On delay-dependent stability of a swarm of networked autonomous vehicles under communication constraints

This paper focuses on the delay-dependent global stability analysis for a swarm of cooperating networked autonomous vehicles modeled using functional differential equations. The cohesiveness of the swarm under realistic communication constraints such as different communication channel delays and dynamically changing communication topology is the main stability property that we are concerned with. Under these constraints, it cannot be guaranteed that the swarm members will converge to an invariant set of equilibrium points, i.e. the configuration of the swarm members converges to a constant arrangement. The novelty of the result lies in the construction of an appropriate Lyapunov-Krasovskii functional and use of Lyapunov-LaSalle invariance theorem in the context of delay differential equations that when combined produce sufficient conditions which guarantee satisfactory performance of swarm dynamics under communication constraints. An explicit bound on communication delay in dynamically changing communication network topology is obtained to ensure stability of the swarm. These conditions are then used to design stable decentralized motion guidance laws for a swarm of networked vehicles.