On linear-quadratic optimal transition in synchronization of homogeneous multi-agent systems

Abstract

Abstract In this paper, a new approach for the optimal synchronization of homogeneous multi-agent systems is presented. In contrast to existing approaches, we offer an intuitive cost for the transition of each agent to a common synchronization trajectory, which facilitates tuning of the cost weights. The introduced LQ optimal tracking problem is solved by reducing it to a LQ regulator problem. By choosing a linear parameterization of the synchronization trajectory, we enable the distributed implementation of the optimal synchronization controller. We give examples how such a parameterization can be chosen and how it influences the required communication between the agents. Furthermore, we derive an optimal communication topology that minimizes the weighted sum of all agents’ transition costs. Finally, we demonstrate our results in a simulation example.