Singular linear-quadratic problem with a terminal condition

Abstract

A singular linear-quadratic optimization problem with a terminal condition is considered. This problem in the space of absolutely continuous functions has no solutions. To ensure the existence of a solution, it is necessary to extend the set of admissible controls. In the case under consideration, we consider the generalized derivatives of functions of bounded variation as admissible controls. As a result, valid controls may contain impulse components. Under some assumptions, an optimal control is constructed containing impulse components at the initial and final instants of time. An illustrative example is provided. © 2021 Author(s).