Consensus for non-linear multi-agent systems modelled by PDEs based on spatial boundary communication

There is spatio-temporal nature for many multi-agent systems such as infight hose-and-drogue aerial refuelling systems. To deal with consensus control of such cases, this study establishes a non-linear leader-following spatio-temporal multi-agent system modelled by partial differential equations. Initially, a boundary controller based on boundary coupling is studied to ensure consensus of the multi-agent system. A sufficient condition on the existence of the controller for consensus is presented in terms of linear matrix inequalities. To simplify the obtained result, a second boundary controller is studied and a simple sufficient condition of its existence is investigated. Finally, two numerical examples demonstrate the effectiveness of the proposed methods. The merits of the proposed controllers lie in making use of only spatial boundary communication and requiring actuators and sensors only at spatial boundary positions.