TITLE:
Synthesis of an Optimal Control for Linear Stationary Discrete Dynamical Systems
AUTHORS:
Arnold Andreevich Baloev
KEYWORDS:
Difference Equations, Multiple Roots, Optimal Control
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.10,
October
30,
2024
ABSTRACT: In this paper, an algorithm designed by the author is used to construct the general solution to difference equations with constant coefficients. It is worth noting that the algorithm does not require any information on the multiple roots of the characteristic equation. This means one does not need to reconfigure the algorithm when changing the multiplicity groups. It is for this reason that the algorithm is called “universal”. In the present study, we solve the task of finding a linear optimal control for linear stationary discrete one- and higher-dimensional systems with scalar control. Moreover, we give analytical expressions for the control that minimize the quadratic criterion and ensure the asymptotic stability of the closed system. The obtained optimal control depends only on the parameters of the initial system and the roots of the characteristic equation.