Adaptive Dynamics Programming for H∞ Control of Continuous-Time Unknown Nonlinear Systems via Generalized Fuzzy Hyperbolic Models

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 50; no. 11; pp. 3996 - 4008
• Main Authors: Su, Hanguang, Zhang, Huaguang, Gao, David Wenzhong, Luo, Yanhong
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive algorithms; Adaptive control; Adaptive dynamic programming (ADP); Approximation algorithms; Artificial neural networks; Attenuation; Control stability; disturbance attenuation; Dynamic programming; Dynamical systems; Fuzzy systems; Games; generalized fuzzy hyperbolic models (GFHMs); H-infinity control; Heuristic algorithms; infinite-horizon (<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H∞ ) control; Liapunov direct method; Mathematical model; Nonlinear control; Nonlinear systems; Optimal control; Stability analysis; System dynamics; Zero sum games
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2019.2900750

In this paper, a novel adaptive dynamic programming (ADP) algorithm is developed for the infinite-horizon (<inline-formula> <tex-math notation="LaTeX">H_{\infty} </tex-math></inline-formula>) optimal control problems with unknown continuous-time (CT) nonlinear systems subject to external disturbances. To facilitate the implementation of the algorithm, generalized fuzzy hyperbolic models (GFHMs) are utilized to establish an identifier-critic architecture, where the identifier is designed to reconstruct the unknown system dynamics, and the GFHM-based critic network is employed to approximate the value functions. The CT <inline-formula> <tex-math notation="LaTeX">H_{\infty} </tex-math></inline-formula> optimal control issue is converted into a two-player zero-sum game and the corresponding Hamilton-Jacobi-Isaacs equation is derived. The learning procedure of the critic design is adaptively implemented with the help of the reconstructed model, thus the requirement of the complete system dynamics is relaxed. Furthermore, by the means of Lyapunov direct method, the uniform ultimate boundedness stability analysis of the closed-loop control system is explicitly provided. Finally, to compare the control performances and disturbance attenuation properties of the proposed method and the existing ADP algorithms, two numerical examples are given.