Singularly Perturbed Algorithms for Velocity Consensus and Shape Control of Single Integrator Multi-Agent Systems

This paper studies a distributed multi-agent control problem in which the agents have single-integrator dynamics. A distributed control law is proposed to drive the agents to attain a desired formation shape and acquire an identical velocity. Using singular perturbation theory and stability results for nonlinear cascade systems, it is shown that agents can achieve the desired formation shape and velocity at different time scales. Moreover, it is shown that there exists an upper bound for a time-scale parameter (perturbation parameter) in the control law such that for time-scale parameters less than this bound, the initial conditions of the shape control error system will remain in a stability basin of the equilibrium. Simulation results are provided to validate the proposed algorithm.