In this paper we investigate the control of leader-follower swarms with time-varying objective functions and under balanced communication topologies. Motivated by shared control strategies for centralized systems, we formulate a control framework for distributed systems in which a leader agent and follower agents are interconnected via virtual cohesive forces in a balanced directed network, and the influence of the leader on the follower agents is regulated through time-varying inter-agent coupling dynamics. For such multi-agent systems, we investigate the stability under the proposed control framework and establish a connection between the bounds on the time-varying coupling and the ultimate swarm size. These results are obtained by studying the algebraic connectivity properties of the underlying weighted communication graph of the multi-agent system. Next, the application of our results to systems with switching communication topologies are discussed, with examples presented in swarm cohesion maintenance and collision avoidance problems. The theoretical results developed in this work are verified through numerical simulations.
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