线性随机系统基于观测器的反馈镇定

Observer-based Feedback Stabilization for Linear Stochastic Systems

关键词:  观测器设计  复合Lyapunov函数  几乎必然稳定性  乘性噪声

Key words:  observer design  composite Lyapunov function  almost sure stability  multiplicative noise

摘要:

针对控制系统测量输出产生的乘性噪声问题,提出基于观测器的反馈控制设计算法.首先,引入状态误差变量,导出反馈控制下Itô型随机微分方程描述的闭环系统.其次,运用复合Lyapunov函数方法并结合随机分析技术,分析闭环系统的均方指数稳定性和几乎必然稳定性,并建立输出反馈控制器存在的充分条件.基于此条件给出了控制增益矩阵和观测器增益矩阵的参数化设计算法.最后,通过倒立摆模型的数值仿真,验证所提出控制策略的有效性.

Abstract:

An observer-based feedback controller was designed for linear systems with multiplicative measurement noise. Firstly,the observer-based feedback controlled system described by an Itô stochastic system was deduced by introducing the state estimation error. Next, by applying composite Lyapunov function approach combined with stochastic analysis techniques,mean square stability and almost sure stability criteria of the closed-loop systems were analyzed,and the sufficient conditions for the existence of the output feedback controller were established.Based on this condition, a parametric design algorithm of control gain matrix and observer gain matrix was given.Finally,the numerical simulation of an inverted pendulum model was used to verify the effectiveness of the proposed control strategy.