The existence of a solution of the controllability problem for linear integral and differential equations with restrictions

Abstract

A controlled process described by linear integral and differential equation with boundary conditions in the presence of phase and integral constraints with the limited control resources is considered. Research of controllability of integral and differential equations is a new direction in the theory of integral and differential equations. The controllability problem that arose from the need to solve urgent problems in the field of natural sciences, medicine, economics, technical sciences sets more sophisticated problems for integral and differential equations. In the previous works, the author studied the controllability problems of the processes described by ordinary differential equations with boundary conditions in the presence of phase and integral constraints with the limited control resources. In this paper an attempt is made to extend these results to the integral and differential equations. The necessary and sufficient conditions for the controllability processes for linear integral and differential equations by non-singular transformation and construction of the general solution of a class of integral equations are obtained.