A Decentralized Optimal Iterative Learning Control Approach With Efficient Computation for Collaborative Tracking

Abstract

In practical industries, multiple subsystems are often required to collaborate on a particular repetitive collaborative tracking task, taking a lot of computation. Norm optimal iterative learning control (NOILC) can effectively improve the tracking accuracy for such tasks, and also provide the monotonic convergence of tracking error. However, the high-dimensional matrices and supervectors generated by the lifting technique lead to a computationally expensive problem in the lifted NOILC approach, making it difficult to apply to the collaborative tracking task with a long trial length. In order to achieve efficient computation, this paper proposes a novel non-lifted NOILC (N-NOILC) approach for collaborative tracking, with only linear computational complexity regarding the trial length. Exploiting the decomposability of the designed performance criterion, the N-NOILC optimization problem is reformulated as a “sharing” problem, and the alternating direction method of multipliers (ADMM) is introduced for its decentralized solution. Theoretical analysis shows that the proposed algorithm makes the error converge monotonically to zero under the corresponding convergence conditions. Its relevant parameter tuning guidelines are also provided. Finally, the effectiveness of the proposed decentralized N-NOILC approach is verified by numerical simulation.