Indefinite Linear Quadratic Optimal Control Problem for Singular Linear Discrete-time System: Krein Space Method  

作　　者：CUI Peng ZHANG Cheng-Hui 

机构地区：[1]School of Control Science and Engineering, Shandong University, Jinan 250061, P. R. China

出　　处：《自动化学报》2007年第6期635-640,共6页Acta Automatica Sinica

基　　金：National Natural Science Foundation of P. R. China (50477042);Ph. D. Programs Foundation of Ministry of Education of P.R.China (20040422052);the Natural Science Foundation of Shandong Province (Z2004G04)

摘　　要：有限时间地平线不定线性二次(LQ ) 为单个线性分离变化时间的系统的最佳的控制问题被讨论。为单个系统的不定的 LQ 最佳的控制问题能在一个合理假设下面为标准州空间的系统被转变到那。不定的 LQ 最佳的控制问题对为向后的随机的系统的设计的双，这被显示出。因此，最佳的 LQ 控制器能被计算 Kalman 过滤器的获得矩阵获得。为不定的 LQ 问题保证一个唯一的答案的必要、足够的条件被给。这个问题的一个明确的解决方案以 Riccati 差别方程的答案被获得。The finite time horizon indefinite linear quadratic（LQ） optimal control problem for singular linear discrete time-varying systems is discussed. Indefinite LQ optimal control problem for singular systems can be transformed to that for standard state-space systems under a reasonable assumption. It is shown that the indefinite LQ optimal control problem is dual to that of projection for backward stochastic systems. Thus, the optimal LQ controller can be obtained by computing the gain matrices of Kalman filter.Necessary and sufficient conditions guaranteeing a unique solution for the indefinite LQ problem are given. An explicit solution for the problem is obtained in terms of the solution of Riccati difference equations.

关 键 词：模糊线性二次最佳控制 单次线性离散时间系统 有限时间 差异方程 KaLman过滤 

分 类 号：TP273.4[自动化与计算机技术—检测技术与自动化装置]