Robust Iterative Learning Control with Higher-Order Feedback for Variable-Trial-Length Nonlinear Systems Under Input Saturation and Disturbances

Abstract

This paper studies a robust composite higher-order feedback iterative learning control method for affine nonlinear discrete-time systems. The considered system is subject to input saturation, randomly varying trial lengths, random initial state shifts, and external disturbances. In the controller formulation phase, a Bernoulli stochastic sequence is used to model the data dropout phenomenon caused by non-uniform trial lengths. To address information loss caused by varying trial lengths, a composite control law is developed by combining a higher-order feedforward learning term with a real-time feedback term. The proposed method uses input and error information from several previous trials to compensate for the loss of learning information caused by non-uniform trial lengths. Based on mathematical induction, it is shown that the mathematical expectation of the tracking error gradually converges towards a strictly bounded residual neighborhood. It can be clearly shown that the analytical limits of this area are related to the magnitude of external disturbances and the variations in the initial state. Moreover, in optimal circumstances, the suggested algorithm ensures the rigorous asymptotic convergence of the anticipated error to zero. Finally, numerical simulations support the theoretical analysis and show that the proposed method maintains satisfactory tracking performance under the considered nonideal factors.