Optimality conditions in problems of control over systems of impulsive differential equations with nonlocal boundary conditions

Existence and uniqueness of the solutions to impulsive nonlinear integro-differential equations with nonlocal boundary conditions

“…Today, there exist a great number of works devoted to ordinary impulsive differential and integro-differential equations with nonlocal boundary conditions in which the theorem on the existence of solutions are proved for different types of nonlocal conditions [3][4][5][6][7][8]11,13,[18][19][20][21][22].…”

Necessary optimality condition for the singular controls in an optimal control problem with nonlocal conditions

“…In spite of the theory of necessary optimality conditions of higher order, while the theory of singular controls has been developed completely for the control problems described by the systems with local conditions [3,5,6,12,13], the study of optimal problems with nonlocal conditions has recently started [1,2,4,[7][8][9][10][11]14]. Now we shall note some earlier works in this direction.…”

Pontryagin’s Maximum Principle for the Optimal Control Problems with Multipoint Boundary Conditions

“…Originally the maximum principle was proved for the Cauchy system of ordinary differential equations [12]. Later on this result was carried over the most complex objects described by the equations with a delay, integral equations, partial equations, stochastic equations, and so forth (see, e.g., [13,14] and the references therein).…”

“…Recently, the optimal control problems with nonlocal conditions are intensively investigated. In the papers [13,[20][21][22][23][24] the necessary optimality conditions for optimal control problems described by the systems of ordinary differential equations with nonlocal conditions were obtained. In these papers the nonlocal conditions contain two-point and integral boundary conditions.…”