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Liu X, Zhao B, Liu D. Fault tolerant tracking control for nonlinear systems with actuator failures through particle swarm optimization-based adaptive dynamic programming. Appl Soft Comput 2020. [DOI: 10.1016/j.asoc.2020.106766] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Xiao Q, Huang T, Zeng Z. Stabilization of Nonautonomous Recurrent Neural Networks With Bounded and Unbounded Delays on Time Scales. IEEE TRANSACTIONS ON CYBERNETICS 2020; 50:4307-4317. [PMID: 31265426 DOI: 10.1109/tcyb.2019.2922207] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
A class of nonautonomous recurrent neural networks (NRNNs) with time-varying delays is considered on time scales. Bounded delays and unbounded delays have been taken into consideration, respectively. First, a new generalized Halanay inequality on time scales is constructed by time-scale theory and some analytical techniques. Based on this inequality, the stabilization of NRNNs with bounded delays is discussed on time scales. The results are also applied to the synchronization of a class of drive-response NRNNs. Furthermore, the stabilization of NRNNs with unbounded delays is investigated. Especially, the stabilization of NRNNs with proportional delays is obtained without any variable transformation. The obtained generalized Halanay inequality on time scales develops and extends some existing ones in the literature. The stabilization criteria for the NRNNs with bounded or unbounded delays cover the results of continuous-time and discrete-time NRNNs and hold the results for the systems that involved on time interval as well. Some examples are given to demonstrate the validity of the results. An application to image encryption and decryption is addressed.
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Adaptive Resonance Theory in the time scales calculus. Neural Netw 2019; 120:32-39. [DOI: 10.1016/j.neunet.2019.08.010] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2019] [Revised: 07/31/2019] [Accepted: 08/09/2019] [Indexed: 11/23/2022]
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Wei C, Luo J, Dai H, Duan G. Learning-Based Adaptive Attitude Control of Spacecraft Formation With Guaranteed Prescribed Performance. IEEE TRANSACTIONS ON CYBERNETICS 2019; 49:4004-4016. [PMID: 30072354 DOI: 10.1109/tcyb.2018.2857400] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This paper investigates a novel leader-following attitude control approach for spacecraft formation under the preassigned two-layer performance with consideration of unknown inertial parameters, external disturbance torque, and unmodeled uncertainty. First, two-layer prescribed performance is preselected for both the attitude angular and angular velocity tracking errors. Subsequently, a distributed two-layer performance controller is devised, which can guarantee that all the involved closed-loop signals are uniformly ultimately bounded. In order to tackle the defect of statically two-layer performance controller, learning-based control strategy is introduced to serve as an adaptive supplementary controller based on adaptive dynamic programming technique. This enhances the adaptiveness of the statically two-layer performance controller with respect to unexpected uncertainty dramatically, without any prior knowledge of the inertial information. Furthermore, by employing the robustly positively invariant theory, the input-to-state stability is rigorously proven under the designed learning-based distributed controller. Finally, two groups of simulation examples are organized to validate the feasibility and effectiveness of the proposed distributed control approach.
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Wunsch Ii DC. Admiring the Great Mountain: A Celebration Special Issue in Honor of Stephen Grossberg's 80th Birthday. Neural Netw 2019; 120:1-4. [PMID: 31587821 DOI: 10.1016/j.neunet.2019.09.015] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
This editorial summarizes selected key contributions of Prof. Stephen Grossberg and describes the papers in this 80th birthday special issue in his honor. His productivity, creativity, and vision would each be enough to mark a scientist of the first caliber. In combination, they have resulted in contributions that have changed the entire discipline of neural networks. Grossberg has been tremendously influential in engineering, dynamical systems, and artificial intelligence as well. Indeed, he has been one of the most important mentors and role models in my career, and has done so with extraordinary generosity and encouragement. All authors in this special issue have taken great pleasure in hereby commemorating his extraordinary career and contributions.
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He S, Fang H, Zhang M, Liu F, Luan X, Ding Z. Online policy iterative-based H∞ optimization algorithm for a class of nonlinear systems. Inf Sci (N Y) 2019. [DOI: 10.1016/j.ins.2019.04.027] [Citation(s) in RCA: 51] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
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Dong L, Zhong X, Sun C, He H. Event-Triggered Adaptive Dynamic Programming for Continuous-Time Systems With Control Constraints. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2017; 28:1941-1952. [PMID: 28113603 DOI: 10.1109/tnnls.2016.2586303] [Citation(s) in RCA: 70] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In this paper, an event-triggered near optimal control structure is developed for nonlinear continuous-time systems with control constraints. Due to the saturating actuators, a nonquadratic cost function is introduced and the Hamilton-Jacobi-Bellman (HJB) equation for constrained nonlinear continuous-time systems is formulated. In order to solve the HJB equation, an actor-critic framework is presented. The critic network is used to approximate the cost function and the action network is used to estimate the optimal control law. In addition, in the proposed method, the control signal is transmitted in an aperiodic manner to reduce the computational and the transmission cost. Both the networks are only updated at the trigger instants decided by the event-triggered condition. Detailed Lyapunov analysis is provided to guarantee that the closed-loop event-triggered system is ultimately bounded. Three case studies are used to demonstrate the effectiveness of the proposed method.
