高阶随机非线性系统的自适应状态反馈镇定

Adaptive State Feedback Stabilization for High-order Stochastic Nonlinear Systems

本文针对一类高阶随机不确定非线性系统,其漂移项与扩散项依赖于所有状态,研究了此系统的自适应状态反馈镇定问题.通过选取恰当的Lyapunov函数,利用自适应增加幂积分方法、反推技术、参数分离原理和一些代数技巧设计参数,构造了一个光滑自适应控制器.所设计的控制器能保证闭环系统对任意初始值几乎处处存在惟一解,平衡点依概率全局稳定并且系统的状态几乎处处调节到零.仿真例子验证了控制方案的有效性.

In this paper, the adaptive state feedback stabilization is studied for a class of high-order stochastic nonlinear systems in which drift and diffusion terms depend on all the states. We design parameters by choosing an appropriate Lyapunov function, the additive a power integrator scheme, the backstepping scheme, the parameter separation lemma and some flexible algebraic techniques. A smooth adaptive controller is constructed which guarantees that the closed-loop system has an almost surely unique solution for any initial state, the equilibrium of interest is globaly stable in probability, and the states can be regulated to origin almost surely. A simulation example is given to illustrate the effectiveness of the control scheme.