含有动态输入不确定性的随机非线性系统的鲁棒控制

Robust control of stochastic nonlinear systems with input dynamic uncertainties

针对一类含有动态输入不确定性的随机非线性系统,从无源性的观点研究了鲁棒控制理论.特别地,将确定性系统中基于无源性的系统设计法推广到该类不确定随机系统中,并以此作为基础给出了该类系统的鲁棒镇定控制器设计方法.与传统的基于系统模型三角形结构的设计方法不同,对于一个一般的系统,也能给出其具体的控制器形式.设计过程主要分两部分,首先给出一类反馈连接形式的随机非线性系统满足无源性的充分条件,在对系统进行合理的设定和分析的基础上,基于此条件对于随机系统在输入通道出现动态不确定性的情况下构造出一种状态反馈控制律,使得闭环系统满足无源性,从而是渐进稳定的;然后,将该无源控制律设计方法扩展到系统同时含有动态和静态模型不确定性的情况.仿真结果验证了设计方法的有效性.

From the viewpoint of passivity, robust control theory was developed for a class of stochastic nonlinear systems with input dynamic uncertainties. In particular, the passivity-based systematic design approach associated with deterministic nonlinear systems is introduced for this type of uncertain stochastic system, and is used to address the robust control design problems. Different from the classical design approach that focuses triangular systems, the control law can be constructed for general systems not restricted to strict-feedback systems. The design procedure mainly contains two parts. Firstly, a stochastic passivity condition is presented for a stochastic non-linear system in feedback interconnection form, and after some proper assumptions and analysis, a state feedback control law is designed under this condition for a type of stochastic nonlinear system in the presence of input dynamic uncertainties. Then, the passivity control law is extended to the stochastic non-linear system with both static model uncertainties and dynamic uncertainties. Simulation results illustrate its effectiveness.