期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 60, 期 10, 页码 2599-2613出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2015.2411911
关键词
LQR control; multiplicative noise; networked control; stabilization; stochastic system
资金
- Taishan Scholar Construction Engineering by Shandong Government
- National Natural Science Foundation of China [61120106011, 61203029, 61034007]
This paper is concerned with the long-standing problems of linear quadratic regulation (LQR) control and stabilization for a class of discrete-time stochastic systems involving multiplicative noises and input delay. These fundamental problems have attracted resurgent interests due to development of networked control systems. An explicit analytical expression is given for the optimal LQR controller. More specifically, the optimal LQR controller is shown to be a linear function of the conditional expectation of the state, with the feedback gain based on a Riccati-ZXL difference equation. It is also shown that the system is stabilizable in the mean-square sense if and only if an algebraic Riccati-ZXL equation has a particular solution. These results are based on a new technical tool, which establishes a non-homogeneous relationship between the state and the costate of this class of systems, and the introduction of a new Lyapunov function for the finite-horizon optimal control design.
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