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Title: Optimal control and Galois theory

An important role is played in the solution of a class of optimal control problems by a certain special polynomial of degree 2(n−1) with integer coefficients. The linear independence of a family of k roots of this polynomial over the field Q implies the existence of a solution of the original problem with optimal control in the form of an irrational winding of a k-dimensional Clifford torus, which is passed in finite time. In the paper, we prove that for n≤15 one can take an arbitrary positive integer not exceeding [n/2] for k. The apparatus developed in the paper is applied to the systems of Chebyshev-Hermite polynomials and generalized Chebyshev-Laguerre polynomials. It is proved that for such polynomials of degree 2m every subsystem of [(m+1)/2] roots with pairwise distinct squares is linearly independent over the field Q. Bibliography: 11 titles.
Authors:
; ;  [1]
  1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
22365880
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 204; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; HERMITE POLYNOMIALS; LAGUERRE POLYNOMIALS; MATHEMATICAL SOLUTIONS; OPTIMAL CONTROL