maintaining a considerable degree of simplicity. In the first place, the formulation of the topological optimization technique is presented, as well as its algorithm. The method is based on 4 fundamental features: (1) the use of a 1-0 characteristic function, as well as the precise identification of the material boundaries from a discrimination function (0-level-set function), (2) the definition of a topological derivative consistent with the ersatz method (used in the state problem), as an approximation to the exact topological derivative, (3) the inclusion of a Laplacian regularization with minimum size control of the different components, and (4) the formulation of an analytical optimality condition aiming at the optimal topology solution. The approach is applied to different topology optimization problems, well-reported in the literature and used as numerical benchmarks (in structural and thermal problems), to examine their performance. In these fields, stiffness and conductivity maximization problems are considered for validation, respectively. In addition, different topological optimization problems of major engineering interest are tackled, including the design of compliant mechanisms within the structural field and thermal cloaking devices within the thermal field. Finally, a comparison of the formulation with other existing topology optimization techniques is performed, including (1) SIMP, (2) ESO/BESO, and (3) Level-set with Hamilton-Jacobi as the updating equation. The analysis of the results provides a comparison in terms of the quality of the topology of each method, the computational cost of the optimal solutions, as well as the simplicity of implementation. The resulting study reveals the potential of the developed methodology in these specific comparison terms. In an attempt to bring the method closer to other researchers and to promote its use, an educational version of the method (written in MATLAB) has been published in an online repository, together with documentation, facilitating its dissemination and subsequent use in other applications of interest.<br>El objetivo de esta tesis doctoral es abordar el problema de optimización topológica a una única escala. En base a este propósito, se desarrolla una nueva técnica de optimización capaz de competir con técnicas ya existentes y extendidas entre la comunidad investigadora sobre el tema. Esta técnica presenta características que superan algunas de las dificultades bien conocidas en optimización topológica manteniendo un buen grado de simplicidad. En primer lugar, se presenta la formulación de la técnica de optimización topológica, así como su algoritmia. El método se fundamenta en 4 aspectos básicos: (1) la utilización de una función característica 1-0, así como la definición precisa de las fronteras materiales a partir de una función de discriminación (isonivel 0 de la función level-set), (2) la definición de una derivada topológica coherente con el método ersatz (utilizado en la ecuación de estado), como aproximación a la derivada topológica exacta, (3) la inclusión de una regularización Laplaciana con control de tamaño mínimo de los diferentes componentes, y (4) la definición de una condición de optimalidad analítica para la determinación de la solución óptima de la topología. La metodología se aplica a diferentes problemas de optimización topológica bien detallados en la literatura y utilizados como ensayos numéricos para examinar su respuesta frente a problemas estructurales y térmicos. En estos campos, se incluyen problemas de maximización de la rigidez y de la conductividad, respectivamente. Además, se resuelven diferentes problemas de optimización topológica con gran interés ingenieril en los campos estructurales con el diseño de mecanismos y térmicos con el diseño de dispositivos de camuflaje térmicos. Finalmente, se realiza una comparación de la formulación con otras técnicas ya existentes, por ejemplo: (1) SIMP, (2) ESO/BESO, y (3) Level-set con Hamilton-Jacobi como ecuación de evolución. El análisis de los resultados permite comparar la calidad de la topología de cada método, el coste computacional de las soluciones óptimas, así como la simplicidad de implementación, demostrando el potencial de la metodología desarrollada principalmente en estos términos de comparación. Con la finalidad de acercar el método a otros investigadores y de promover su utilización, se ha publicado una versión educativa del mismo (en MATLAB) en un repositorio online, junto a documentación, permitiendo así la divulgación del mismo y la posible utilización en otras aplicaciones de interés.<br>Enginyeria mecànica, fluids i aeronàutica

We define Γ(E), a subset of C³, related to the structured singular value μ of 2x2 matrices. μ is used to analyse performance and robustness of linear feedback systems in control engineering. We find a characterisation for the elements of Γ(E) and establish a necessary and sufficient condition for the existence of an analytic function from the unit disc into Γ(E) satisfying an arbitrary finite number of interpolation conditions. We prove a Schwarz Lemma for Γ(E) when one of the points in Γ(E) is (0,0,0), then we show that in this case, the Carathéodory and Kobayashi distances between the two points in Γ(E) coincide. We also give a characterisation of the interior, the topological boundary and the distinguished boundary of Γ(E), then we define Γ(E)-inner functions and show that if there exists an analytic function from the unit disc into Γ(E) that satisfies the interpolating conditions, then there is a rational Γ(E)-inner function that interpolates.

