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.© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. QC 20120131</p

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.© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. QC 20120131</p