Positivity of trigonometric polynomials

Author

Megretski, Alexandre

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., MIT, Cambridge, MA, USA

Volume

4

fYear

2003

fDate

9-12 Dec. 2003

Firstpage

3814

Abstract

The paper introduces a modification of the well-known sum-of-squares relaxation scheme for semi-algebraic programming by Shor based on replacing the ordinary polynomials by their trigonometric counterparts. It is shown that the new scheme has certain theoretical advantages over the classical one: in particular, a trigonometric polynomial is positive if and only if it can be represented as a sum of squares of a finite number of trigonometric polynomials. A dual version of the SOS relaxation is also introduced and discussed. An example of a quantized finite horizon optimal control application with state constraints, typical for model predictive control, is discussed.

Keywords

optimal control; optimisation; polynomials; predictive control; SOS relaxation; finite number; optimal control; optimisation; predictive control; semialgebraic programming; state constraints; sum of squares relaxation; trigonometric polynomials; Functional analysis; Optimal control; Paper technology; Polynomials; Predictive control; Predictive models; System analysis and design; Testing; Vectors; Zinc;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2003. Proceedings. 42nd IEEE Conference on

ISSN

0191-2216

Print_ISBN

0-7803-7924-1

Type

conf

DOI

10.1109/CDC.2003.1271743

Filename

1271743