Non-lifted norm optimal iterative learning control for networked dynamical systems: A computationally efficient approach

Iterative learning control (ILC) is widely used for trajectory tracking in networked dynamical systems, which execute repetitive tasks. Traditional norm optimal ILC (NOILC) based on the lifted approach provides an analytical expression for the optimal ILC update law, but it raises a computational complexity issue. As the trial length N (i.e., the number of sampling points in one trial) increases, the computational cost of the lifted approach increases exponentially, which is obviously impractical for long trials. To address this issue, this paper proposes a non- lifted norm optimal ILC (N-NOILC) approach by developing a new non-lifted cost function to improve computationally efficiency. The N-NOILC approach achieves monotonic convergence in the iteration domain, and the computational complexity decreases from O(N3) ( N 3 ) of the lifted NOILC approach to O(N). ( N ) . Therefore, the proposed approach can be applied to large repetitive tasks. Based on the N-NOILC approach, this paper develops a centralized as well as a distributed algorithm for networked dynamical systems. Simulations are presented to validate the effectiveness of two algorithms and demonstrate the significant advantage of the N-NOILC approach in computational efficiency.