Average Consensus with Prescribed Performance Guarantees for Multi-agent Double-Integrator Systems

Abstract: The problem of consensus reaching with prescribed transient behaviour for a group of agents with dynamics described by a double integrator model is addressed. In order to achieve prescribed performance we employ an appropriately designed transformation of the output error, that reects performance speci- cations such as minimum speed of convergence, maximum allowed overshoot and steady state error. Assuming that the information exchange is described by a static communication network, we initially impose time-dependent constraints on the relative positions between neighbouring agents and we design a distributed control law consisting of a proportional term of the transformed error through a transformation related gain and an additional damping term depending on the agent's absolute velocity. Also a second controller is proposed that utilizes the relative velocities between agents that exchange information instead of the absolute velocities. Furthermore, we design a controller that can additionally achieve prescribed performance for the velocity error by imposing time-dependent constraints for a combined error, linear combination of the relative positions and velocities. In this case, the distributed controller has the same structure of the rst one enriched with term proportional to the transformed combined error with time variant gains. Under a sucient condition for the damping gains, the proposed nonlinear time-dependent controllers guarantee that the predened constraints are not violated and that consensus is achieved with a convergence rate independent of the topology of the communication network. Furthermore, connectivity maintenance can be ensured by appropriately designing the performance bounds. Theoretical results are supported by simulations.