Relevant bibliographies by topics / Barrier Lyapunov functionals

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Academic literature on the topic 'Barrier Lyapunov functionals'

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Published: 6 September 2023

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Journal articles on the topic "Barrier Lyapunov functionals"

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Li, Dong-Juan, Jing Li, and Shu Li. "Adaptive control of nonlinear systems with full state constraints using Integral Barrier Lyapunov Functionals." Neurocomputing 186 (April 2016): 90–96. http://dx.doi.org/10.1016/j.neucom.2015.12.075.

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Wu, Yuxiang, Tian Xu, and Hongqiang Mo. "Adaptive tracking control for nonlinear time-delay systems with time-varying full state constraints." Transactions of the Institute of Measurement and Control 42, no. 12 (March 6, 2020): 2178–90. http://dx.doi.org/10.1177/0142331220908987.

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This paper presents an adaptive tracking control approach for a class of uncertain nonlinear strict-feedback systems subject to time-varying full state constraints and time-delays. To stabilize such systems, an adaptive tracking controller is structured by combining the neural networks and the backstepping technique. To guarantee all states do not violate the time-varying constraint sets, the appropriate time-varying Barrier Lyapunov functions are employed at each stage of the backstepping procedure. By using the Lyapunov-Krasovskii functionals, the effect of time delay is eliminated. It is proved that the output follows the desired signal well without violating any constraints, and all the signals in the closed-loop system are semiglobal uniformly ultimately bounded by using the Lyapunov analysis. Finally, a comparison study simulation is provided to illustrate the effectiveness of the proposed control strategy.
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Liu, Yan-Jun, Shaocheng Tong, C. L. Philip Chen, and Dong-Juan Li. "Adaptive NN Control Using Integral Barrier Lyapunov Functionals for Uncertain Nonlinear Block-Triangular Constraint Systems." IEEE Transactions on Cybernetics 47, no. 11 (November 2017): 3747–57. http://dx.doi.org/10.1109/tcyb.2016.2581173.

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Li, Dongjuan, Dongxing Wang, and Ying Gao. "Adaptive Neural Control and Modeling for Continuous Stirred Tank Reactor with Delays and Full State Constraints." Complexity 2021 (October 7, 2021): 1–12. http://dx.doi.org/10.1155/2021/9948044.

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In this paper, an adaptive neural network control method is described to stabilize a continuous stirred tank reactor (CSTR) subject to unknown time-varying delays and full state constraints. The unknown time delay and state constraints problem of the concentration in the reactor seriously affect the input-output ratio and stability of the entire system. Therefore, the design difficulty of this control scheme is how to debar the effect of time delay in CSTR systems. To deal with time-varying delays, Lyapunov–Krasovskii functionals (LKFs) are utilized in the adaptive controller design. The convergence of the tracking error to a small compact set without violating the constraints can be identified by the time-varying logarithm barrier Lyapunov function (LBLF). Finally, the simulation results on CSTR are shown to reveal the validity of the developed control strategy.
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Ai, Xiang, Ya Zhang, and Yang-Yang Chen. "Spherical Formation Tracking Control of Non-Holonomic UAVs with State Constraints and Time Delays." Aerospace 10, no. 2 (January 26, 2023): 118. http://dx.doi.org/10.3390/aerospace10020118.

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This paper addresses a novel spherical formation tracking control problem of multiple UAVs with time-varying delays in the directed communication network, where the dynamics of each UAV is non-holonomic and in the presence of spatiotemporal flowfields. The state constraints (that is, position and velocity constraints) are derived from our previous differential geometry method and the F–S formulas. The state constraints and time delays in the directed communication network bring many difficulties to controller design. To this end, a virtual-structure-like design is given to achieve a formation with delayed information by using Lyapunov–Krasovskii functionals, and then proposing a barrier Lyapunov function for the satisfaction of state constraints to design a novel spherical formation tracking algorithm. The general assumption of the rate of change of time-varying delays, and a certain initial position and velocity adjustment range are given. Simulation results show the feasibility and effectiveness of the proposed algorithm.
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Li, Menghan, Shaobo Li, Junxing Zhang, Fengbin Wu, and Tao Zhang. "Neural Adaptive Funnel Dynamic Surface Control with Disturbance-Observer for the PMSM with Time Delays." Entropy 24, no. 8 (July 26, 2022): 1028. http://dx.doi.org/10.3390/e24081028.

