一类随机线性系统的鲁棒自适应非线性控制设计

Design of Robust Adaptive Nonlinear Control for a Class of Stochastic Linear Systems

论文讨论了一类具有随机输入的线性控制系统的自适应鲁棒跟踪控制问题 .将M .Krstic等提出的自适应非线性控制器设计方法与鲁棒控制基本原理相结合 ;证明了当控制系统的随机输入满足一定条件时 ,采用随机Backstepping自适应控制方法 ,能确保系统输出与参考信号误差的均方值全局有界 ,并能渐近收敛到一个预先任意置定的精度内 .仿真实例表明这种控制器具有很好的鲁棒跟踪效果 .

This paper discusses the robust adaptive output tracking problem of a class of linear control system with stochastic input. It introduces the design principles of M.Krstic's adaptive nonlinear controller and robust control for a class of stochastic systems. The paper proves that when a system has stochastic input satisfying some assumptions, if stochastic backstepping robust adaptive control is used, the output tracking error of the stochastic control system can be guaranteed to be globally bounded and asymptotically converge within the precision prescribed in actual problems. At the end of the paper, a simulation example is given.