一种多变量滚动式LQG自适应控制及其稳定性

Receding Horizon LQG Control and its Stability Properties

提出了一种新的基于状态空间模型设计的多变量滚动式优化多步目标函数的ＬＱＧ自适应控制算法，分析了这种滚动优化ＬＱＧ控制闭环系统的稳定性，给出了一些新的稳定性条件，证明了存在有限时域使闭环系统指数稳定，而且至少具有１／α的稳定度，其中α可由设计者给定，从而将闭环系统的极点配置在预期的区域内，提高了系统的鲁棒度，增强了系统的鲁棒性。

Although a number of predictive controls based on input-output models were reported to have been successfully applied to real processes,their stability properties are still not analyzed in depth.We now present a receding horizon LoG(linear quadratic Gaussian)control,one general class of predictive controls,and analyze its stability properties in depth.The receding horizon LoG control law was derived from the standard LoG problem by using the receding horizon concept.We employed state -space models in our analysis, which shows that there exists a finite cost horizon over which the closed loop systems are always asymptotically stable.Our analysis also shows that the receding horizon LoG control with a design parameter a in eq.(4) provides robust stability properties.