Universal regulators for optimal tracking of polyharmonic signals in systems with delays

摘要

This paper addresses an optimal control problem under uncertainty. As a rule, the optimal process in such problems depends on unknown parameters and cannot be determined beforehand. For this reason, instead of determining an optimal process, we search for a feedback operator that transfers the system's outputs to control actions such that it does not depend on the unknown parameters and yields an optimal process for all parameter values. According to the nomenclature adopted in [1-7] such an operator is called an optimal universal regulator1 (OUR) (in the given class of parameters). As in [1-5], the existence of an OUR in the linear-quadratic optimal tracking problem (and more general problems) is analyzed in the presence of an external disturbance in the system. It is assumed that the reference signal and the external disturbance are polyharmonic functions with a known spectrum but unknown amplitudes. In contrast to [1-5], we consider systems with delays. Conditions for the existence of an OUR in the problem are obtained, and it is shown that such a regulator can be chosen as linear. The entire set of linear OURs is described.