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In this paper, a decentralized stochastic control system consisting of oneleader and many homogeneous followers is studied. The leader and followers arecoupled in both dynamics and cost, where the dynamics are linear and the costfunction is quadratic in the states and actions of the leader and followers.The objective of the leader and followers is to reach consensus whileminimizing their communication and energy costs. The leader knows its localstate and each follower knows its local state and the state of the leader. Thenumber of required links to implement this decentralized information structureis equal to the number of followers, which is the minimum number of links for acommunication graph to be connected. In the special case of leaderless, no linkis required among followers, i.e., the communication graph is not evenconnected. We propose a near-optimal control strategy that converges to theoptimal solution as the number of followers increases. One of the salientfeatures of the proposed solution is that it provides a design scheme, wherethe convergence rate \edit{as well as} the collective behavior of the followerscan be designed by choosing appropriate cost functions. In addition, thecomputational complexity of the proposed solution does not depend on the numberof followers. Furthermore, the proposed strategy can be computed in adistributed manner, where the leader solves one Riccati equation and eachfollower solves two Riccati equations to calculate their strategies. Twonumerical examples are provided to demonstrate the effectiveness of the resultsin the control of multi-agent systems.

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