Optimal consensus control models on the sphere

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.

Keywords

• Optimal control
• Swarm sphere model
• Aggregation
• Synchronization
• Pontryagin Minimum Principle