Implicit higher-order moment matching technique for model reduction of quadratic-bilinear systems |
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| Authors: | Mian Mohammad Arsalan Asif Mian Ilyas Ahmad Peter Benner Lihong Feng Tatjana Stykel |
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| Institution: | 1. Research Center of Modelling and Simulation, National University of Sciences and Technology, Islamabad, Pakistan;2. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany, and Faculty of Mathematics, Otto-von-Guericke University Magdeburg, Germany;3. Institut für Mathematik, Unversität Augsburg, Universitätsstr. 14, Augsburg 86159, Germany;1. Department of Electronics and Telecomunication Engineering, State University of Rio de Janeiro (DETEL/UERJ), Rio de Janeiro, Brazil;2. Graduation Program of Electrical Engineering, Federal University of Rio de Janeiro (COPPE/UFRJ), Rio de Janeiro, Brazil;1. School of Electronic and Electric Engineering, Shanghai University of Engineering Science, China;2. Science and Technology on Underwater Vehicle Laboratory, Harbin Engineering University, Harbin 150001, China;3. School of Electronic Information and Electrical Engineering, Shanghai Jiaotong University, China;4. School of Physics and Electronic Engineering, Guangzhou University, Guangzhou, China;1. Communication Engineering at Al-Hussein bin Talal University, Ma’an, Jordan;2. Electrical Engineering at Jordan University of Science and Technology, Irbid, Jordan;1. Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands;2. Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands |
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| Abstract: | We propose a projection based multi-moment matching method for model order reduction of quadratic-bilinear systems. The goal is to construct a reduced system that ensures higher-order moment matching for the multivariate transfer functions appearing in the input-output representation of the non-linear system. An existing technique achieves this for the first two multivariate transfer functions, in what is called the symmetric form of the multivariate transfer functions. We extend this framework to an equivalent and simplified form, the regular form, which allows us to show moment matching for the first three multivariate transfer functions. Numerical results for three benchmark examples of quadratic-bilinear systems show that the proposed framework exhibits better performance with reduced computational cost in comparison to existing techniques. |
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