Higher Order Barrier Certificates for Leader–Follower Multiagent Systems

Abstract

This paper presents control strategies based on time-varying convergent higher order control barrier functions for a class of leader-follower multi-agent systems under signal temporal logic (STL) tasks. Each agent is assigned a local STL task which may be dependent on the behavior of agents involved in other tasks. We consider one or more than one leader in the multi-agent system. The leader has knowledge on the associated tasks and controls the performance of the subgroup involved agents. The followers are not aware of the tasks, and do not have any control authority to reach them. They follow the leader commands indirectly, according to their dynamics interconnections, for the task satisfaction. We further assume that the input-to-state stability (ISS) property for the multi-agent system is fulfilled. First, robust solutions for the task satisfaction, based on the leader's accessibility to the follower agents' states are suggested. In addition, using the notion of higher order barrier functions, individual barrier certificates for each agent evolving in a formation dynamic structure are proposed. For the case of presence of more leaders in the subgroups, we provide decentralized barrier certificates. Our approach finds solutions to guarantee the satisfaction of STL tasks independent of the agents' initial conditions.