A Robust Finite-Time Control for Leader-Follower Consensus for Perturbed Double Integrator Agents

This work discusses the design of a robust control strategy for leader-follower consensus of multi-agent systems for agents modelled as perturbed double integrator dynamics. The prime objective is to achieve a finite time consensus in the presence of unknown bounded external perturbations. The adopted distributed consensus protocol is based on integral sliding mode (ISM) with the nominal control as a finite-time consensus protocol. The robust control is designed using an adaptive switching term, which rejects the external disturbance. The proposed combination of these two control laws guarantees robustness while preserving the finite time consensus, and additionally, the adaptive gain relaxes the knowledge of the upper bound of disturbance. The robust stability of the closed-loop system is established using Lyapunov analysis, ensuring the fixed time convergence of the MAS with uniform boundedness. A simulation example is included to verify the theoretical results.