一类不确定随机非线性系统的采样扩张状态观测器设计与观测误差的收敛性分析

Design of Sampled Extended State Observer for a Class of Uncertain Stochastic Nonlinear Systems and Convergence Analysis of Observation Errors

实际系统中普遍存在各种干扰和不确定性因素,并且对控制系统的性能造成负面影响,因此设计对干扰和不确定性具有优异估计性能的观测器显得尤为重要.针对一类具有采样输出的不确定随机非线性系统,设计相应的采样扩张状态观测器用于在线估计不可量测状态和影响系统性能的随机总干扰.所估计的随机总干扰包含系统内部未建模动态、统计特性未知的外部有界噪声干扰以及不确定性因素的非线性耦合作用.在每个采样区间内,设计一个输出预估器用于估计实际输出,相应的输出估计值用于采样扩张状态观测器的设计.证明了所设计的采样扩张状态观测器对不可量测状态和随机总干扰的观测误差的均方收敛性.最后,一个具体仿真实例用于证实理论结果.

There are various disturbances and uncertainties in practical systems,which have a negative impact on the performance of the control system.Therefore,it is particu larly important to design observers with excellent estimation performance for disturbances and uncertainties.For a class of uncertain stochastic nonlinear systems with sampled out-put,a corresponding sampled extended state observer is designed for real-time estimation of unmeasurable states and stochastic total disturbance influencing system performance.The estimated stochastic total disturbances include unmodeled dynamics of the system,external bounded noise disturbances of unknown statistical characteristics and nonlinear coupling effects of uncertainties.In each sampling interval,an output estimator is designed in this paper to estimate the actual output,and the corresponding output estimates are used for the desgin of sampled extended state observer.This paper proves that the observation errors of the designed sampled extended state observer for unmeasurable states and stochastic total disturbance are mean square convergent.Finally,a specific simulation example is used to verify the theoretical results.