Lipschitz非线性系统未知输入观测器设计

Design of Observer with Unknown Input for Lipschitz Nonlinear Systems

针对观测器匹配条件不满足情况下的Lipschitz非线性系统状态估计和未知输入重构问题,提出了一种未知输入观测器设计方法。首先,通过构造辅助输出向量,突破了观测器匹配条件的限制,并设计高阶、高增益滑模微分器实现对辅助输出向量及其微分的精确估计;之后,在辅助输出及其微分精确估计的基础上,设计具有滑模控制律和自适应调节律的自适应鲁棒滑模观测器,并提出了一种未知输入重构方法。该观测器设计方法不需知道Lipschitz常数,其大小可通过自适应调节律调节,且信息重构具有避免直接使用系统输出微分的优点。仿真结果表明,所设计的未知输入观测器不仅在观测器匹配条件不满足情况下可以实现对状态的渐进估计以及对未知输入重构之目的,而且自适应调节律能够在约5s时间内实现对Lipschitz常数的自适应调节。

A scheme to design observer with unknown input and unknown input reconstruction for Lipschitz nonlinear systems is proposed when the observer matching condition is not satisfied. An auxiliary output vector is constructed to satisfy the observer matching condition, and a highorder sliding mode differentiator with highgain is designed to exactly estimate the auxiliary output vector and its derivative. Then, an adaptive robust sliding mode observer which complies with a robust sliding mode control law and an adaptation law is developed based on the estimations of the auxiliary output vector and its derivative, and an unknown input reconstruction method is derived without using the derivative information of system’s output vector. The Lipschitz constant does not need to be known and is adjusted using the adaptive law. The method of unknown input reconstruction avoids the direct use of the derivative information of system’s output. Simulation results show that states and unknown inputs can be gradually estimated by the proposed unknown input observer when the observer matching condition is not satisfied, and that the Lipschitz constant can be adjusted within 5 seconds by the proposed adaptation law.