In this paper, we develop decentralized control to drive a swarm of mobile agents into a moving target region while avoiding collisions among themselves. This is achieved with the help of target potential functions and collision avoidance potential functions in Lyapunov synthesis. A basic control framework is designed on a kinematic model. There are neither requirements for pre-specified desired trajectories outside the target region nor desired pinpoint positions inside the target region . The framework docs not depend on a fixed ordering of agents, and thus, flexibility is improved. Simulation results illustrate the performance of the proposed approach.