不确定随机非线性系统自适应观测器设计

Adaptive observer design for uncertain stochastic nonlinear systems

考虑带非参数不确定项的随机非线性系统自适应观测器设计问题.不同于已有结果,系统的不确定项无需满足Lipschitz连续性条件,也不必要仅仅是系统输出的函数.通过设计一个带参数自适应律的非线性观测器来重构系统状态,该观测器结构简单且易于实现.应用Lyapunov稳定性理论和随机微分理论证明该观测器是最终有界的,并且它的界可以通过选取适当的参数进行调节.最后,数值仿真结果表明了该观测器的有效性.

The problem of adaptive observer design is investigated for a class of stochastic nonlinear systems with nonparametric uncertainties. Different from the existing results, the uncertainties of the systems need neither satisfy Lipschitz condition nor only contain output variable. Through the design of a nonlinear observer with an adaptive law of pa/ameters, the system states are reconstructed. The observer has a simple structure and easy to implement. Lyapunov theorem and It6 stochastic differential theory are applied to show that the observation error convergences to the neighborhood of the origin, whose size can be adjusted by observer parameters. Finally, numerical simulation results show the effectiveness of the proposed observer.