Structure-Preserving Interpolation of Bilinear Control Systems
Benner, P. ; https://orcid.org/0000-0003-3362-4103, Gugercin, S., Werner, S.
Abstract
In this paper, we extend the structure-preserving interpolatory model reduction framework, originally developed for linear systems, to structured bilinear control systems. Specifically, we give explicit construction formulae for the model reduction bases to satisfy different types of interpolation conditions. First, we establish the analysis for transfer function interpolation for single-input single-output structured bilinear systems. Then, we extend these results to the case of multi-input multi-output structured bilinear systems by matrix interpolation. The effectiveness of our structure-preserving approach is illustrated by means of various numerical examples.
Topics & Concepts
Bilinear interpolationInterpolation (computer graphics)MathematicsReduction (mathematics)Bilinear mapLinear interpolationTransfer functionLinear systemApplied mathematicsStairstep interpolationTrilinear interpolationBicubic interpolationAlgebra over a fieldAlgorithmMathematical optimizationMultivariate interpolationComputer sciencePure mathematicsMathematical analysisPolynomialGeometryArtificial intelligenceStatisticsElectrical engineeringMotion (physics)EngineeringModel Reduction and Neural NetworksNumerical methods for differential equationsReal-time simulation and control systems