Plotnikov A. Research of dynamic systems with variable dimensionality

The systems of variable dimension of linear differential inclusions, linear and nonlinear differential inclusions of variable dimension, and controlled systems of variable dimension of linear differential equations are considered. The properties of solutions of such systems are obtained: the conditions for the existence of solutions and their properties. For controlled systems of variable dimension, the Mayer problem is considered and necessary and sufficient conditions for optimality are obtained. For all types of systems, the possibility of using complete and step-by-step averaging schemes is justified.