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Optimal Control and Stabilization for Itô Systems with Input Delay

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Abstract

The paper considers the linear quadratic regulation (LQR) and stabilization problems for Ito stochastic systems with two input channels of which one has input delay. The underlying problem actually falls into the field of asymmetric information control because of the nonidentical measurability induced by the input delay. In contrast with single-channel single-delay problems, the challenge of the problems under study lies in the interaction between the two channels which are measurable with respect to different filtrations. The key techniques conquering such difficulty are the stochastic maximum principle and the orthogonal decomposition and reorganization technique proposed in a companion paper. The authors provide a way to solve the delayed forward backward stochastic differential equation (D-FBSDE) arising from the maximum principle. The necessary and sufficient solvability condition and the optimal controller for the LQR problem are given in terms of a new Riccati differential equation established herein. Further, the necessary and sufficient stabilization condition in the mean square sense is provided and the optimal controller is given. The idea proposed in the paper can be extended to solve related control problems for stochastic systems with multiple input channels and multiple delays.

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Authors and Affiliations

  1. School of Electrical and Automation Engineering, Shandong University of Science and Technology, Qingdao, 266590, China

    Hongxia Wang & Huanshui Zhang

  2. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    Lihua Xie

Authors
  1. Hongxia Wang
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  2. Huanshui Zhang
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  3. Lihua Xie
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Corresponding authors

Correspondence to Hongxia Wang, Huanshui Zhang or Lihua Xie.

Additional information

This work was supported by Science and Technology Project of Qingdao West Coast New Area (2019–32, 2020–20, 2020-1-4), High-level Talent Team Project of Qingdao West Coast New Area (RCTD-JC-2019-05), Key Research and Development Program of Shandong Province (2020CXGC01208).

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Wang, H., Zhang, H. & Xie, L. Optimal Control and Stabilization for Itô Systems with Input Delay. J Syst Sci Complex 34, 1895–1926 (2021). https://doi.org/10.1007/s11424-021-1226-6

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  • DOI: https://doi.org/10.1007/s11424-021-1226-6

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