Online approximate solution of HJI equation for unknown constrained-input nonlinear continuous-time systems

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• 作者：Xiong Yang ^{xiong.yang@ia.ac.cn" class="auth_mail" title="E-mail the corresponding author} ; Derong Liu ; ^{derong.liu@ia.ac.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{derongliu@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Hongwen Ma ^{mahongwen2012@ia.ac.cn" class="auth_mail" title="E-mail the corresponding author} ; Yancai Xu ^{yancai.xu@ia.ac.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Adaptive dynamic programming ; Hamilton&ndash ; Jacobi&ndash ; Isaacs equation ; Input constraint ; Neural network ; Optimal control ; Reinforcement learning
• 刊名：Information Sciences
• 出版年：2016
• 出版时间：20 January 2016
• 年：2016
• 卷：328
• 期：Complete
• 页码：435-454
• 全文大小：833 K

文摘

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.