Evolving and adaptive strategies for consensus and synchronization of multi-agent systems

We investigate evolving and adaptive strategies, in network of dynamical agents, for solving general types of consensus and synchronization. First, we analyse the problem of max/min consensus in directed networks of integrators. Extending edge snapping method with a three-well potential, we are able to show the effectiveness of our strategy to achieve general types of consensus, different from the average. Theoretical results are validated via a number of numerical examples. Then we move to synchronization of coupled non identical oscillators. We design an evolutionary strategy for network synchronization. Our results suggest that heterogeneity is the driving force determining the evolution of state-dependent functional networks. Minimal emergent networks show enhanced synchronization properties and high levels of degree-frequency assortativity. We analyse networks of N = 100 and N = 1000 Kuramoto oscillators showing that hubs in the network tend to emerge as nodes' heterogeneity is increased. Finally, we study synchronization of multi-agent systems from a contraction theory viewpoint. Contraction theory is a useful tool to study convergence of dynamical systems and networks, recently proposed in the literature. In detail, we recall three strategies: virtual systems method, convergence to a flow-invariant subspace and hierarchical approach. While the former is simple to apply, the latter is suited for larger networks.