Near-Optimal Control Strategy in Leader-Follower Networks: A Case Study for Linear Quadratic Mean-Field Teams

TL;DR

This paper presents a decentralized control strategy for leader-follower networks that is near-optimal, scalable, and can be computed in a distributed manner, effectively managing communication and energy costs in large multi-agent systems.

Contribution

It introduces a near-optimal control scheme for linear quadratic leader-follower networks with minimal communication links, scalable to large systems, and computationally efficient.

Findings

The control strategy converges to the optimal as followers increase.

The approach requires only one Riccati equation for the leader and two for each follower.

Numerical examples validate the effectiveness of the proposed method.

Abstract

In this paper, a decentralized stochastic control system consisting of one leader and many homogeneous followers is studied. The leader and followers are coupled in both dynamics and cost, where the dynamics are linear and the cost function is quadratic in the states and actions of the leader and followers. The objective of the leader and followers is to reach consensus while minimizing their communication and energy costs. The leader knows its local state and each follower knows its local state and the state of the leader. The number of required links to implement this decentralized information structure is equal to the number of followers, which is the minimum number of links for a communication graph to be connected. In the special case of leaderless, no link is required among followers, i.e., the communication graph is not even connected. We propose a near-optimal control strategy that converges to the optimal solution as the number of followers increases. One of the salient features of the proposed solution is that it provides a design scheme, where the convergence rate \edit{as well as} the collective behavior of the followers can be designed by choosing appropriate cost functions. In addition, the computational complexity of the proposed solution does not depend on the number of followers. Furthermore, the proposed strategy can be computed in a distributed manner, where the leader solves one Riccati equation and each follower solves two Riccati equations to calculate their strategies. Two numerical examples are provided to demonstrate the effectiveness of the results in the control of multi-agent systems.