Optimal Control and Stabilization for It?Systems with Input Delay  

作　　者：WANG Hongxia ZHANG Huanshui XIE Lihua 

机构地区：[1]School of Electrical and Automation Engineering,Shandong University of Science and Technology,Qingdao 266590,China [2]School of Electrical and Electronic Engineering,Nanyang Technological University,Singapore 639798,Singapore

出　　处：《Journal of Systems Science & Complexity》2021年第5期1895-1926,共32页系统科学与复杂性学报（英文版）

基　　金：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)。

摘　　要：The paper considers the linear quadratic regulation(LQR)and stabilization problems for It?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.

关 键 词：Input delay It?systems LQR optimal control stochastic systems 

分 类 号：O232[理学—运筹学与控制论] O211.6[理学—数学]