Formation Control of Multiagent System Based on Higher Order Partial Differential Equations

We propose a method of controlling the formation in a multiagent system using partial differential equations (PDEs). In this method, the behavior of the entire multiagent system is modeled by second-order or higher order PDEs. We also propose a boundary controller that exponentially stabilizes the PDE model. By discretizing the PDE model under the proposed controller, the follower agents' control laws can be derived. Moreover, the boundary controller corresponds to the leader agents' control laws. The use of higher order PDEs leads to the generation of various formations that cannot be generated by using lower order PDEs. Finally, we conduct numerical simulations and experiments to validate the proposed method.