Input design using cylindrical algebraic decomposition

• Experiment design for system identification has seen significantprogress in the last decade. One contribution has been to deriveconvex relaxations of such problems. Consider that only a scalar functionof the system parameters is of interest. A standard step in sucha case is to first linearize this function with respect tothe estimated parameters. The objective of this contribution istwofold: firstly, to examine if there are cases where the linearizedapproximation is inadequate, and secondly to explore how to improveupon this approximation. By way of examples we show that it is notdifficult to construct examples where linearization isinsufficient. Furthermore, we introduce the use of higher orderapproximations and we formally show that this leads topolynomial optimization problems under Gaussian assumptions. We propose the use of cylindricalalgebraic decomposition as a method to obtain exact solutions forthis type of problems. Numerical examples are provided.

Keyword

input design

system identification

SRA - ICT

SRA - Informations- och kommunikationsteknik

Publication and Content Type

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kon (subject category)