Abstract: In this paper, an iterative learning control profile for a class of discrete linear time-invariant systems is designed by employing a conjugate direction optimization scheme. The control design is formulated in the trial/iteration domain on basis of the lifted system representation, where both input and output sampled during the trials are grouped into super vectors. In this form, the control input signal of the next trial is generated by compensating for the current one with a searching direction described as the current tracking error vector minus its projections on historical searching directions. Both monotonic convergence and quadratic termination of the proposed iterative learning control algorithm are analyzed by the technique of the mathematical induction according to the properties of the conjugate direction. Effectiveness and validity of the control algorithm are illustrated in numerical simulations. Moreover, compared with existing proportional-type and norm-optimal iterative learning control methods, the superiority of the proposed method is also demonstrated.

Key words: conjugate direction, iterative learning control, tracking error, termination at a finite iteration