Consensus control for multi-agent systems with distributed parameter models

This paper addresses the consensus control problem for a class of multi-agent systems with distributed parameter models, and all the agents in the considered systems are governed by the one-dimensional parabolic equations or the one-dimensional second-order hyperbolic equations. The main contribution of this paper is to apply Lyapunov functional approach to the multi-agent systems with distributed parameter models, and solve the consensus control problem of such multi-agent systems on an appropriate Sobolev space. The distributed consensus-based feedback control protocols are obtained based on the virtual leader approach, and when the feedback control laws are applied to the systems, consensus on L2(0, 1) space (corresponding to the parabolic equations) or on W1, 2(0, 1) × L2(0, 1) space (corresponding to the hyperbolic equations) is achieved for all the directed communication graphs with spanning trees. Simulation examples illustrate the effectiveness of the proposed method.