Singularly perturbed problems with multi-tempo fast variables

The article contains a survey of publications studying problems characterized by the presence of fast variables with various rates of change (time scales). We consider the passage to the limit from the solution of a perturbed problem to the solution of a degenerate one, asymptotic solutions of initial and boundary value problems, stability and controllability, asymptotic solutions of optimal control problems, and problems with “hidden” multi-tempo variables. In addition, problems with control constraints, game problems, and stochastic systems are given. The last section presents practical problems with multi-tempo fast motions.