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

TL;DR

This paper addresses distributed optimal consensus in multi-agent networks with single and double integrator dynamics, incorporating convex constraints, and proposes a control law with proven convergence.

Contribution

It introduces a novel distributed control law combining interior-point methods with consensus protocols for constrained multi-agent optimization.

Findings

Proposed control law guarantees convergence to the optimal consensus point.

The approach handles agents with different dynamics and convex constraints.

Lyapunov stability analysis confirms the effectiveness of the method.

Abstract

This paper fully studies distributed optimal consensus problem in non-directed 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 neighborhood set. In this setup, all agents coordinate with their neighbors to seek the consensus point that minimizes the networks global objective function. In the current paper, we consider agents with single-integrator and double-integrator dynamics. We further suppose 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 optimization algorithm with a consensus protocol and propose a distributed control law. The associated convergence analysis based on Lyapunov stability analysis is provided.