Step averaging differential inclusions with variable dimension on a finite interval (Q2407965)

In this paper, the author considers differential inclusions with variable dimension. Such differential inclusions can be attributed to impulsive differential inclusions. However, unlike ordinary impulsive systems, in this case, at the moment of impulse realization, the dimension of the system changes and the impulse connects the ends of the solution of the given system at this moment of time. Systems considered in the mathematical theory of optimal control, i.e. optimization problems with phase space change, step systems, systems with variable structure, systems with step-by-step variable dynamics, etc. can be reduced to differential inclusions with variable dimension. A stepwise averaging scheme for studying nonlinear differential inclusions of this type on a finite interval is also justified in this paper.