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Using particle swarms to track and optimize dynamic systems is described. Issues related to tracking and optimizing dynamic systems are briefly reviewed. Three kinds of dynamic systems are defined for the purposes of this paper. One of them is chosen for preliminary analysis using the particle swarm on the parabolic benchmark function. Successful tracking of a 10-dimensional parabolic function with a severity of up to 1.0 is demonstrated. A number of issues related to tracking and optimizing dynamic systems with particle swarms are identified. Directions for future research and applications are suggested.