Velocity-free distributed coordinated optimal control for second-order multi-agent systems

This paper solves the coordinated optimal consensus problem for second-order multi-agent systems without velocity information from the distributed perspective. Particularly, all the agents are driven towards a consensus at an optimal solution inside the intersection of multiple feasible sets that minimizes a global target function aggregated by a group of convex local ones. Each local target function is exclusively assigned to a respective agent. Also, each feasible set constructed by inequality and set constraints privately belongs to a respective agent. Resorting to a novel auxiliary dynamics, a velocity-free distributed coordinated optimal control strategy is proposed without relying on global topology information. Using convex theory under the Lyapunov framework, it is demonstrated that the concerned coordinated optimal control objective is fulfilled by implementing the proposed distributed control strategy despite no velocity information. Examples are finally given to confirm the control effectiveness.