On linear-quadratic optimal control problems for time-varying descriptor systems

Abstract

The solvability of a linear-quadratic optimal control problem in a Hilbert space for time-varying descriptor systems is established under some conditions. Unlike previous works of other authors that are devoted to time-invariant descriptor systems in the finite-dimensional case we do not use the regularity of the pencil of the operators from the state equation, the factorability of the operator from the cost functional, and also the reduction of the operator preceding the derivative to a diagonal form.