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This paper suggests an adaptive funnel dynamic surface control method with a disturbance observer for the permanent magnet synchronous motor with time delays. An improved prescribed performance function is integrated with a modified funnel variable at the beginning of the controller design to coordinate the permanent magnet synchronous motor with the output constrained into an unconstrained one, which has a faster convergence rate than ordinary barrier Lyapunov functions. Then, the specific controller is devised by the dynamic surface control technique with first-order filters to the unconstrained system. Therein, a disturbance-observer and the radial basis function neural networks are introduced to estimate unmatched disturbances and multiple unknown nonlinearities, respectively. Several Lyapunov-Krasovskii functionals are constructed to make up for time delays, enhancing control performance. The first-order filters are implemented to overcome the “complexity explosion” caused by general backstepping methods. Additionally, the boundedness and binding ranges of all the signals are ensured through the detailed stability analysis. Ultimately, simulation results and comparison experiments confirm the superiority of the controller designed in this paper.
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Zhao, Wei, Yanjun Liu, and Lei Liu. "Observer-Based Adaptive Fuzzy Tracking Control Using Integral Barrier Lyapunov Functionals for A Nonlinear System With Full State Constraints." IEEE/CAA Journal of Automatica Sinica 8, no. 3 (March 2021): 617–27. http://dx.doi.org/10.1109/jas.2021.1003877.

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Wei, Yan, Pingfang Zhou, Yueying Wang, Dengping Duan, and Jiwei Tang. "Adaptive finite-time neural backstepping control for multiple-input–multiple-output uncertain nonlinear systems with full state constraints." Transactions of the Institute of Measurement and Control 43, no. 11 (February 7, 2021): 2450–60. http://dx.doi.org/10.1177/0142331221989121.

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This paper investigates the issue of finite-time tracking control for multiple-input–multiple-output nonlinear systems subject to uncertainties and full state constraints. To deal with full state constraints directly, integral barrier Lyapunov functionals (iBLF) are introduced. By using finite-time stability theory, an iBLF-based adaptive finite-time neural control scheme is presented. To solve the problem of “explosion of complexity” in the design of traditional backstepping control, a new finite-time convergent differentiator is presented. Through stability analysis, all closed-loop signals are proved to be semi-globally uniformly ultimately bounded, the finite time convergence can be guaranteed, and the state constraints are never violated. Finally, the attitude tracking simulations for an autonomous airship are conducted to verify the effectiveness of the proposed scheme.
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Xu, Tian, Yuxiang Wu, Haoran Fang, and Fuxi Wan. "Adaptive finite-time tracking control for full state constrained nonlinear systems with time-varying delays and input saturation." Transactions of the Institute of Measurement and Control 44, no. 9 (December 30, 2021): 1824–35. http://dx.doi.org/10.1177/01423312211065851.

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This paper investigates the adaptive finite-time tracking control problem for a class of nonlinear full state constrained systems with time-varying delays and input saturation. Compared with the previously published work, the considered system involves unknown time-varying delays, asymmetric input saturation, and time-varying asymmetric full state constraints. To ensure the state constraint satisfaction, the appropriate time-varying asymmetric Barrier Lyapunov Functions and the backstepping technique are utilized. Meanwhile, the finite covering lemma and the radial basis function neural networks are employed to solve the unknown time-varying delays. The assumption that the time derivative of time-varying delay functions is required to be less than one in traditional Lyapunov–Krasovskii functionals is removed by the proposed method. Moreover, the asymmetric input saturation is handled by an auxiliary design system. Taking the norm of the neural network weight vector as an adaptive parameter, a novel adaptive finite-time tracking controller with minimal learning parameters is constructed. It is proved that the proposed controller can guarantee that all signals in the closed-loop system are bounded, all states are constrained within the predefined sets, and the tracking error converges to a small neighborhood of the origin in a finite time. Finally, a comparison study simulation is given to demonstrate the effectiveness of our proposed strategy. The simulation results show that our proposed strategy has good advantages of high tracking precision and disturbance rejection.
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Luo, Zhenguo, Liping Luo, Liu Yang, Zhenghui Gao, and Yunhui Zeng. "Existence and Uniqueness of Positive Periodic Solutions for a Delayed Predator-Prey Model with Dispersion and Impulses." Journal of Applied Mathematics 2014 (2014): 1–21. http://dx.doi.org/10.1155/2014/592543.

