Optimal Retention of the Trajectories of a Discrete-Time Stochastic System in a Tube: One Problem Statement

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Abstract

This paper considers an optimal control problem for a time-invariant linear stochastic system with discrete time, scalar unbounded control, additive noise, and a probabilistic criterion for retaining its trajectories in a given neighborhood of zero. We use dynamic programming and two-sided Bellman function estimates to derive analytical expressions for the optimal control at two time steps and a suboptimal control on any control horizon. The effectiveness of these controls is illustrated on a numerical example.

About the authors

A. N Tarasov

Moscow Aviation Institute

Email: tarrapid@gmail.com
Moscow, Russia

V. M Azanov

Moscow Aviation Institute

Email: azanov59@gmail.com
Moscow, Russia

A. I Kibzun

Moscow Aviation Institute

Author for correspondence.
Email: kibzun@mail.ru
Moscow, Russia

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