Distributed formation control for port-Hamiltonian multi-agent systems by average state estimation

In recent years, propelled by the rapid development of information technology and the Internet, the formation control of multi-agent systems has gradually emerged as a research hotspot. This paper focuses on the formation control problem of multi-agent mechanical systems with port-Hamiltonian (PH) dynamics. Firstly, the formation problem is converted into an optimization problem whose solution meets the formation requirements. Subsequently, in order to guide the closed-loop system to converge to the solution of this optimization problem, we propose two distributed controllers. The first controller is designed for multi-agent systems where the formation output is defined by position. Notably, this controller preserves the PH structure in the closed-loop, which simplifies the selection of candidate Lyapunov functions for proving the asymptotic convergence of the system to the desired formation. To characterize the minimum convergence rate of the closed-loop system, the second controller is proposed. Based on this controller, the exponential stability and the minimum convergence rate of the closed-loop system are provided. Additionally, these controllers only require agents to exchange estimations of the average state with their neighbors, thereby protecting the privacy of their state and value function information. Finally, the effectiveness of these controllers is verified through an application case on nonholonomic wheeled robots.