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An impulsive Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments and time delays is investigated, where we assume the model of patches with a barrier only as far as the prey population is concerned, whereas the predator population has no barriers between patches. By applying the continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are obtained to guarantee the existence, uniqueness, and global stability of positive periodic solutions of the system. Some known results subject to the underlying systems without impulses are improved and generalized. As an application, we also give two examples to illustrate the feasibility of our main results.
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Dissertations / Theses on the topic "Barrier Lyapunov functionals"

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Annam, Chandrakanth. "Advanced Guidance Laws for Field-of-View and Impact Angle Constrained Engagements." Thesis, 2020. https://etd.iisc.ac.in/handle/2005/4820.

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This thesis deals with the development of guidance laws for interceptors with seeker field-of-view (FOV) and impact angle constraints. Two classes of guidance problems, namely, field-of- view and impact angle constrained guidance; midcourse guidance of dual pulse interceptors with look angle constraints, are considered in this thesis. In the first problem, decision variables are lateral acceleration commands whereas the second problem has an additional decision variable of second thrust pulse firing time. For the first problem, three guidance laws are proposed using nonlinear control theory. These are (i) Backstepping control based guidance law (ii) Nonlinear mapping based guidance law for three dimensional engagements, and (iii) Partial integrated guidance and control based guidance law. For the second problem, singular perturbation technique is used to derive the guidance law. First, backstepping control based guidance law is proposed for impact angle and field-of-view constrained engagements in a planar geometry. The kinematic equations governing the problem are modified to strict feedback form for deriving the guidance law using backstepping technique. The look-angle, which is virtual input to the backstepping structure, is designed such that it is within the feasible domain and achieves the desired impact angle. Barrier Lyapunov functionals are used to derive a guidance law to track the virtual input without violating the field-of-view constraints. Further, capturability of the proposed guidance law is analyzed in the relative velocity plane. Simulation results are presented using a constant speed as well as a realistic interceptor model to show the efficacy of the guidance law. Next, backstepping control based guidance law is further extended to intercept targets in three dimensional space using nonlinear transformation. The interception geometry is controlled by defining impact angles in terms of flight path angles of interceptor and target. The impact angles are related to line-of-sight angles and the problem is converted to line-of-sight angle tracking problem. The state model for the control design is transformed into a new domain using tangent hyperbolic functions to handle the FOV constraints. The look angles which are constrained in the original domain are free from constraints in the transformed domain. Error surfaces are defined in the transformed domain and Lyapunov theory is used to derive the guidance law. Simulation studies performed using constant speed as well as realistic models of interceptor demonstrates the effectiveness of the proposed guidance law for three dimensional engagements. Approximations considering kinematic look angle may degrade guidance law performance. A partial integrated guidance and control (PIGC) based guidance law is proposed considering look angle without any approximations. A three dimensional engagement geometry and six degree of freedom (6-DOF) model of interceptor are used in the guidance law design. The partial integrated guidance and control uses a two loop architecture, wherein the outer loop generates body rate commands and the inner loop tracks the desired body rates by deflecting the fins. Both the loops are designed using Lyapunov theory. The look angle constraints are accounted for in the outer loop by using barrier functionals in the error surfaces. The guidance law efficiently uses the available look angle freedom to intercept the target with the desired impact angle. Simulation results using the 6-DOF model demonstrate the effectiveness of the PIGC law. Finally, Monte-Carlo studies highlight the robustness of the proposed guidance law against uncertainties in aerodynamic coefficients. In the last part of the thesis, the problem of midcourse guidance of dual pulse interceptors with look angle constraints is addressed using singular perturbation (SP) technique. This guidance law is applicable in the midcourse phase where the objective is to conserve the kinetic energy to maximize the range. This is achieved by choosing a combination of terminal velocity and flight time as a performance measure. In addition to seeker field-of-view limit, constraints in the optimization problem include minimum dynamic pressure limit arising due to aerodynamic controllability. Using the time scale separation between the state variables, the full order problem is reduced into lower order sub-problems and a closed-form solution for the guidance law is derived. It is shown that the performance of the interceptor is not very sensitive to perturbation of pulse firing time and an offline generated lookup table is used to time the second thrust pulse firing. The proposed guidance law is computationally efficient and its performance is benchmarked with that of pseudospectral based feedback guidance with much lower computational cost. Simulation studies with point mass and 6-DOF model are presented highlighting the accuracy and efficacy of the proposed guidance law.
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Book chapters on the topic "Barrier Lyapunov functionals"

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Kabziński, Jacek, Przemysław Mosiołek, and Marcin Jastrzębski. "Adaptive Position Tracking with Hard Constraints—Barrier Lyapunov Functions Approach." In Advanced Control of Electrical Drives and Power Electronic Converters, 27–52. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45735-2_2.

