标题：Control for Ito Stochastic Systems With Input Delay
作者：Zhang, Huanshui; Xu, Juanjuan
作者机构：[Zhang, Huanshui; Xu, Juanjuan] Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Shandong, Peoples R China.
通讯作者地址：[Zhang, HS]Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Shandong, Peoples R China.
来源：IEEE TRANSACTIONS ON AUTOMATIC CONTROL
关键词：Input delay; Ito system; stabilization; stochastic LQR
摘要：This paper examines the long-standing problem of linear quadratic regulation and stabilization for Ito stochastic systems with input delay. This problem remains a primary challenge because the separation principle does not hold for Ito stochastic systems. This paper presents a complete solution to the problem: 1) The (sufficient and necessary) solvability condition of the optimal control and the analytical controller are given based on the modified Riccati differential equation defined herein. 2) The sufficient and necessary stabilization condition in mean square sense is explored. We show that the Ito stochastic system with input delay is stabilized if and only if the modified algebraic Riccati equation developed in this paper has a unique positive-definite solution. The essential obstacle encountered in this paper concerns a Delayed Forward-Backward Stochastic Differential Equation (D-FB-SDE), which is mathematical challenging.