期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 62, 期 1, 页码 350-365出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2016.2551371
关键词
Input delay; Ito system; stabilization; stochastic LQR
资金
- Taishan Scholar Construction Engineering by Shandong Government
- National Natural Science Foundation of China [61120106011, 61403235, 61573221, 61633014]
- Natural Science Foundation of Shandong Province [ZR2014FQ011]
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.
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