Saturation-tolerant average consensus with controllable rates of convergence

This paper considers the static average consensus problem for a multi-agent system and proposes a distributed algorithm that enables individual agents to set their own rate of convergence. The algorithm has a two-time scale structure and is constructed using a singular perturbation approach. A fast information processing state uses a Laplacian consensus strategy to calculate the agreement value in a distributed manner. The slow-time dynamic part, termed motion phase, allows each agent to move towards the agreement point at its own desired speed. We provide a complete analysis of the proposed consensus algorithm. This covers the rate of convergence of individual agents, effects of communication delays, robustness to changes in the network topology, implementation in discrete time, and performance guarantees under limited control authority. Our analysis is based on tools from matrix theory, algebraic graph theory and stability analysis. Numerical examples illustrate the benefits of the proposed algorithm.