Output Consensus of Multiagent Systems Based on PDEs With Input Constraint: A Boundary Control Approach

There are few results concerning consensus of multiagent systems (MASs) based on partial differential equations (PDEs), and the problem of how to act boundary control based on distributed measurement on spatial boundary points of MASs has not been solved. This paper addresses boundary control based on distributed measurement for output consensus of leader-following directed MASs modeled by parabolic PDEs. First, a boundary controller acting on spatial boundary points is designed by considering the delivered information produced by agents communicating with neighborhoods. Without considering input constraint, the Lyapunov's direct method is used to obtain a sufficient condition on the existence of the boundary controller to achieve output consensus. The condition is expressed as a form of the feasibility of LMIs. After that, the whole input constraint for MASs is given. And then, one more condition on control gains is obtained to ensure the existence of the boundary controller with input constraint. Finally, one numerical example with two cases illustrates the theoretical analysis results.