不确定离散系统具有H_∞性能界的鲁棒LQG状态反馈控制

ROBUST LQG STATE-FEEDBACK CONTROL WITH H_∞ PERFORMANCE BOUND FOR UNCERTAIN DISCRETE TIME SYSTEMS

研究了含有范数有界参数不确定线性离散系统具有H∞性能界的鲁棒LQG状态反馈控制问题,考虑了有限时域时变及无限时域时不变两种情形.所得的控制器对于所有可容许的参数不确定都能满足给定的H∞性能界,且为最坏情形H2性能指标提供了一个最优上界.对于无限时域时不变情形,该控制器还能保证闭环系统渐近稳定.结果仅需求解一含有一个尺度参数的Riccati方程.

The paper studies the problem of robust LQG state feedback control with H_∞ performance bound for uncertain linear discrete time systems that are subjected to norm bounded parameter uncertainty. Both the cases of finite horizon time varying and infinite horizon time invariant are considered. The controller derived can satisfy a given H ∞ performance bound and provide an optimized bound for the worst case H 2 performance index for all admissible parameter uncertainties, and also make the closed loop systems asymptotically stable for the case of infinite horizon time invariant. The obtained result only needs to solve a single parameter dependent Riccati equation.