Data-driven model order reduction of quadratic-bilinear systems

Ion Victor Gosea, Athanasios C. Antoulas
2018 Numerical Linear Algebra with Applications  
We introduce a data-driven model order reduction (MOR) approach which can be viewed as the generalization of the Loewner framework for quadratic-bilinear (QB) control systems. For certain types of nonlinear systems, one can always find an equivalent QB model without performing any approximation. Proceed with appropriately defining generalized higher order transfer functions for QB systems. These multi-variate rational functions play an important role in the MOR process. We construct reduced
more » ... r systems for which the associated transfer functions match those corresponding to the original system at selected interpolations points. The generalizations of the Loewner matrices can be directly computed by solving generalized Sylvester equations with quadratic terms. The advantage is that the approach is data-driven since one would only need computed/measured samples to construct a reduced order QB system. We illustrate the practical applicability of the proposed method by means of several numerical experiments resulting from semi-discretized nonlinear partial differential equations. † Data-Driven System Reduction and Identification Group,
doi:10.1002/nla.2200 fatcat:b2qri6ktxzaftbye6zuzdcqaxe