This dissertation explores aspects of control in rigid-body and robotic systems. The first and second paper analyze the attitude stabilization problem and its generalization to n-dimensional rigid bodies. The third and fourth paper are on cooperative control design for systems that evolve on the n-sphere and related topics such as rigid-body reduced attitude synchronization. The fifth, and final, paper proposes a hybrid systems approach to task-priority based control for mobile manipulation. he first and second paper concern the problem of attitude tracking by kinematic actuation for a class of almost globally asymptotically stabilizing feedback laws on SO(n). The closed-loop systems are solved exactly for the rotation matrices as functions of time. Exact solutions provide insight into both the transient and asymptotical behavior of a system. Applications of these results are found in model predictive control and in sampled systems. The second paper also solves the optimal control problem of geodesic reduced attitude stabilization subject to full attitude stabilization. The third and fourth paper concern three cooperative control problems on the n-sphere with applications to reduced attitude synchronization and formation control. The global behavior of a consensus protocol is studied both forwards and backwards in time. The forward time stability properties of all equilibria are characterized for a non-trivial class of graph topologies. The reverse time behavior in the case of cyclic graph topologies results in two types of formations depending on the parity of the number of agents. A third control protocol renders the centroid of agent states constant. The fifth, and final, paper proposes a hybrid control approach to task priority based planar mobile manipulation, i.e., control on the n-torus. The end-effector path following problem for a nonholonomic mobile manipulator is solved subject to constraints on the input norm, feasible joint configurations, and distance to singularities. The hybrid system is well-posed; there is no Zeno behavior or chattering. A continuous, time-independent feedback law is derived based on the hybrid control design.<br><p>QC 20151015</p>

Projeto de Graduação apresentado à Universidade Fernando Pessoa como parte dos requisitos para obtenção do grau de Licenciado em Fisioterapia<br>Introdução: A lombalgia está associada a alterações da atividade muscular e da cinemática lombo-pélvica provocada, em parte, pela fraqueza da musculatura do core. O teste de Thomas é utilizado nas áreas clínica e desportiva para determinar o encurtamento do ilíopsoas e do reto femoral, músculos constituintes do core. O encurtamento destes músculos é um dos fatores de risco de lesão músculo-esquelética nos membros inferiores e de dor lombar. A técnica de suster-relaxar, aumenta a amplitude de movimento articular, normalizando o tónus muscular. Objetivo: Avaliar o efeito da técnica de suster-relaxar na cinemática tridimensional do teste de Thomas, na função neuromuscular e sintomatologia álgica de um atleta de crossfit com dor lombar à direita. Metodologia: Análise da cinemática tridimensional do teste de Thomas através do sistema de captura e análise de movimento 3D, Qualisys Oqus Camera Series, e força isocinética dos joelhos pela dinamometria isocinética, antes e após a aplicação técnica suster-relaxar num atleta de crossfit de 25 anos. Resultados: Após a análise dos dados obtidos, verificou-se um aumento da amplitude de extensão da anca, do peak torque e diminuição da sintomatologia álgica, no lado afetado do atleta, em resultado da aplicação da técnica de suster-relaxar. Conclusão: A técnica suster-relaxar aumenta a amplitude de movimento articular, e o peak torque e diminui a sintomatologia de dor lombar associado a uma disfunção sacroilíaca num atleta de crossfit.<br>Introduction: Low back pain is associated with changes in muscle activity and lumbar- pelvic kinematics caused, partly by the weakness of the core musculature. The Thomas test is widely used in clinical and sports areas to determine the shortening of the iliopsoas and rectus femoris, core constituent muscles. The shortening of these muscles is one of the risk factors for musculoskeletal injury in the lower limbs and back pain. The technique of hold-relax, increases range of motion, normalizing muscle tone. Objective: To access the effect of the hold-relax technique in the three-dimensional kinematics of the Thomas test, neuromuscular function and symptoms of a crossfit athlete with right low back pain. Methodology: Analysis of three-dimensional kinematics of the Thomas test through the capture system and 3D motion analysis, Qualisys Oqus Camera Series, and isokinetic strength of the knee by isokinetic dynamometer before and after the hold-relax technique application in a 25 years crossfit athlete. Results: After analysing the data, there was an increase in hip extension range, peak torque and reduction of pain symptoms on the affected side of the athlete, as a result of the technical application of hold-relax. Conclusion: The hold-relax technique increases range of motion andpeak torque and decreases lumbar pain symptoms associated with a sacroiliac dysfunction in a crossfit athlete.<br>N/A