Overview of V.A. Plotnikov’s research on averaging of differential inclusions

In this review, we will first look in detail at Plotnikov’s results on the substantiation of full and partial schemes of averaging of differential inclusions of the standard form on finite and infinite intervals. Then we will consider the algorithms where it is not possible to find the average, but there is a possibility to find its estimation from below and from above. Such an approach is also used when the average can be found only approximately. This situation is common for differential inclusions with fast and slow variables. In the end, we will present the results on the substantiation of the full and partial averaging methods for impulsive differential inclusions on finite and infinite intervals.