Constrained optimal consensus in multi-agent systems with single- and double-integrator dynamics

This paper fully studies distributed optimal consensus problem in undirected dynamical networks. We consider a group of networked agents that are supposed to rendezvous at the optimal point of a collective convex objective function. Each agent has no knowledge about the global objective function and only has access to its own local objective function, which is a portion of the global one, and states information of agents within its neighbourhood set. In this setup, all agents coordinate with their neighbours to seek the consensus point that minimises the network's global objective function. In the current paper, we consider agents with single-integrator and double-integrator dynamics. Further, it is supposed that agents' movements are limited by some convex inequality constraints. In order to find the optimal consensus point under the described scenario, we combine the interior-point optimisation algorithm with a consensus protocol and propose a distributed control law. The associated convergence analysis based on Lyapunov stability analysis is provided.