New Results on Higher-Order Iterative Learning Control for Discrete Linear Systems

Iterative learning control is applicable to systems that make sweeps or passes through dynamics defined over a finite duration. Once each pass is complete all information generated as its dynamics evolve are available for use in designing the control action to be applied on the next sweep. The design problem is to construct a sequence of control inputs to enforce convergence to a specified reference of the sequence formed from the output produced on each pass and in this form of control the input is that used on the previous pass plus a correction term computed using previous pass output. A critical feature is the ability to use information that would be non-causal in the standard setting provided it is generated on a previous pass. Higher order iterative learning control uses information from more than the previous pass and is the subject of this paper where the generalized KalmanYakubovich-Popov lemma is used to develop new designs.