Optimal Output Consensus of Heterogeneous Linear Multi-Agent Systems Over Weight-Unbalanced Directed Networks

TL;DR

This paper presents a new distributed control method for heterogeneous linear multi-agent systems over unbalanced directed networks, ensuring their outputs reach the optimal solution of a global cost function with exponential convergence.

Contribution

It introduces a novel continuous-time state feedback controller and extends it to an observer-based output feedback scheme for optimal output consensus.

Findings

Exponential convergence of the multi-agent system to the optimal output.

Effectiveness demonstrated through two illustrative examples.

Applicable under strongly connected unbalanced directed networks.

Abstract

This paper investigates the distributed optimal output consensus problem of heterogeneous linear multi-agent systems over weight-unbalanced directed networks. A novel distributed continuous-time state feedback controller is proposed to steer the outputs of all the agents to converge to the optimal solution of the global cost function. Under the standard condition that the unbalanced digraph is strongly connected and the local cost functions are strongly convex with global Lipschitz gradients, the exponential convergence of the closed-loop multi-agent system is established. Then, the proposed state feedback control law is extended to an observer-based output feedback setting. Two examples are finally provided to illustrate the effectiveness of the proposed control schemes.