Distributed optimization for unknown linear systems: A direct data-driven approach

This paper studies the distributed-optimization problems of general linear multi-agent systems (MASs) with unknown dynamics. The goal is to collaboratively optimize the global objective function composed of the sum of convex objective functions. Firstly, a noise-free data-driven adaptive distributed optimization protocol based on edges is designed for MASs, which is able to achieve asymptotical consensus tracking by adjusting the weight of each edge online, while minimizing the global objective function. Then, an improved data-driven adaptive distributed optimization protocol is established for the scenario with noisy data, which is able to achieve asymptotic consensus by updating weights solely based on state-errors under bounded noise, while minimizing the global objective function. Importantly, compared with existing distributed optimization protocols, the two proposed distributed optimization protocols do not rely on system model knowledge. Finally, two examples are provided in the paper to verify the effectiveness of the proposed noise-free and noisy data-driven adaptive distributed optimization protocols, respectively.