On Nonlinear Control Systems with Multiple Time Scales
Journal of Dynamical and Control Systems
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We describe the limit behavior of admissible trajectories in a singularly perturbed control system as the small parameter tends to zero. A general case is considered where, in the limit, the fast motion may infinitely rapidly oscillate in time. Invariant measures of the parameterized fast flow are employed to describe the limit behavior and construct the limit control problem. The notion of relatively slow controls is introduced. Approximating properties of the limit problem within the families of relatively slow controls are verified. The results are illustrated by examples.