An Open-loop criterion for the solvability of a closed-loop guidance problem with incomplete information: Linear control systems

Constructing a strategy for the guaranteed positioning guidance of a linear controlled system with incomplete data

“…We introduce the function (3) According to the results of [7], note that there exists the equality Theorem 1 [7,Theorem 2]. Each of the expanded software guidance, package guidance, and guaranteed positioning guidance problems can be solved when and only when (4) In this formulation of the theorem, ᏸ is an arbitrary set in expanded phase space n that has the fol lowing property: For an arbitrary family of vectors ∈ n such that = 1, λ and , λ ≥ > 0 exist such that ∈ ᏸ.…”

“…Let us therefore focus on the derivation of the last problem. To describe the packages, we shall use the terminology of [7].…”

“…It is devoted to producing a software package method [5][6][7] as a tool for analyzing guaranteeing position ing control problems with incomplete data on the states of a controlled system. The heart of the method lies in its statement of the equivalence of guaranteeing control problems in the positioning strategy and software package classes.…”

A guaranteed control problem for a linear stochastic differential equation

“…The method tested on the guidance problems under incomplete information for linear controlled systems of ODEs consists in reducing the problems of guaranteed control formulated in the class of closed-loop strategies to equivalent problems in the class of open-loop control packages. The latter class contains the families of open-loop controls parameterized by admissible initial states and possessing the property of nonanticipation with respect to the dynamics of observations [5][6][7].…”

“…By the equations of the method of moments [8,9], the problem for the SDE is reduced to an equivalent problem for systems of ODEs describing the mathematical expectation and covariance matrix of the original process. The technique of the method of open-loop control packages developed in [5][6][7] is applied to the systems obtained.…”