Optimal output consensus for linear systems: A topology free approach

TL;DR

This paper presents a topology-free optimal control approach for finite and infinite time consensus in homogeneous linear systems, providing explicit feedback laws without relying on communication graph constraints.

Contribution

It introduces a novel topology-free solution for optimal output consensus in linear systems, applicable to both finite and infinite time horizons, with explicit feedback control laws.

Findings

Solution is topology-free and explicit for finite time consensus.

Induces a complete communication graph topology.

Extends to infinite time horizon consensus problems.

Abstract

In this paper, for any homogeneous system of agents with linear continuous time dynamics, we formulate an optimal control problem. In this problem a convex cost functional of the control signals of the agents shall be minimized, while the outputs of the agents shall coincide at some given finite time. This is an instance of the rendezvous or finite time consensus problem. We solve this problem without any constraints on the communication topology and provide a solution as an explicit feedback control law for the case when the dynamics of the agents is output controllable. It turns out that the communication graph topology induced by the solution is complete. Based on this solution for the finite time consensus problem, we provide a solution to the case of infinite time horizon. Furthermore, we investigate under what circumstances it is possible to express the controller as a feedback control law of the output instead of the states.