|Online approximate solution of HJI equation for unknown constrained-input nonlinear continuous-time systems|
|Yang, Xiong; Liu, Derong; Ma, Hongwen; Xu, Yancai
|Source Publication||INFORMATION SCIENCES
|Abstract||This paper is concerned with the approximate solution of Hamilton-Jacobi-Isaacs (HJI) equation for constrained-input nonlinear continuous-time systems with unknown dynamics. We develop a novel online adaptive dynamic programming-based algorithm to learn the solution of the HJI equation. The present algorithm is implemented via an identifier-critic architecture, which consists of two neural networks (NNs): an identifier NN is applied to estimate the unknown system dynamics and a critic NN is constructed to obtain the approximate solution of the HJI equation. An advantage of the proposed architecture is that the identifier NN and the critic NN are tuned simultaneously. With introducing two additional terms, namely, the stabilizing term and the robustifying term to update the critic NN, the initial stabilizing control is no longer required. Meanwhile, the developed critic tuning rule not only ensures convergence of the critic to the optimal saddle point but also guarantees stability of the closed-loop system. Moreover, the uniform ultimate boundedness of the weights of the identifier NN and the critic NN are proved by using Lyapunov's direct method. Finally, to illustrate the effectiveness and applicability of the developed approach, two simulation examples are provided. (C) 2015 Elsevier Inc. All rights reserved.|
|Keyword||Adaptive Dynamic Programming
|WOS Headings||Science & Technology
|WOS Keyword||ZERO-SUM GAMES
; DYNAMIC-PROGRAMMING ALGORITHM
; ADAPTIVE OPTIMAL-CONTROL
; STATE-FEEDBACK CONTROL
; H-INFINITY CONTROL
; LEARNING ALGORITHM
; CONTROL DESIGN
|Funding Organization||National Natural Science Foundation of China(61034002
; Beijing Natural Science Foundation(4132078)
; Early Career Development Award of the State Key Laboratory of Management and Control for Complex Systems (SKLMCCS)
|WOS Research Area||Computer Science
|WOS Subject||Computer Science, Information Systems
|Affiliation||Chinese Acad Sci, Inst Automat, State Key Lab Management & Control Complex Syst, Beijing 100190, Peoples R China|
|First Author Affilication||Chinese Acad Sci, Inst Automat, State Key Lab Management & Control Complex Syst, Beijing 100190, Peoples R China
Yang, Xiong,Liu, Derong,Ma, Hongwen,et al. Online approximate solution of HJI equation for unknown constrained-input nonlinear continuous-time systems[J]. INFORMATION SCIENCES,2016,328:435-454.
Yang, Xiong,Liu, Derong,Ma, Hongwen,&Xu, Yancai.(2016).Online approximate solution of HJI equation for unknown constrained-input nonlinear continuous-time systems.INFORMATION SCIENCES,328,435-454.
Yang, Xiong,et al."Online approximate solution of HJI equation for unknown constrained-input nonlinear continuous-time systems".INFORMATION SCIENCES 328(2016):435-454.
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