Averaging in optimal switching control problems (Q1976464)

This paper presents two cases in optimal switching control problems: (1) the switching cost does not depend on \(\varepsilon\) and (2) the switching cost vanishes as \(\varepsilon\) tends to zero. It is proved that the value function of the original fast problem converges locally uniformly to the value function of the averaged problem in both cases. In case (1) the limit problem is a switching control problem. The limit problem in case (2) is a classical control problem and the controls are involved in averaging.