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An improved iterative algorithm for solving optimal tracking control problems of stochastic systems

Author

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  • Xing, Shuangyun
  • Liu, Yifan
  • Liu, Da-Yan

Abstract

This paper proposes an improved iterative algorithm based on a Newton iterative algorithm, which is used to research the stochastic linear quadratic optimal tracking (SLQT) control for stochastic continuous-time systems. Firstly, a Newton iterative algorithm for solving stochastic algebraic Riccati equations (SAREs) is derived based on the Frechet derivative. Secondly, an improved iterative algorithm in an incremental form for indirectly solving SAREs is presented by combining the numerical iterative method with the incremental Newton iterative (INI) algorithm and introducing a tuning parameter. Under a suitable initial condition, the convergence of the improved iterative algorithm is talked over. Finally, numerical simulation experiments are carried out to compare our proposed improved iterative algorithm with some known works. The results show that the improved iterative algorithm has a faster convergence rate.

Suggested Citation

  • Xing, Shuangyun & Liu, Yifan & Liu, Da-Yan, 2023. "An improved iterative algorithm for solving optimal tracking control problems of stochastic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 213(C), pages 515-526.
    • Handle: RePEc:eee:matcom:v:213:y:2023:i:c:p:515-526
    DOI: 10.1016/j.matcom.2023.06.020
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