Distributed Optimal Coordinated Control of Heterogeneous Linear Multi-agent Systems over Directed Communication Topologies: A Tracking-Based Approach

The distributed optimal coordinated control problem of heterogeneous linear multi-agent systems is studied in this paper. Specifically, each agent in the system under consideration has a local private cost function, which is assumed to be strongly convex with a Lipschitz continuous gradient. The agents aim to achieve output consensus on the optimal solution of a global cost function, which is the sum of local cost functions. The communication topology among agents is assumed to be a weight-unbalanced and strongly connected directed graph. To solve such a control problem, a tracking-based approach is suggested and utilized, where an auxiliary system is designed to seek the optimal solution. Based on the output regulation technique, distributed tracking control inputs are proposed for the agents, which ensure that the outputs of the agents track the trajectories generated by the auxiliary system. Under the assumptions on the local cost functions, the communication topology and system matrices, it is proved that with the proposed control scheme, the outputs of all agents can achieve consensus on the optimal solution. Finally, two numerical simulation examples are presented to illustrate the effectiveness of the proposed tracking control scheme.