Optimal Connectivity during Multi-agent Consensus Dynamics via Model Predictive Control

In this paper, we solve an optimal consensus control problem of maximizing the state-dependent communication connectivity during a multi-agent consensus dynamics. A proportional-derivative type consensus controller is leveraged to drive agents into a symmetric formation. The asymptotic stability of the closed-loop system dynamics is established using Lyapunov theory, which helps us to deduce an intuitive time-varying gain profile based on a sufficient condition for convergence. Further, a Model Predictive Control approach is adopted to minimize a quadratic cost over a finite prediction horizon by adjusting the controller gains, such that the optimal connectivity is attained on the way with less control efforts, while handling constraints to agents’ states, inputs, turn-rates and disturbances injected into agent velocities. Simulation results with time-varying controller gains demonstrate the impact of our proposed technique.