Dynamic coverage is one of the fundamental problems in multi-agent systems (MASs), and is related to optimal placement of nodes to observe a physical space. In a typical coverage problem, a set of targets are required to be monitored. The problem becomes more challenging when the targets are allowed to move as well. Efficient coverage control by mobile agents in a specific area poses many challenges, such as optimal coverage of all targets, dynamic redeployment of agents as targets change their location, trajectory control of each agent during redeployment and determining the number of mobile agents to cover specific targets. In particular, for dynamic coverage problems, agents are deployed to provide coverage to the mobile targets and the agents dynamically redeploy themselves in such a way that they provide maximum coverage to targets not only when they are stationary but also when they are in motion. In many scenarios, such as disaster recovery or public event coverage, dynamic behavior of agents to reach to the next optimal position, plays an important role in determining the performance of the system. In this paper, we propose an augmented Lagrangian based algorithm, which provides a mechanism to control the trajectory of agents to reach the optimal position. By adjusting the gain parameters of the proposed algorithm, we achieve negligible overshoot in response to fast dynamics that is not possible by using conventional Lagrangian. Also, the proposed algorithm is close to the optimal trajectory. Thus, by using the proposed algorithm, we can improve the dynamic performance without compromising the optimal deployment of the agents. The numerical evaluation results show significant improvement in dynamic performance for an example scenario of an MAS.INDEX TERMS Distributed optimization, multi agent dynamical system, optimal coverage problem, optimized transient control, tracking trajectory.