Consensus analysis of large-scale nonlinear homogeneous multi-agent formations with polynomial dynamics
For control theorists working on multi-agent systems, this provides a scalable consensus analysis method for polynomial dynamics.
The paper proposes an LMI-based method to prove consensus in large-scale nonlinear multi-agent systems with polynomial dynamics, validated on two academic examples.
Drawing inspiration from the theory of linear "decomposable systems", we provide a method, based on linear matrix inequalities (LMIs), which makes it possible to prove the convergence (or consensus) of a set of interacting agents with polynomial dynamic. We also show that the use of a generalised version of the famous Kalman-Yakubovic-Popov lemma allows the development of an LMI test whose size does not depend on the number of agents. The method is validated experimentally on two academic examples.