一类双线性随机系统M量测不定LQ控制

摘要

The finite horizon indefinite linear quadratic (LQ) optimal output feedback control problem for discrete time stochastic systems with multiplicative noises and disturbed measurements is considered. In this problem, the weighting matrices of the quadratic cost functional are indefinite, and the optimal control does have the so-called dual effect. In order to make a compromise between the optimality and the computation complexity, a kind of M-measurements feedback control design approach is adopted. Based on the dynamic programming, the M-measurements feedback control for the bilinear stochastic systems (BLSS), which incorporates future measurements into the current control computation, can be solved in backward time, and the optimal solution is given in terms of a kind of generalized difference Riccati equation of the same dimensions as that of the plant. Simulation results show the superiority of the proposed algorithm over other widely used methods based on the certainty equivalence.%研究了带有乘性噪声和受扰动观测的离散时间随机系统不定线性二次(Linear quadratic,LQ)最优输出反馈控制问题.对此类问题而言,二次成本函数的加权矩阵不定号,并且最优控制具有对偶效果.为在最优性和计算复杂度间进行折衷,本文采用了一种M量测反馈控制设计方法.基于动态规划方法,将未来的测量结合到当前控制计算当中的M量测反馈控制可以通过倒向求解一类与原系统维数相同的广义差分Riccati方程(Generalized difference Riccati equation,GDRE)得到.仿真结果表明本文提出的算法与目前普遍采用的确定等价性方法相比具有优越性.