Quasi-singular controls in the optimal control problems described of hyperbolic integro-differential equations

Among the problems of optimal control of systems with distributed parameters, a special place is occupied by problems of optimal control described by hyperbolic integro-differential equations. The paper considers the optimal control problem described by a hyperbolic Volterra type integro-differential equation with Goursat boundary conditions. And quality functionality of the terminal type. Under the assumption that the control region is convex, using one version of the increment method, an analog of the linearized maximum condition and the general necessary optimality condition of the second order are proved. The case of quasi-singular controls is separately studied.