Finite-time Consensus for Second-order Multi-agent Systems with State Constraints

This study addresses the finite-time consensus issue within second-order multi-agent systems subjected to state constraints. By leveraging an undirected graph, a distributed constrained controller is formulated by amalgamating the homogeneous system approach with a penalty mechanism. Leveraging the principles of homogeneous system theory, we establish that consensus among the constrained states of multi-agent systems can be attained within a finite time frame. Furthermore, through a contradiction argument, our analysis demonstrates that system states consistently adhere to the imposed constraints with the introduction of the penalty mechanism. Finally, to validate the efficacy of the proposed control strategy, a numerical simulation is conducted.