Consensus of double-integrator multi-agent systems without relative states derivative under relative-state dependent measurement noises*

This paper proposes a consensus protocol for continuous-time double-integrator multi-agent systems under noisy communication in directed topologies. Each agent’s control input relies on its own velocity and the relative positions with neighbours; it does not require the relative velocities. The agent receives its neighbours’ positions information corrupted by time-varying measurement noises whose intensities are proportional to the absolute relative distance that separates the agent from the neighbours. The consensus protocol is mainly based on the velocity damping gain to derive conditions under which the unbiased mean square χ-consensus is achieved in directed fixed topologies, and the unbiased mean square average consensus is achieved in directed switching topologies. The mean square state errors are quantified for both the positions and velocities. Finally, to illustrate the approach presented, some numerical simulations are performed.