Data‐driven policy iteration algorithm for continuous‐time stochastic linear‐quadratic optimal control problems
This paper studies a continuous‐time stochastic linear‐quadratic (SLQ) optimal control problem on infinite‐horizon. Combining the Kronecker product theory with an existing policy iteration algorithm, a data‐driven policy iteration algorithm is proposed to solve the problem. In contrast to most exist...
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| Vydáno v: | Asian journal of control Ročník 26; číslo 1; s. 481 - 489 |
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| Jazyk: | angličtina |
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01.01.2024
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| ISSN: | 1561-8625, 1934-6093 |
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| Abstract | This paper studies a continuous‐time stochastic linear‐quadratic (SLQ) optimal control problem on infinite‐horizon. Combining the Kronecker product theory with an existing policy iteration algorithm, a data‐driven policy iteration algorithm is proposed to solve the problem. In contrast to most existing methods that need all information of system coefficients, the proposed algorithm eliminates the requirement of three system matrices by utilizing data of a stochastic system. More specifically, this algorithm uses the collected data to iteratively approximate the optimal control and a solution of the stochastic algebraic Riccati equation (SARE) corresponding to the SLQ optimal control problem. The convergence analysis of the obtained algorithm is given rigorously, and a simulation example is provided to illustrate the effectiveness and applicability of the algorithm. |
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| AbstractList | This paper studies a continuous‐time stochastic linear‐quadratic (SLQ) optimal control problem on infinite‐horizon. Combining the Kronecker product theory with an existing policy iteration algorithm, a data‐driven policy iteration algorithm is proposed to solve the problem. In contrast to most existing methods that need all information of system coefficients, the proposed algorithm eliminates the requirement of three system matrices by utilizing data of a stochastic system. More specifically, this algorithm uses the collected data to iteratively approximate the optimal control and a solution of the stochastic algebraic Riccati equation (SARE) corresponding to the SLQ optimal control problem. The convergence analysis of the obtained algorithm is given rigorously, and a simulation example is provided to illustrate the effectiveness and applicability of the algorithm. |
| Author | Li, Na Zhang, Heng |
| Author_xml | – sequence: 1 givenname: Heng orcidid: 0000-0003-2508-1137 surname: Zhang fullname: Zhang, Heng organization: Shandong University – sequence: 2 givenname: Na surname: Li fullname: Li, Na email: naibor@163.com organization: Shandong University of Finance and Economics |
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| Cites_doi | 10.1016/j.neucom.2017.03.053 10.1109/9.788532 10.1109/TAC.2022.3181248 10.3934/math.2023519 10.1016/j.automatica.2006.09.019 10.1137/0306044 10.1016/j.automatica.2012.06.096 10.1109/TNNLS.2022.3209154 10.1002/asjc.2306 10.1137/15M103532X 10.1016/j.ins.2012.07.006 10.1007/s11432-020-3177-8 10.3934/jimo.2020030 10.1007/s11768-021-00046-y 10.1109/TASE.2022.3183610 10.1109/TII.2022.3168434 10.1080/00207179.2013.790562 10.1007/s00245-017-9402-8 10.1016/j.automatica.2022.110561 10.1109/TNNLS.2020.3042120 10.1002/asjc.61 10.1109/9.863597 10.1007/978-1-4612-1466-3 10.1109/TCYB.2021.3070352 10.1002/asjc.406 10.1016/j.automatica.2011.03.005 10.1016/j.sysconle.2009.11.006 10.1016/j.automatica.2008.08.017 10.1109/TIE.2021.3076729 10.1109/ACC.1994.735224 |
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| Copyright | 2023 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd 2024 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd |
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| SubjectTerms | Data collection data‐driven Iterative algorithms Optimal control policy iteration Riccati equation stochastic algebraic Riccati equation stochastic linear‐quadratic optimal control problem Stochastic systems |
| Title | Data‐driven policy iteration algorithm for continuous‐time stochastic linear‐quadratic optimal control problems |
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