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The problem of consensus reaching with prescribed transient behavior for a group of double-integrator agents is addressed. The information exchange of the multi-agent system is described by a static communication network. We initially set time-dependent constraints on the transient response of the relative positions between neighboring agents and we propose a distributed control law consisting of a proportional term of the transformed error and an additional damping term based on absolute velocities measurements. We also design an agreement protocol that can additionally achieve prescribed performance for a combined error of positions and velocities. Under a sufficient condition for the damping gains, the proposed nonlinear time-dependent distributed controllers guarantee that the predefined constraints are not violated and that consensus is achieved with a convergence rate independent of the underlying communication graph. Furthermore, connectivity maintenance can be ensured by appropriately designing the performance bounds. Theoretical results are supported by simulations.
Macellari et al. (Wed,) studied this question.