Constrained Optimal Consensus in Multi-agent Systems with First and Second Order Dynamics

摘要

This paper fully studies distributed optimal consensus problem innon-directed dynamical networks. We consider a group of networked agents thatare supposed to rendezvous at the optimal point of a collective convexobjective function. Each agent has no knowledge about the global objectivefunction and only has access to its own local objective function, which is aportion of the global one, and states information of agents within itsneighborhood set. In this setup, all agents coordinate with their neighbors toseek the consensus point that minimizes the networks global objective function.In the current paper, we consider agents with single-integrator anddouble-integrator dynamics. We further suppose that agents movements arelimited by some convex inequality constraints. In order to find the optimalconsensus point under the described scenario, we combine the interior-pointoptimization algorithm with a consensus protocol and propose a distributedcontrol law. The associated convergence analysis based on Lyapunov stabilityanalysis is provided.