N. Strelkovskii

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

The method of open-loop control packages is a tool for stating the solvability of guaranteed closed-loop control problems under incomplete information on the observed states. In this paper, a solution method is specified for the problem of guaranteed closed-loop guidance of a linear control system to a convex target set at a prescribed point in time. It is assumed that the observed signal on the system’s states is linear and the set of its admissible initial states is finite. It is proved that the problem under consideration is equivalent to the problem of open-loop guidance of an extended linear control system to an extended convex target set. Using a separation theorem for convex sets, we derive a solvability criterion, which reduces to solving a finite-dimensional optimization problem. An illustrative example is considered.

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

The development of the software package method created by Yu.S. Osipov and A.V. Kryazhimskii for the problem of guaranteed positioning guidance on a closed convex target set is considered at a given time for a linear controlled system. The observed signal of the system state is linear; its set of acceptable initial states is assumed to be finite. An algorithm for constructing the guidance package and the corresponding guidance positioning strategy is described structurally using the stated equivalence of the guaranteed positioning, package, and expanded program guidance problems.

Algorithm for Constructing a Guaranteeing Program Package in a Control Problem with Incomplete Information

A package control problem is considered for a target set at a moment of time. The dynamic system under control is described by linear differential equations, the control area is a convex compact, and the target set is convex and closed. A version of the subsequent approximations method in extended space is proposed for constructing elements of a guaranteeing program package in the case of regular clusters.