PDE-based Multi-agent Deployment in 3-D Space via Bilateral Boundary control

In this paper, the problem of dynamic deployment control for a large scale multi-agent system (MAS) in 3-D space is studied. We describe collective dynamics by a pair of thermal diffusion partial differential equations (PDEs) which are defined in a 2-D symmetry plane, and this plane allows a leader-follower meshgrid communication topology of the MAS. We apply a bilateral boundary control law, so that the agents located on the upper and lower boundaries are leaders which drive the system from two sides. The H
2
exponential stability proves the stability of the system. Simulation results verify that the MAS with the bilateral control shows better performance at the settling time compared to the MAS with single boundary control.