Iterative Learning Control with Forgetting Factor for MIMO Nonlinear Systems with Randomly Varying Iteration Lengths and Disturbances

Abstract

In this paper, a PD-type iterative learning control algorithm with a forgetting factor is developed for MIMO nonlinear systems with randomly varying iteration lengths, initial state shifts and disturbances. Firstly, considering the randomly varying iteration lengths, a modified tracking error is designed. Secondly, for the initial state shift and disturbances, a PD-type iterative learning control algorithm with a forgetting factor (PDILCFF) method is proposed. A contraction mapping method is exploited to obtain the convergence property of the proposed control scheme, which can guarantee that the tracking error is bounded. Considering the iteration-varying trial lengths, the proposed PDILCFF algorithm is closely related to symmetry. Symmetry can provide prior information about the system’s structure and characteristics for the proposed PDILCFF method, which is helpful for designing more efficient control algorithms. On the other hand, the proposed PDILCFF method exploits system symmetries across different intervals through iterative processes to achieve accurate control and performance optimization of MIMO unknown nonlinear systems. Finally, two simulations are presented, one with a subway train tracking control system and the other with a two-degree-of-freedom robot manipulator system, to verify the effectiveness of the theoretical studies.