Distributed Optimal Coordination for Heterogeneous Linear Multiagent Systems

This article studies the problem of distributed optimal coordination (DOC) for heterogeneous linear multiagent systems. Compared with the existing results where the structure constraints on local gradients or system matrices are required, the considered DOC framework is sufficiently general in the sense that no extra assumption is required except for the convexity/differentiability of local objective functions and the controllability/observability of linear systems. A necessary and sufficient condition for the existence of the solution to the DOC problem is derived in terms of the relationship between the objective function and so-called steady-state reachable set of linear systems. Under this fundamental condition, the original DOC problem is transformed into the one with additive equality constraint, without loss of the optimality, which generates a trackable solution for agent dynamics. By using a new state transformation technique, it is proved that the proposed DOC algorithm guarantees the global asymptotical convergence by utilizing only local interaction. Simulation results on the motion coordination illustrate the proposed algorithm.