An Optimal Cooperative Control Design for State Consensus of Periodic Multiagent Systems

The problem of cooperative optimal control of multiagent systems with linear periodic continuous-time dynamics is considered. The state consensus problem is formulated as an optimal control problem in which the consensus requirement is reflected in the cost. The cost optimization of each subsystem is considered over finite horizon while the states of the agents converge to a common value, with a control signal that depends on the interactions of the neighboring subsystems. The proposed control law consists of a local and regional terms to capture local measurements and measurements due to interactions with the neighboring agents, respectively. These two terms are obtained by solving a Hamilton-Jacobi-Bellman partial differential equation. A numerical example is presented to demonstrate the effectiveness of the proposed method