Interpolation-Based Model Order Reduction for Quadratic-Bilinear Systems and $${\mathcal {H}_{2}}$$ H 2 Optimal Approximation

Xingang Cao (), Joseph Maubach (), Wil Schilders () and Siep Weiland ()
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Xingang Cao: Eindhoven University of Technology, Department of Mathematics and Computer Science
Joseph Maubach: Eindhoven University of Technology, Department of Mathematics and Computer Science
Wil Schilders: Eindhoven University of Technology, Department of Mathematics and Computer Science
Siep Weiland: Eindhoven University of Technology, Department of Electrical Engineering

A chapter in Realization and Model Reduction of Dynamical Systems, 2022, pp 117-135 from Springer

Abstract: Abstract The work of this paper focuses on model order reduction for a special class of nonlinear dynamical systems, that is, the class of quadratic-bilinear dynamical systems. This kind of systems can be used to represent other nonlinear dynamical systems with strong nonlinearities such as exponent and high-order polynomials. This paper addresses the $${\mathcal {H}_{2}}$$ H 2 optimal model approximation problem for this class of systems. To solve the model order reduction problem, a notion of generalized transfer functions and the $${\mathcal {H}_{2}}$$ H 2 norm are first discussed. A Volterra series interpolation scheme is proposed to interpolate the system from both the input-to-output and the output-to-input directions. In contrast to existing methods, we propose to interpolate all Volterra kernels, which can be achieved by solving Sylvester equations. The necessary $${\mathcal {H}_{2}}$$ H 2 optimality conditions are fulfilled by the proposed interpolation scheme. A fixed point method is applied to solve the nonlinear Sylvester equations. A numerical example demonstrates the effectiveness of the proposed methods.

Keywords: Model order reduction; Quadratic bilinear dynamical systems; $${\mathcal {H}_{2}}$$ H 2 Optimal approximation; Volterra series interpolation; Generalized Sylvester equations (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-95157-3_7

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DOI: 10.1007/978-3-030-95157-3_7

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