Multiplex PID Consensus for Single Integrator Agents

In this paper, we propose a multiplex proportional-integral-differential(PID) algorithm to achieve a leader following consensus of multi-agent systems, where the agents are modeled by a single integrator with input saturation and disturbances. The P, I, and D controllers are designed to be composed of different networks. Then, we investigate the conditions of communication graphs and control gains to achieve the consensus, and show that the communication graph of I controller only needs to be connected. Finally, we conduct simulations to reveal the effectiveness of the proposed algorithm.