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Chatterjee, Krishnendu, Thomas A. Henzinger, Mathias Lechner, and Đorđe Žikelić. "A Learner-Verifier Framework for Neural Network Controllers and Certificates of Stochastic Systems." In Tools and Algorithms for the Construction and Analysis of Systems, 3–25. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30823-9_1.

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AbstractReinforcement learning has received much attention for learning controllers of deterministic systems. We consider a learner-verifier framework for stochastic control systems and survey recent methods that formally guarantee a conjunction of reachability and safety properties. Given a property and a lower bound on the probability of the property being satisfied, our framework jointly learns a control policy and a formal certificate to ensure the satisfaction of the property with a desired probability threshold. Both the control policy and the formal certificate are continuous functions from states to reals, which are learned as parameterized neural networks. While in the deterministic case, the certificates are invariant and barrier functions for safety, or Lyapunov and ranking functions for liveness, in the stochastic case the certificates are supermartingales. For certificate verification, we use interval arithmetic abstract interpretation to bound the expected values of neural network functions.
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Reis, Matheus F., Pallov Anand, and A. Pedro Aguiar. "Cooperative Path Following with Collision Avoidance Guarantees Using Control Lyapunov and Barrier Functions." In CONTROLO 2022, 181–93. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-10047-5_16.

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Truong, Hoa Thi, and Xuan Bao Nguyen. "Adaptive Control Using Barrier Lyapunov Functions for Omnidirectional Mobile Robot with Time-Varying State Constraints." In Advances in Asian Mechanism and Machine Science, 401–10. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-91892-7_38.

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Yang, Zhengfeng, Li Zhang, Xia Zeng, Xiaochao Tang, Chao Peng, and Zhenbing Zeng. "Hybrid Controller Synthesis for Nonlinear Systems Subject to Reach-Avoid Constraints." In Computer Aided Verification, 304–25. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-37706-8_16.

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AbstractThere is a pressing need for learning controllers to endow systems with properties of safety and goal-reaching, which are crucial for many safety-critical systems. Reinforcement learning (RL) has been deployed successfully to synthesize controllers from user-defined reward functions encoding desired system requirements. However, it remains a significant challenge in synthesizing provably correct controllers with safety and goal-reaching requirements. To address this issue, we try to design a special hybrid polynomial-DNN controller which is easy to verify without losing its expressiveness and flexibility. This paper proposes a novel method to synthesize such a hybrid controller based on RL, low-degree polynomial fitting and knowledge distillation. It also gives a computational approach, by building and solving a constrained optimization problem coming from verification conditions to produce barrier certificates and Lyapunov-like functions, which can guarantee every trajectory from the initial set of the system with the resulted controller satisfies the given safety and goal-reaching requirements. We evaluate the proposed hybrid controller synthesis method on a set of benchmark examples, including several high-dimensional systems. The results validate the effectiveness and applicability of our approach.
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Zhang, Tengfei, and Yingmin Jia. "Adaptive Neural Network Control for Uncertain Robotic Manipulators with Output Constraint Using Integral-Barrier Lyapunov Functions." In Proceedings of 2018 Chinese Intelligent Systems Conference, 71–84. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-2291-4_8.

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Panagou, Dimitra, Dušan M. Stipanović, and Petros G. Voulgaris. "Distributed Control of Robot Swarms." In Robotic Systems, 1450–88. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-1754-3.ch070.

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This chapter considers the problem of multi-agent coordination and control under multiple objectives, and presents a set-theoretic formulation which is amenable to Lyapunov-based analysis and control design. A novel class of Lyapunov-like barrier functions is introduced and used to encode multiple control objectives, such as collision avoidance, proximity maintenance and convergence to desired destinations. The construction is based on recentered barrier functions and on maximum approximation functions. Thus, a single Lyapunov-like function is used to encode the constrained set of each agent, yielding simple, gradient-based control solutions. The derived control strategies are distributed, i.e., based on information locally available to each agent, which is dictated by sensing and communication limitations. The proposed coordination protocol dictates semi-cooperative conflict resolution among agents, as well as conflict resolution with respect to an agent (the leader) which is not actively participating in collision avoidance, except when necessary. The considered scenario is pertinent to surveillance tasks and involves nonholonomic vehicles. The efficacy of the approach is demonstrated through simulation results.
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Zouari, Farouk, and Amina Boubellouta. "Neural Approximation-Based Adaptive Control for Pure-Feedback Fractional-Order Systems With Output Constraints and Actuator Nonlinearities." In Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems, 468–95. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-5418-9.ch015.

