一类非线性时变系统的迭代学习控制

针对一类具有任意初态的不确定非线性时变系统,应用校正期望轨迹方法把任意初态问题转换为零初始误差的变期望轨迹的迭代学习控制问题,提出了求解校正期望轨迹的过渡轨迹的计算方法.然后,针对变期望轨迹问题提出了一种新的迭代学习控制算法,在算法中引入了期望轨迹的高阶导数来克服期望轨迹的变化,并通过设计稳定的跟踪误差滑动面来处理系统中非线性时变不确定性.论文给出了相关定理,并应用类Lyapunov方法给出了详细证明.仿真结果表明所提出的算法是有效的,该算法不需要系统的模型结构信息,比自适应迭代学习控制算法具有更宽的适用范围.

Iterative learning control for a class of nonlinear time-varying system

To a class of uncertain nonlinear time-varying systems with arbitrary initial states, we apply the method of rectifying desired trajectory to transform the problem of arbitrary initial states into the problem of varying desired trajectories with zero initial error. The computational procedures for obtaining the transition trajectories for the varying desired trajectories are presented. Then, a new iterative learning control (ILC) algorithm is developed for determining the varying desired trajectory, in which higher order derivatives of the desired trajectory is incorporated to handle the variations of the desired trajectory. A stable sliding-surface of tracking errors is designed to deal with the time-varying nonlinear uncertainty of the controlled system. The corresponding theorems are given in this paper and are proved in details by using the Lyapunov-like method. Simulation results validate the effectiveness of the proposed algorithm in which there is no need of the model structure information of the controlled system, thus extending the application scope of the adaptive ILC algorithm.