非线性时变系统自适应backstepping学习控制

针对含有混合未知参数的高阶非线性系统,利用backstepping方法,提出了一种自适应重复学习控制方法,该方法与分段积分机制相结合,可以处理时变参数在一个未知紧集内周期性快时变的非线性系统,通过构造微分-差分参数自适应律,设计了一种自适应控制策略,使跟踪误差在误差平方范数意义下渐近收敛于零,利用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有效性.

Adaptive Backstepping Learning Control for a Class of Nonlinear Time-varying Systems

Combining the backstepping approach with the pointwise integral mechanism, a novel adaptive repetitive learning control for high-order nonlinear systems with time-varying and time-invariant parameters is proposed. It can be applied to the time-varying parametric uncertainty systems with unknown compact set, non-vanishing, rapid time-varying, periodic and where the prior knowledge is the periodicity only. A differential-difference adaptive law and an adaptive repetitive learning control one are constructed to ensure the asymptotic convergence of the tracking error in the sense of square error norm. Also, a sufficient condition of the convergence of the method is given. A simulation example illustrates the effectiveness of the proposed method.