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In this chapter, an adaptive control approach-based neural approximation is developed for a category of uncertain fractional-order systems with actuator nonlinearities and output constraints. First, to overcome the difficulties arising from the actuator nonlinearities and nonaffine structures, the mean value theorem is introduced. Second, to deal with the uncertain nonlinear dynamics, the unknown control directions and the output constraints, neural networks, smooth Nussbaum-type functions, and asymmetric barrier Lyapunov functions are employed, respectively. Moreover, for satisfactorily designing the control updating laws and to carry out the stability analysis of the overall closed-loop system, the Backstepping technique is used. The main advantage about this research is that (1) the number of parameters to be adapted is much reduced, (2) the tracking errors converge to zero, and (3) the output constraints are not transgressed. At last, simulation results demonstrate the feasibility of the newly presented design techniques.
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Wu, Zhe, Fahad Albalawi, Zhihao Zhang, Junfeng Zhang, Helen Durand, and Panagiotis D. Christofides. "Model Predictive Control for Process Operational Safety: Utilizing Safeness Index-Based Constraints and Control Lyapunov-Barrier Functions." In 13th International Symposium on Process Systems Engineering (PSE 2018), 505–10. Elsevier, 2018. http://dx.doi.org/10.1016/b978-0-444-64241-7.50079-3.

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Conference papers on the topic "Barrier Lyapunov functionals"

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Tian, Dongzuo, and Xingyong Song. "Control of a Downhole Drilling System Using Integral Barrier Lyapunov Functionals." In 2019 American Control Conference (ACC). IEEE, 2019. http://dx.doi.org/10.23919/acc.2019.8815370.

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Tee, Keng Peng, and Shuzhi Sam Ge. "Control of state-constrained nonlinear systems using Integral Barrier Lyapunov Functionals." In 2012 IEEE 51st Annual Conference on Decision and Control (CDC). IEEE, 2012. http://dx.doi.org/10.1109/cdc.2012.6426196.

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Li, Jing, and Yan-Jun Liu. "Control of nonlinear systems with full state constraints using integral Barrier Lyapunov Functionals." In 2015 International Conference on Informative and Cybernetics for Computational Social Systems (ICCSS). IEEE, 2015. http://dx.doi.org/10.1109/iccss.2015.7281151.

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Romdlony, Muhammad Zakiyullah, and Bayu Jayawardhana. "Uniting Control Lyapunov and Control Barrier Functions." In 2014 IEEE 53rd Annual Conference on Decision and Control (CDC). IEEE, 2014. http://dx.doi.org/10.1109/cdc.2014.7039737.

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Wei, Yihao, Chuanjiang Li, Yanchao Sun, and Guangfu Ma. "Backstepping approach for controlling a quadrotor using Barrier Lyapunov Functions." In 2017 36th Chinese Control Conference (CCC). IEEE, 2017. http://dx.doi.org/10.23919/chicc.2017.8028349.

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Xiao, Wei, Calin A. Belta, and Christos G. Cassandras. "High Order Control Lyapunov-Barrier Functions for Temporal Logic Specifications." In 2021 American Control Conference (ACC). IEEE, 2021. http://dx.doi.org/10.23919/acc50511.2021.9483028.

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Zhao, Pan, Yanbing Mao, Chuyuan Tao, Naira Hovakimyan, and Xiaofeng Wang. "Adaptive Robust Quadratic Programs using Control Lyapunov and Barrier Functions." In 2020 59th IEEE Conference on Decision and Control (CDC). IEEE, 2020. http://dx.doi.org/10.1109/cdc42340.2020.9303829.

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Duan, Hongtao, Yang Yang, and Wenjun Gao. "Backstepping Sliding Approach for Controlling a Quadrotor Using Barrier Lyapunov Functions." In 2019 3rd International Conference on Electronic Information Technology and Computer Engineering (EITCE). IEEE, 2019. http://dx.doi.org/10.1109/eitce47263.2019.9094998.

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Ren, Wei. "Razumikhin-type Control Lyapunov and Barrier Functions for Time-Delay Systems." In 2021 60th IEEE Conference on Decision and Control (CDC). IEEE, 2021. http://dx.doi.org/10.1109/cdc45484.2021.9682928.

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Du, Desong, Shaohang Han, Naiming Qi, Haitham Bou Ammar, Jun Wang, and Wei Pan. "Reinforcement Learning for Safe Robot Control using Control Lyapunov Barrier Functions." In 2023 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2023. http://dx.doi.org/10.1109/icra48891.2023.10160991.

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