Distributed optimisation algorithm based on iterative learning control

In this paper, we study the distributed optimisation problem in an iterative environment, where the global objective function consists of agents' local objective functions, and each agent with the local objective function performs repeated tasks in finite time. The objective is to minimise the global objective function by the local communication of agents in the repeated running system. To solve this problem, we propose a distributed optimisation algorithm based on iterative learning methods that combines the terminal iterative learning strategy with the subgradient strategy. When the initial states of all agents are the same in each iteration, by the proposed algorithm, it is proved that all agents' states asymptotically converge to the optimal solution. Moreover, considering that the initial states of agents in each iteration may not be accurately measured, we further study the distributed optimisation problem under different initial states. We find that all agents' states asymptotically converge to the neighbourhood of the optimal solution. Finally, the effectiveness of the algorithm is verified by the numerical simulations.