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Title: Optimal control and stabilization for Itô systems with input delay
Authors: Wang, Hongxia
Zhang, Huanshui
Xie, Lihua
Keywords: Engineering::Electrical and electronic engineering
Issue Date: 2021
Source: Wang, H., Zhang, H. & Xie, L. (2021). Optimal control and stabilization for Itô systems with input delay. Journal of Systems Science and Complexity, 34(5), 1895-1926.
Journal: Journal of Systems Science and Complexity
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.
ISSN: 1009-6124
DOI: 10.1007/s11424-021-1226-6
Rights: © 2021 The Editorial Office of JSSC & Springer-Verlag GmbH Germany. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
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