Nesir Huseyin

Conflicts of Interest The authors declare no conflicts of interest. Data Availability Statement Data sharing is not applicable. The article describes entirely theoretical research. References 1, Functional Analysis, Sobolev Spaces and Partial Differential Equations (Springer, 2011). 2, Integral Equations and Applications (Cambridge University Press, 1991). 3, Integral Equations (J. Wiley & Sons Inc., 1973).

In this paper, the set of trajectories of the control system described by Urysohn type integral equation is considered. It is assumed that the system is nonlinear with respect to the state vector and affine with respect to the control vector. The closed ball of the space , is chosen as the set of admissible control functions. The trajectory of the system is defined as multivariable Lebesgue measurable function from the space that satisfies the system's equation almost everywhere.