Optimal consensus control models on the sphere

TL;DR

This paper studies optimal control strategies for consensus problems on the sphere, considering both first and second order systems, and demonstrates their effectiveness through simulations.

Contribution

It introduces the existence of optimal control-trajectory pairs and derives first order optimality conditions for consensus models on the sphere.

Findings

Optimal control accelerates consensus formation.

Existence of optimal control-trajectory pairs established.

First order optimality conditions derived using Pontryagin Minimum Principle.

Abstract

In this paper, we investigate the consensus models on the sphere with control signals, where both the first and second order systems are considered. We provide the existence of the optimal control-trajectory pair and derive the first order optimality condition taking the form of the Pontryagin Minimum Principle. Numeric simulations are also presented to show that the obtained optimal control can help to accelerate the process of reaching a consensus.