Neural-Network-Based Online HJB Solution for Optimal Robust Guaranteed Cost Control of Continuous-Time Uncertain Nonlinear Systems

In this paper, the infinite horizon optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems is investigated using neural-network-based online solution of Hamilton-Jacobi-Bellman (HJB) equation. By establishing an appropriate bounded function and defining a modified cost...

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Vydané v:	IEEE transactions on cybernetics Ročník 44; číslo 12; s. 2834 - 2847
Hlavní autori:	Liu, Derong, Wang, Ding, Wang, Fei-Yue, Li, Hongliang, Yang, Xiong
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	United States IEEE 01.12.2014 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	Adaptive critic designs adaptive/approximate dynamic programming (ADP) Algorithms Artificial Intelligence Computer Simulation Control systems Cost function Dynamical systems Equations Feedback Feedback control Hamilton-Jacobi-Bellman (HJB) equation Mathematical analysis Models, Statistical Neural networks Neural Networks (Computer) Nonlinear Dynamics Nonlinear systems Online Optimal control optimal robust guaranteed cost \hbox{control} Optimization Robustness uncertain nonlinear systems optimal robust guaranteed cost control uncertain nonlinear systems adaptive/approximate dynamic programming (ADP) Adaptive critic designs Hamilton–Jacobi–Bellman (HJB) equation neural networks
ISSN:	2168-2267, 2168-2275, 2168-2275
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Abstract	In this paper, the infinite horizon optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems is investigated using neural-network-based online solution of Hamilton-Jacobi-Bellman (HJB) equation. By establishing an appropriate bounded function and defining a modified cost function, the optimal robust guaranteed cost control problem is transformed into an optimal control problem. It can be observed that the optimal cost function of the nominal system is nothing but the optimal guaranteed cost of the original uncertain system. A critic neural network is constructed to facilitate the solution of the modified HJB equation corresponding to the nominal system. More importantly, an additional stabilizing term is introduced for helping to verify the stability, which reinforces the updating process of the weight vector and reduces the requirement of an initial stabilizing control. The uniform ultimate boundedness of the closed-loop system is analyzed by using the Lyapunov approach as well. Two simulation examples are provided to verify the effectiveness of the present control approach.
AbstractList	In this paper, the infinite horizon optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems is investigated using neural-network-based online solution of Hamilton-Jacobi-Bellman (HJB) equation. By establishing an appropriate bounded function and defining a modified cost function, the optimal robust guaranteed cost control problem is transformed into an optimal control problem. It can be observed that the optimal cost function of the nominal system is nothing but the optimal guaranteed cost of the original uncertain system. A critic neural network is constructed to facilitate the solution of the modified HJB equation corresponding to the nominal system. More importantly, an additional stabilizing term is introduced for helping to verify the stability, which reinforces the updating process of the weight vector and reduces the requirement of an initial stabilizing control. The uniform ultimate boundedness of the closed-loop system is analyzed by using the Lyapunov approach as well. Two simulation examples are provided to verify the effectiveness of the present control approach.In this paper, the infinite horizon optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems is investigated using neural-network-based online solution of Hamilton-Jacobi-Bellman (HJB) equation. By establishing an appropriate bounded function and defining a modified cost function, the optimal robust guaranteed cost control problem is transformed into an optimal control problem. It can be observed that the optimal cost function of the nominal system is nothing but the optimal guaranteed cost of the original uncertain system. A critic neural network is constructed to facilitate the solution of the modified HJB equation corresponding to the nominal system. More importantly, an additional stabilizing term is introduced for helping to verify the stability, which reinforces the updating process of the weight vector and reduces the requirement of an initial stabilizing control. The uniform ultimate boundedness of the closed-loop system is analyzed by using the Lyapunov approach as well. Two simulation examples are provided to verify the effectiveness of the present control approach. In this paper, the infinite horizon optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems is investigated using neural-network-based online solution of Hamilton-Jacobi-Bellman (HJB) equation. By establishing an appropriate bounded function and defining a modified cost function, the optimal robust guaranteed cost control problem is transformed into an optimal control problem. It can be observed that the optimal cost function of the nominal system is nothing but the optimal guaranteed cost of the original uncertain system. A critic neural network is constructed to facilitate the solution of the modified HJB equation corresponding to the nominal system. More importantly, an additional stabilizing term is introduced for helping to verify the stability, which reinforces the updating process of the weight vector and reduces the requirement of an initial stabilizing control. The uniform ultimate boundedness of the closed-loop system is analyzed by using the Lyapunov approach as well. Two simulation examples are provided to verify the effectiveness of the present control approach.
Author	Li, Hongliang Wang, Ding Wang, Fei-Yue Liu, Derong Yang, Xiong
Author_xml	– sequence: 1 givenname: Derong surname: Liu fullname: Liu, Derong email: dliu@ece.uic.edu organization: State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China – sequence: 2 givenname: Ding surname: Wang fullname: Wang, Ding email: ding.wang@ia.ac.cn organization: State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China – sequence: 3 givenname: Fei-Yue surname: Wang fullname: Wang, Fei-Yue email: feiyue.wang@ia.ac.cn organization: State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China – sequence: 4 givenname: Hongliang surname: Li fullname: Li, Hongliang email: hongliang.li@ia.ac.cn organization: State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China – sequence: 5 givenname: Xiong surname: Yang fullname: Yang, Xiong email: xiong.yang@ia.ac.cn organization: State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China
BackLink	https://www.ncbi.nlm.nih.gov/pubmed/25415951$$D View this record in MEDLINE/PubMed
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Copyright	Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Dec 2014
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Keywords	optimal robust guaranteed cost control uncertain nonlinear systems adaptive/approximate dynamic programming (ADP) Adaptive critic designs Hamilton–Jacobi–Bellman (HJB) equation neural networks
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Snippet	In this paper, the infinite horizon optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems is investigated using...
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SubjectTerms	Adaptive critic designs adaptive/approximate dynamic programming (ADP) Algorithms Artificial Intelligence Computer Simulation Control systems Cost function Dynamical systems Equations Feedback Feedback control Hamilton-Jacobi-Bellman (HJB) equation Mathematical analysis Models, Statistical Neural networks Neural Networks (Computer) Nonlinear Dynamics Nonlinear systems Online Optimal control optimal robust guaranteed cost \hbox{control} Optimization Robustness uncertain nonlinear systems
Title	Neural-Network-Based Online HJB Solution for Optimal Robust Guaranteed Cost Control of Continuous-Time Uncertain Nonlinear Systems
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