Optimal Control of Nonlinear Systems With Time Delays: An Online ADP Perspective | Zendy

Jing Zhu | Zendy; Yijing Hou | Zendy; Tao Li | Zendy

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Optimal Control of Nonlinear Systems With Time Delays: An Online ADP Perspective

Author(s) -

Jing Zhu,

Yijing Hou,

Tao Li

Publication year - 2019

Publication title -

ieee access

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.587

H-Index - 127

ISSN - 2169-3536

DOI - 10.1109/access.2019.2945970

Subject(s) - optimal control , artificial neural network , nonlinear system , stability (learning theory) , computer science , control theory (sociology) , upper and lower bounds , perspective (graphical) , convergence (economics) , mathematics , adaptive control , mathematical optimization , control (management) , artificial intelligence , physics , quantum mechanics , mathematical analysis , machine learning , economics , economic growth

Drawing upon Lyapunov stability theories and online adaptive dynamic programming (ADP) technique, we propose a novel optimal control scheme for the nonlinear time delay system. Our contribution is twofold. First, we investigate the asymptotical stability problem and obtain a generalized stability condition in terms of linear matrix inequalities (LMIs). An explicit, easy-computing delay bound is presented by virtue of Gronwall’s inequality. Second, we propose the neural network (NN)-based optimal control strategy by utilizing two approximate NNs. The NN-based optimal control law converges to the real optimal control law since that the estimation errors of NNs weights converge to zero. Numerical examples are presented to illustrate our results.

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