H_∞滤波问题数值求解的精细积分算法  

PRECISE INTEGRATION METHOD FOR NUMERICAL SOLUTION TO H_∞ FILTERING PROBLEM

作　　者：吴志刚[1] 钟万勰[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116023

出　　处：《自动化学报》2002年第2期201-208,共8页Acta Automatica Sinica

基　　金：国家重点基础研究发展规划项目(G1 9990 3 2 80 5 );中国博士后科学基金 (1 999)资助

摘　　要：有限时间 H∞ 滤波的 Riccati方程和滤波方程分别为非线性矩阵微分方程和线性变系数微分方程 ,而且 Riccati微分方程解的存在性还依赖于参数γ- 2 ,因此求这些方程的数值解一般比较困难 .按照结构力学与最优控制的模拟关系 ,Riccati方程解存在的临界参数γ- 2cr 对应于广义 Rayleigh商的一阶本征值 .因此可以用精细积分法结合扩展的 Wittrick- Williams( W- W)算法计算 γ- 2cr 并求解 Riccati方程 。For finite horizon H∞ filtering problem, the Riccati equation is a nonlinear matrix differential equation and the filtering equation is a linear time-variant one. Furthermore, the existence of the solution to the Riccati equation depends on γ-2. So it is not very easy to solve these equations by general numerical algorithm. According to the analogy between structural mechanics and optimal control, the critical parameter γcr-2 corresponds to the fundamental eigenvalue of a generalized Rayleigh quotient. Therefore, the precise integration method can be employed to solve the Riccati differential equation and to computer γcr-2 with the tended Wittrick-Williams (W-W) algorithm. The numerical solution to the filtering equation can also be obtained by the precise integration method, although it is a time-variant differential equation.

关 键 词：H∞滤波 RICCATI方程 H∞控制系统 扩展Wittrick-Williams算法 精细积分算法 数值求解 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] O231[自动化与计算机技术—控制科学与工程]