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Dong L, Zhong X, Sun C, He H. Adaptive Event-Triggered Control Based on Heuristic Dynamic Programming for Nonlinear Discrete-Time Systems. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2017; 28:1594-1605. [PMID: 27071197 DOI: 10.1109/tnnls.2016.2541020] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.
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Zhong X, He H, Zhang H, Wang Z. A neural network based online learning and control approach for Markov jump systems. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2014.01.060] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Neural-network-based approach to finite-time optimal control for a class of unknown nonlinear systems. Soft comput 2013. [DOI: 10.1007/s00500-013-1170-z] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Zhang D, Liu D, Wang D. Approximate optimal solution of the DTHJB equation for a class of nonlinear affine systems with unknown dead-zone constraints. Soft comput 2013. [DOI: 10.1007/s00500-013-1062-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Liu D, Wei Q. Finite-Approximation-Error-Based Optimal Control Approach for Discrete-Time Nonlinear Systems. IEEE TRANSACTIONS ON CYBERNETICS 2013; 43:779-789. [PMID: 23070311 DOI: 10.1109/tsmcb.2012.2216523] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite-horizon discrete-time nonlinear systems with finite approximation errors. The idea is to use an iterative ADP algorithm to obtain the iterative control law that makes the iterative performance index function reach the optimum. When the iterative control law and the iterative performance index function in each iteration cannot be accurately obtained, the convergence conditions of the iterative ADP algorithm are obtained. When convergence conditions are satisfied, it is shown that the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some mild assumptions. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.
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Luo B, Wu HN. Approximate Optimal Control Design for Nonlinear One-Dimensional Parabolic PDE Systems Using Empirical Eigenfunctions and Neural Network. ACTA ACUST UNITED AC 2012; 42:1538-49. [DOI: 10.1109/tsmcb.2012.2194781] [Citation(s) in RCA: 61] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Biao Luo
- Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University (formerly Beijing University of Aeronautics and Astronautics), Beijing 100191, China.
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Optimal Tracking Control for a Class of Nonlinear Discrete-Time Systems With Time Delays Based on Heuristic Dynamic Programming. ACTA ACUST UNITED AC 2011; 22:1851-62. [DOI: 10.1109/tnn.2011.2172628] [Citation(s) in RCA: 148] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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Bartosiewicz Z, Martins N, Torres DF. The Second Euler-Lagrange Equation of Variational Calculus on Time Scales. EUROPEAN JOURNAL OF CONTROL 2011. [DOI: 10.3166/ejc.17.9-18] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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Fei-Yue Wang, Ning Jin, Derong Liu, Qinglai Wei. Adaptive Dynamic Programming for Finite-Horizon Optimal Control of Discrete-Time Nonlinear Systems With $\varepsilon$-Error Bound. ACTA ACUST UNITED AC 2011; 22:24-36. [DOI: 10.1109/tnn.2010.2076370] [Citation(s) in RCA: 243] [Impact Index Per Article: 18.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Martins N, Torres DF. Noether’s symmetry theorem for nabla problems of the calculus of variations. APPLIED MATHEMATICS LETTERS 2010. [DOI: 10.1016/j.aml.2010.07.013] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
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Girejko E, Malinowska AB, Torres DFM. Delta-nabla optimal control problems. JOURNAL OF VIBRATION AND CONTROL 2010. [DOI: 10.1177/1077546310381271] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
We present a unified treatment to control problems on an arbitrary time scale by introducing the study of forward-backward optimal control problems. Necessary optimality conditions for delta-nabla isoperimetric problems are proved, and previous results in the literature are obtained as particular cases. As an application of the results of the paper we give necessary and sufficient Pareto optimality conditions for delta-nabla bi-objective optimal control problems.
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Affiliation(s)
- Ewa Girejko
- Faculty of Computer Science, Białystok University of Technology, Poland
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Seiffertt J, Wunsch DC. Backpropagation and Ordered Derivatives in the Time Scales Calculus. ACTA ACUST UNITED AC 2010; 21:1262-9. [DOI: 10.1109/tnn.2010.2050332] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Pawłuszewicz E, Torres DF. Backward linear control systems on time scales. INTERNATIONAL JOURNAL OF CONTROL 2010. [DOI: 10.1080/00207179.2010.483562] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
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