Distributed Iterative Learning Control for Constrained Consensus Tracking Problem

High precision consensus tracking of networked systems working repetitively has found important applications in various areas. To achieve the high precision tracking, iterative learning control (ILC) has recently been applied. This paper considers the constrained consensus tracking problem in ILC design. We develop a novel constrained ILC algorithm based on the successive projection framework. The resulting algorithm guarantees the satisfaction of the constraints and has appealing convergence properties: when perfect consensus tracking is possible, the tracking error norm converges monotonically to zero; otherwise, it converges monotonically to a ‘best fit’ solution. The proposed algorithm can be applied to both homogeneous and heterogeneous systems, as well as non-minimum phase systems, which is desirable in practice. Furthermore, we provide a distributed implementation for the proposed ILC algorithm using the idea of the alternating direction method of multipliers, allowing the proposed algorithm to be applied to large scale networked systems using only local information. Convergence properties of the algorithm are analysed rigorously and numerical examples are given to demonstrate its effectiveness.