离散跳变无限不定随机线性二次控制

Infinitehorizon indefinite stochastic LQC for discrete-time Markov jump systems

主要论述了伴有状态和控制独立噪音的无限离散时间系统的带马尔科夫跳的随机线性二次控制问题.该问题给出了一个包含等式和不等式约束的广义代数黎卡提方程(GARE).跳变不定线性二次控制(LQC)问题的适定性被证明与一个线性矩阵不等式(LMI)的可行性是等价的;并且GARE一个镇定解的存在性等价于跳变线性二次控制问题的可达性.最后给出了一个基于LMI的方法通过半定规划来解决GARE.

This paper primarily discusses discrete-time infinite horizon stochastic linear quadratic control （LQC） problem with state and control dependent noise and Markov jump. The problem provides a generalized algebraic Riccati equation （GARE） that involves equality and inequality constraints. The well-posedness of the indefinite LQC problem with Markov jump is equivalent to the feasibility of a linear matrix inequality （LMI）. In addition, the existence of a stabilizing solution to the GARE is equivalent to the attainability of the LQC problem with Markov jump. Definitively, we give an LMI-based approach to figure out the GARE by a semidefinite programming.