Distributed Norm Optimal Iterative Learning Control for Formation of Networked Dynamical Systems

Abstract

High accuracy formation control of networked dynamical systems operating repetitively has many applications in a wide range of areas. To achieve the high formation control performance, the idea of iterative learning control (ILC) has been recently applied to avoid the use of accurate model information required by conventional control design methods. However, most existing ILC based design approaches use simple structures of control updating laws, often resulting in limited convergence performance. To address this problem, this paper proposes a novel optimisation based ILC algorithm for formation control using the idea of a well-known norm optimal ILC design framework. The algorithm guarantees monotonic convergence in the formation error norm, and can handle both heterogeneous networked systems and non-minimum phase dynamics. In addition, compared to most existing algorithms, the proposed algorithm has a distinguished feature that it converges to the minimum control energy solution for a particular choice of initial control input. Furthermore, using the idea of the alternating direction method of multipliers (ADMM), we develop a distributed implementation of the proposed algorithm in which each subsystem can update its own input using only local information so the algorithm can be applied to large scale network. Numerical simulations are presented to demonstrate the effectiveness of the proposed algorithm.