Zero‐sum game optimal control for the nonlinear switched systems based on heuristic dynamic programming
In this article, the zero‐sum game problem of control and disturbance is studied for discrete affine nonlinear switched systems with unknown dynamical models. A two‐level heuristic dynamic programming iterative algorithm for solving the zero‐sum game problem is proposed, which can be used to solve t...
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| Veröffentlicht in: | Optimal control applications & methods 2023-09, Vol.44 (5), p.2821-2837 |
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| container_title | Optimal control applications & methods |
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| creator | Fu, Xingjian Li, Zizheng |
| description | In this article, the zero‐sum game problem of control and disturbance is studied for discrete affine nonlinear switched systems with unknown dynamical models. A two‐level heuristic dynamic programming iterative algorithm for solving the zero‐sum game problem is proposed, which can be used to solve the Hamilton‐Jacobi‐Isaacs equation associated with the optimal regulation control problem. The convergence analysis based on the value function and control strategy is given. For algorithm implementation, neural networks are used to approximate the control strategy, disturbance strategy, and value function of the game dynamic programming, respectively. A model network is used to approximate the system states with an unknown dynamical model. The iterative algorithm steps are given. Finally, the validity of the method is verified by simulation examples. |
| doi_str_mv | 10.1002/oca.3005 |
| format | Article |
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A two‐level heuristic dynamic programming iterative algorithm for solving the zero‐sum game problem is proposed, which can be used to solve the Hamilton‐Jacobi‐Isaacs equation associated with the optimal regulation control problem. The convergence analysis based on the value function and control strategy is given. For algorithm implementation, neural networks are used to approximate the control strategy, disturbance strategy, and value function of the game dynamic programming, respectively. A model network is used to approximate the system states with an unknown dynamical model. The iterative algorithm steps are given. 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A two‐level heuristic dynamic programming iterative algorithm for solving the zero‐sum game problem is proposed, which can be used to solve the Hamilton‐Jacobi‐Isaacs equation associated with the optimal regulation control problem. The convergence analysis based on the value function and control strategy is given. For algorithm implementation, neural networks are used to approximate the control strategy, disturbance strategy, and value function of the game dynamic programming, respectively. A model network is used to approximate the system states with an unknown dynamical model. The iterative algorithm steps are given. Finally, the validity of the method is verified by simulation examples.</description><subject>Dynamic models</subject><subject>Dynamic programming</subject><subject>Game theory</subject><subject>Games</subject><subject>Heuristic</subject><subject>Iterative algorithms</subject><subject>Iterative methods</subject><subject>Neural networks</subject><subject>Nonlinear control</subject><subject>Nonlinear systems</subject><subject>Optimal control</subject><subject>Strategy</subject><issn>0143-2087</issn><issn>1099-1514</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNotkM1KAzEcxIMoWKvgIwS8eNn6z2azH0cpfkHBi168hGw-2i2bpCZZpDcfwWf0SUypp2FgmGF-CF0TWBCA8s5LsaAA7ATNCHRdQRipTtEMSEWLEtrmHF3EuAWAhtByhoYPHfzv90-cLF4Lq7HfpcGKEUvvUvAjNj7gtNHYeTcOTouA49eQ5EYrHPcxaRtxL2J23uGNnsIQ0yCx2jths-6CXwdh7eDWl-jMiDHqq3-do_fHh7flc7F6fXpZ3q8KWTKWCmVazYDJKtu-1EyItlXSgFadKlndMGVMb-rGVKyrKBig0IsKJK1ZpxijdI5ujr15-3PSMfGtn4LLk7xs68yEQQs5dXtMyeBjDNrwXci_w54T4AeQPIPkB5D0DxXRaMo</recordid><startdate>202309</startdate><enddate>202309</enddate><creator>Fu, Xingjian</creator><creator>Li, Zizheng</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0002-0544-0289</orcidid></search><sort><creationdate>202309</creationdate><title>Zero‐sum game optimal control for the nonlinear switched systems based on heuristic dynamic programming</title><author>Fu, Xingjian ; Li, Zizheng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c255t-df8e505c4c25b2e5aa88dcf0ed9d25675dffbf67f459430f030ba40c3659d5533</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Dynamic models</topic><topic>Dynamic programming</topic><topic>Game theory</topic><topic>Games</topic><topic>Heuristic</topic><topic>Iterative algorithms</topic><topic>Iterative methods</topic><topic>Neural networks</topic><topic>Nonlinear control</topic><topic>Nonlinear systems</topic><topic>Optimal control</topic><topic>Strategy</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fu, Xingjian</creatorcontrib><creatorcontrib>Li, Zizheng</creatorcontrib><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Optimal control applications & methods</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fu, Xingjian</au><au>Li, Zizheng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Zero‐sum game optimal control for the nonlinear switched systems based on heuristic dynamic programming</atitle><jtitle>Optimal control applications & methods</jtitle><date>2023-09</date><risdate>2023</risdate><volume>44</volume><issue>5</issue><spage>2821</spage><epage>2837</epage><pages>2821-2837</pages><issn>0143-2087</issn><eissn>1099-1514</eissn><abstract>In this article, the zero‐sum game problem of control and disturbance is studied for discrete affine nonlinear switched systems with unknown dynamical models. 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| subjects | Dynamic models Dynamic programming Game theory Games Heuristic Iterative algorithms Iterative methods Neural networks Nonlinear control Nonlinear systems Optimal control Strategy |
| title | Zero‐sum game optimal control for the nonlinear switched systems based on heuristic dynamic programming |
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