有限时间H∞控制系统设计的精细积分方法

The Precise Integtation Method for Finite Horizon H-infinity Control System Synthesis

中文关键词  H_∞控制  精细积分  Riccati方程  广义Rayleigh商

英文关键词  H-infinity control  precise integration  Riccati equation  generalized Rayliegh quotient

中文摘要

      按照结构力学与最优控制的模拟理论, H_∞ 状态反馈控制系统的最优H_∞ 范数γop 可以通过求广义Rayleigh商的最小本征值得到. 利用精细积分法和扩展的Wittrick_Williams(W_W )方法, 可以求解有限时间H_∞ 状态反馈控制的Riccati微分方程, 并确定其最优H_∞ 范数γop, 实现控制系统的设计. 在此基础上, 闭环H_∞ 控制系统状态方程的解也可以由精细积分法计算, 虽然

英文摘要

      Based on the analogy between structural mechanics and optimal control, the optimal H-infinity norm γop of H-infinity state feedback control system can be obtained through the computation of fundamental eigenvalue of a generalized Rayleigh quotient. To synthesise finite horizon H-infinity state feedback control system, the precise integration method is utilized to solve the Riccati differential equation and to compute the corresponding optimal H ∞ norm combined with the extended Wittrick-Williams (W-W) algorithm. The state equation of closed loop system is also solved by the precise integration method, although it is time varying. Therefore the simulation of response of H-infinity state feedback control system under the initial value disturbance can be accomplished by the precise integration method also, which is helpful for the design of control system and the evaluation of system performance.