Attenuation on non-repetitive disturbances in robust iterative learning control schemes designed over repetitive setting

Abstract

This paper addresses the design of a robust iterative learning control (ILC) scheme for a class of linear systems with time-varying uncertainties and non-repetitive disturbances. The proposed design method modifies two-dimensional/repetitive setting to include the requirement for $\mathcal{H}_{\infty}$ disturbance attenuation. Also, it is shown that the conversion of the control problem to one of stability along the trial for a linear repetitive process leads to design based on linear matrix inequality (LMI) computations. In particular, sufficient conditions for the existence of a robust ILC updating law are derived together with the design algorithms for the associated controller matrices. Obtained results show that the proposed control law is able to fulfil the imposed requirements, i.e., they are suitable for the systems with time-varying uncertainties as well as non-repetitive disturbances. An illustrative example is given to highlight the principles, effectiveness and possible applicability of the proposed method.