The dynamic coverage problem is increasingly found in a wide variety of areas, for example, from the development of mobile sensor networks, to the analysis of clustering in spatio-temporal dynamics of brain signals. In this paper, we apply control-theoretic methods to locate and track cluster center dynamics and show that dynamic control design is necessary to achieve dynamic coverage of mobile objects under acceleration fields. This is the first work to consider tracking cluster centers when site dynamics involve accelerations. We focus on the relationship between the objective of maximizing coverage in real-time and the Maximum Entropy Principle, and develop the ability to identify inherent cluster dynamics in a dataset. Algorithms are presented that guarantee asymptotic tracking of cluster centers, and for which we prove continuity and boundedness of the corresponding control laws. Simulations are provided to corroborate these results.