Reachable Set Estimation of Multiagent Systems: An Approximate Consensus Perspective

Abstract

This paper is concerned with the estimation of reachable set for leaderless multi-agent systems (MASs) under fixed topology with bounded disturbances and nonzero initial conditions. In-neighbors' information is collected to design the protocol such that all agents' state trajectories are constrained within a compact set, and asymptotic consistency is regulated for disturbance-free MASs in the exponential stability sense while approximate consistency is regulated for noise-disturbed MASs in the input-to-state stability sense. The agreement dynamics are characterized by the consensus function with determined initial condition, whose estimated reachable set has non-empty intersection with that of MAS. The analytical framework is also applied to Markovian topology switching subject to completely and partially known transition rates, respectively. Numerical simulations confirm the theoretical results.