Formation tracking control for multi-agent systems: A wave-equation based approach

This paper considers the formation tracking control problem of large-scaled Multi-Agent Systems (MAS) for which the model is based on a system of mutually independent wave Partial Differential Equations (PDEs). The spatial derivatives in the equation correspond to the underlying communication topology of the agents. A leader-follower mode is employed in the control algorithm, with which the agents on the boundary of PDEs are chosen as leaders knowing the tracking trajectory and all the other agents are followers. Each follower has only the information of its own relative position and velocity to its topological neighbors. With a designed distributed controller, the formation tracking error is bounded by a constant proportional to the acceleration of the desired trajectory. Robustness of the control law to a perturbation in the velocity measurement is also discussed. Furthermore, some simulation studies are provided to show the effectiveness of the control algorithm.