Optimally Selected Cycle-Based ILC for System With Randomly Varying Initial State

Abstract

Iterative learning control (ILC) is a widely used method for controlling repetitive processes. However, its superior learning capability from cycle to cycle is mostly predicated on the assumption that the initial state for all cycles is identical and at the desired point. In engineering practice, this assumption can be overly strict. A more common scenario involves the initial state varying randomly from cycle to cycle. In this article, we propose an optimally selected cycle-based ILC scheme to address the issue of randomly varying initial states. Our approach involves selecting an optimal cycle for iterative learning by evaluating both the potential impact of initial state variations and the tracking performance of historical cycles. By extending the learning mechanism of ILC from learning from the previous cycle to learning from the past optimally selected cycle, our scheme ensures improvement after each iteration of learning. In addition, our scheme has been adapted to accommodate uncertain systems with greater generality. The feasibility and convergence properties of our scheme are investigated through theoretical analysis. Finally, we demonstrate the effectiveness and other properties of the proposed method through a benchmark numerical example.