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Multiscale singularly perturbed control systems: Limit occupational measures sets and averaging. (English) Zbl 1027.34071

The authors develop an averaging technique for nonlinear multiscale singularly perturbed control systems. They also discuss the issues concerning the existence and structures of limit occupational measures sets generated by these systems. General results and special cases are provided.

MSC:

34H05 Control problems involving ordinary differential equations
34C29 Averaging method for ordinary differential equations
34E13 Multiple scale methods for ordinary differential equations
93C70 Time-scale analysis and singular perturbations in control/observation systems
34E15 Singular perturbations for ordinary differential equations
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