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∞ Performane Bound for Uncertain Discrete-Time Systems
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摘要: 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H∞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.Abstract: 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∞ 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.
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