Linear-Quadratic Discrete Optimal Control Problems for Descriptor Systems in Hilbert Space

The solvability of the linear-quadratic discrete optimal control problem is established for descriptor systems with variable coefficients in a Hilbert space. The basic result is the theorem on reducing the implicit discrete system, following from the control optimality condition, to the explicit nonnegative standard Hamiltonian system, for which the necessary two-point boundary value problem has a unique solution. The regularity of the pencil of the operators from the state equation and the causality of considered systems are not required here.