Abstract:

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.