严格反馈非线性时变系统的迭代学习控制

Iterative Learning Control of Strict-feedback Nonlinear Time-varying Systems

针对一类含未知时变参数的严格反馈非线性系统,提出一种实现有限作业区间轨迹跟踪控制的迭代学习算法.基于Lyapunov-like方法设计控制器,回避了常规迭代学习控制中受控系统非线性特性需满足全局Lipschitz连续条件的要求.以反推设计(Backstepping)方法设计控制器,为使得虚拟控制项可导,引入一级数收敛序列;将时变参数展开为有限项多项式形式,在控制器设计中采取双曲正切函数处理余项对于系统跟踪性能的影响.理论分析表明,闭环系统所有信号有界,并能够实现系统输出完全收敛于理想轨迹.

In this paper, an iterative learning controller is presented for a class of strict-feedback nonlinear systems with time-varying uncertainties. The learning controller is designed based on the Lyapunov-like synthesis, which can handle system dynamics with non-global Lipschitz nonlinearities. For the con- troller design, the time-varying parameters are expanded into Taylor series with bounded remained term, and backstepping design technique is applied. Hyperbolic tangent function is used with a typical series introduced in order to guarantee the differentiabillty of the virtue control variables. Theoretical analysis shows that all signals in the closed-loop system remain bounded and that complete tracking over a pre-specified time interval is achieved.