Optimal Consensus Seeking in a Network of Multiagent Systems: An LMI Approach

In this paper, an optimal control design strategy for guaranteeing consensus achievement in a network of multiagent systems is developed. Minimization of a global cost function for the entire network guarantees a stable consensus with an optimal control effort. In solving the optimization problem, it is shown that the solution of the Riccati equation cannot guarantee consensus achievement. Therefore, a linear-matrix-inequality (LMI) formulation of the problem is used to address the optimization problem and to simultaneously resolve the consensus achievement constraint. Moreover, by invoking an LMI formulation, a semidecentralized controller structure that is based on the neighboring sets, i.e., the network underlying graph, can be imposed as an additional constraint. Consequently, the only information that each controller requires is the one that it receives from agents in its neighboring set. The global cost function formulation provides a deeper understanding and insight into the optimal system performance that would result from the global solution of the entire network of multiagent systems. Simulation results are presented to illustrate the capabilities and characteristics of our proposed multiagent team in achieving consensus.