Distributed Norm Optimal Iterative Learning Control for Networked Dynamical Systems

This paper considers the high performance consensus tracking problem of networked dynamical systems working in a repetitive manner that find applications in a wide range of areas. To achieve the high performance requirement, recent design uses iterative learning control (ILC) to avoid the use of accurate model information in traditional control methods. However, existing learning based methods either use simple forms of ILC design or explicitly utilise the model inverse, limiting their performance in practice. To address this limitation, this paper proposes an optimisation based ILC design using the well-known norm optimal ILC (NOILC) framework by designing a novel performance index. The resulting algorithm achieves monotonic convergence of the tracking error norm to zero, and can be applied to both heterogeneous and nonminimum phase systems. Using the alternating direction method of multipliers (ADMM), a distributed implementation of the algorithm is developed. Convergence properties of the algorithm are analysed in detail and numerical examples are presented to demonstrate the effectiveness of the proposed design.