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Bang-bang controls in the singular perturbations limit. (English) Zbl 1167.49316

Summary: A general form of the dynamics obtained as a limit of trajectories of singularly perturbed linear control systems is presented. The limit trajectories are described in terms of probability measure-valued maps. This allows to determine the extent to which the bang-bang principle for linear control systems is carried over to the singular limit.

MSC:

49K40 Sensitivity, stability, well-posedness
93E20 Optimal stochastic control
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
93C70 Time-scale analysis and singular perturbations in control/observation systems
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