Distributed Norm Optimal Iterative Learning Control for High Performance Consensus Tracking

High-performance consensus tracking problem, which requires all the subsystems operating repetitively to track a desired reference, has found a number of important applications in the last decade. To achieve the high-performance requirement, recent designs use iterative learning control (ILC) to avoid the use of an accurate model that is usually required in conventional control methods. However, most of the existing distributed ILC algorithms have poor scalability (i.e., they will have difficulties when applied to large-scale and/or changing networks). Their performance (e.g., monotonic tracking error norm convergence) is heavily dependent on the choice of control parameters and they cannot handle general point-to-point tasks either. To address these limitations, this article proposes a novel distributed ILC algorithm using the well-known norm optimal ILC framework. By designing a performance index that explicitly incorporates the convergence performance, the resulting ILC design guarantees the tracking error norm converges monotonically to zero, which is appealing in practice. Using the alternating direction method of multipliers, a distributed implementation of the algorithm is obtained, where each subsystem's input is updated locally, such that the algorithm can be applied to large-scale and/or changing networks without any issues. Furthermore, the proposed algorithm can be extended to solve point-to-point consensus tracking problem, and applied to both homogeneous and heterogeneous networks, as well as nonminimum phase systems, which is of great practical relevance. Convergence and robustness of the algorithms are analyzed rigorously. Numerical examples are given to verify the effectiveness of the proposed algorithms.