A frequency criterion for the existence of an optimal control for Ito equations

TL;DR

This paper establishes a frequency-based criterion for the existence of optimal controls in linear Ito equations, linking stochastic control problems to deterministic quadratic optimization.

Contribution

It introduces a necessary and sufficient frequency inequality condition for optimal control existence in linear Ito equations, bridging stochastic and deterministic control methods.

Findings

Frequency inequalities characterize optimal control existence.

Optimal controls can be derived from linear-quadratic deterministic problems.

The approach provides a clear criterion for control design in stochastic systems.

Abstract

The following optimization problem is considered. For a linear vector Ito equation. it is required to find an optimal deterministic control vector which minimizes a quadratic the functional. A necessary and sufficient condition for the existence of a optimal control are formulated in the form of frequency inequalities. It is shown that an optimal control can be found by solving a certain linear-quadratic deterministic optimization problem.