Adaptive Dynamics Programming for H∞ Control of Continuous-Time Unknown Nonlinear Systems via Generalized Fuzzy Hyperbolic Models
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 syste...
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| Published in | IEEE transactions on systems, man, and cybernetics. Systems Vol. 50; no. 11; pp. 3996 - 4008 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.11.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2168-2216 2168-2232 |
| DOI | 10.1109/TSMC.2019.2900750 |
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| Abstract | 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. |
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| AbstractList | 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. In this paper, a novel adaptive dynamic programming (ADP) algorithm is developed for the infinite-horizon ([Formula Omitted]) 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 [Formula Omitted] 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. |
| Author | Gao, David Wenzhong Zhang, Huaguang Su, Hanguang Luo, Yanhong |
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| SubjectTerms | 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 |
| Title | Adaptive Dynamics Programming for H∞ Control of Continuous-Time Unknown Nonlinear Systems via Generalized Fuzzy Hyperbolic Models |
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