Affine Formation Maneuver Control of Multiagent Systems With Disturbances Based on RISE Controller

In the affine formation maneuver control for multiagent systems with a leader-follower structure, external disturbances easily cause deformation of the formation shape, thereby affecting a series of cascading reactions. Hence, robustness against disturbances in affine formation control has been a subject remaining to be determined. To address this problem, a continuous robust controller is introduced in this study, leveraging the robust integral of the sign of the error (RISE) approach, aiming to suppress external disturbances while ensuring efficient convergence speed of the system under various collective formation maneuvers determined by the leader. The controller is designed to handle two types of disturbance models: one involving general disturbances and the other considering time-delay disturbances. It consists of formation tracking terms based on stress matrices and graph theory, as well as disturbance suppression terms utilizing RISE. Sufficient conditions for the stability of affine formations under both types of disturbances are derived. By designing a Lyapunov function that integrates a class-P function, the exponential stability of the closed-loop system is rigorously demonstrated. Finally, simulation results are provided to verify the performance and effectiveness of the proposed control strategy.