一类高阶非线性参数化系统自适应重复学习控制

Adaptive repetitive learning control for a class of nonlinearly parameterized uncertain systems

针对一类高阶非线性参数化系统,利用参数重组技巧,提出了一种自适应重复学习控制方法.该方法结合反馈线性化,可以处理参数在一个未知紧集内周期性、快时变的非线性系统.通过引进微分-差分参数自适应律,设计了一种自适应控制策略,使广义跟踪误差在误差平方范数意义下渐近收敛于零.通过构造Lyapunov泛函,给出了闭环系统收敛的一个充分条件.实例仿真结果说明了该方法的可行性和有效性.

An adaptive repetitive learning control method for high-order nonlinearly parameterized uncertain systems with time-varying and time-invariant parameters is proposed. Combining the parameter regrouping technique with the feedback linearization approach, the method can be applied to the nonlinear systems in which the parameters are rapid time-varying and periodic in a unknown compact set. By introducing a differential-difference adaptive law, an adaptive repetitive learning control strategy is designed to ensure the asymptotic convergence of the extended tracking error in the sense of square error norm. Also, a sufficient condition for the convergence of the method is given. A simulation example illustrates the effectiveness and the feasibility of the proposed method.