# Integral representations in the theory of controlled systems

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## Abstract

We consider methods of analysis of controlled dynamical systems based on integral representations: the transition of the system from one admissible state to another is associated with some integral transformations of the configuration space. The main focus is on transforms with respect to integration over the Euler characteristic, which make it possible to study the topological properties of systems. An analog of the Gauss-Ostrogradskii theorem is proved for integration over the Euler characteristic.

## Keywords

Singular Point Maximum Principle Optimal Control Problem Integral Representation Support Function
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