Data-driven policy iteration algorithm for optimal control of continuous-time Ito stochastic systems with Markovian jumps

Jun Song, Shuping He, Fei Liu, Yugang Niu, Zhengtao Ding

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    Abstract

    This paper studies the infinite horizon optimal control problem for a class of continuous-time systems subjected to multiplicative noises and Markovian jumps by using a data-driven policy iteration algorithm. The optimal control problem is equivalent to solve a stochastic coupled algebraic Riccatic equation (CARE). An off-line iteration algorithm is first established to converge the solutions of the stochastic CARE, which is generalized from a implicit iterative algorithm. By applying subsystems transformation (ST) technique, the off-line iterative algorithm is decoupled into N parallel Kleinman's iterative equations. To learn the solution of the stochastic CARE from N decomposed linear subsystems data, a ST-based data-driven policy iteration algorithm is proposed and the convergence is proved. Finally, a numerical example is given to illustrate the effectiveness and applicability of the proposed two iterative algorithms.
    Original languageEnglish
    Pages (from-to)1431-1439
    Number of pages9
    JournalI E T Control Theory and Applications
    Volume10
    Issue number12
    Early online date25 Jul 2016
    DOIs
    Publication statusPublished - 8 Aug 2016

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