带有初态学习的指数变增益迭代学习控制

摘要

A new learning control algorithm is presented aiming at the trajectory tracking problem realized within a limited time region for a class of nonlinear time-varying systems. The new algorithm simultaneously adopts close-loop iterative learning rule with time-varying exponential gain for both control input and initial state of systems. Using the operator theory, the convergence of systems with any initial states is strictly proven under the operation of the iterative rule. Meanwhile, a sufficient convergence condition in the spectral radius form of the learning algorithm is provided. Compared with iterative learning control with the fixed learning gain, the proposed algorithm can not only significantly enhance the convergent speed but also solve the problem that the iterative learning control with time-varying exponential gain needs the rigid repetition of initial state. Simulation results illustrate the effectiveness of the proposed algorithm.%针对一类非线性时变系统在有限时间区间上的轨迹跟踪问题,提出一种新的迭代学习控制算法,该算法对系统的控制输入和初始状态同时采用闭环指数变增益迭代学习律.基于算子理论,对具有任意初始状态的系统,在该迭代学习律作用下的收敛性进行严格证明,同时给出该迭代学习算法收敛的谱半径形式的充分条件.该算法与固定增益的迭代学习控制相比较,不仅加快了收敛速度,而且还解决了指数变增益迭代学习控制要求初始状态严格重复的问题.仿真结果表明了该算法的有效性.