基于Lyapunov方法的非线性系统自适应观测器设计

Adaptive Observer for Nonlinear System Based on Lyapunov Approach

针对一类满足L ipsch itz条件的具有未知参数的非线性系统,利用Lyapunov方法对L ipsch itz非线性系统自适应观测器的设计问题进行了研究。基于分析求解代数R iccati方程给出求解问题的不完善性、特征结构配置理论给出设计方法的重特征值限制性、对不同形式的观测器增益矩阵求解方法进行比较,最终选用线性矩阵不等式来改进观测器增益矩阵的选取方法。在观测误差稳定的条件下,得出了基于线性矩阵不等式方程设计状态观测器的增益矩阵,保证系统的状态估计误差收敛到零,并对其进行了仿真研究。结果证明,本文所构造的非线性观测器增益矩阵方法明显优越于其他方法,增强了系统的鲁棒性。

Aimed at a class of nonlinear system satisfying Lipschitz conditions with the unknown parameter,this paper studies the design of the adaptive state observer of the Lipschitz nonlinear system with the Lyapunov approach. Different solutions to different forms in the observer gain matrix are compared, be- cause the design is incomplete to obtain a solution to the algebraic Riccati equation. Thus the design based on eigenstructure assignment theory is limited, and the choice of the gain matrix L is concealed. Finally the linear matrix inequality （LMI） is utilized to improve the selection method of the observer gain matrix. Under stable conditions of observer error dynamics, the design state observer gain matrix is based on the linear matrix inequality, and in the meantime the state estimation errors are converged to zero asymptotically. An example demonstrates the superiority of the nonlinear observer gain matrix based on LMI than other methods and enhances the systematic robust.