A framework for Lyapunov certificates for multi-vehicle rendezvous problems

In this paper we present a dynamical systems representation for multi-agent rendezvous on the phase plane. We restrict our attention to two agents, each with scalar dynamics. The problem of rendezvous is cast as a stabilization problem, with a set of constraints on the trajectories of the agents, defined on the phase plane. We also describe a method to generate control Lyapunov functions that when used in conjunction with a stabilizing control law, such as Sontag's formula, makes sure that the two-agent system attains rendezvous. The main result of this paper is a Lyapunov-like certificate theorem that describes a set of constraints, which when satisfied are sufficient to guarantee rendezvous.