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

Abstract

A method of solution of the controllability problem for the processes described by linear integral and differential equations with boundary conditions in the presence of phase and integral constraints with the constraints of the control values is supposed. The origin boundary value problem is immersed to the boundary value problem of a linear differential equation by introducing the auxiliary control functions. The set of all controls are determined, each element of which translates the trajectory of the linear system from any starting point to any desired end state. This approach yields to obtain the equivalent identities and reduce the solutions of the origin boundary value problem to an initial optimal control problem. Minimizing sequences which limit points are the solutions of the controllability problem of linear integral and differential equations with restrictions are constructed. Constructiveness of the proposed method is shown in the example.