Positivity of trigonometric polynomials

被引：0
|
作者：
Megretski, A [1 ]
机构：
[1] MIT, Dept Elect Engn & Comp Sci, Cambridge, MA 02139 USA
来源：
42ND IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-6, PROCEEDINGS | 2003年
关键词：
non-convex optimization; semidefinite relaxations; model predictive control;
D O I：
暂无
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The paper introduces a modification of the well-known sum-of-squares relaxation scheme for semi-algebraic programming by Shor [1], 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.
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页码：3814 / 3817
页数：4
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