| Positivity of Trigonometric Polynomials (2003) | |||||||||||||||||
Abstract | |||||||||||||||||
| The paper introduces a modi cation of the well-known sum-ofsquares 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 nite number of trigonometric polynomials. A dual version of the SOS relaxation is also introduced and discussed. An example of a quantized nite horizon optimal control application with state constraints, typical for model predictive control, is discussed. | |||||||||||||||||
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