In general, model reduction techniques fall into two categories — moment —matching and Krylov techniques and balancing techniques. The present contribution is concerned with the former. The present contribution proposes the use of a perturbative representation as an alternative to the bilinear representation [4]. While for weakly nonlinear systems, either approximation is satisfactory, it will be seen that the perturbative method has several advantages over the bilinear representation. In this contribution, an improved reduction method is proposed. Illustrative examples are chosen, and the errors obtained from the different reduction strategies will be compared.
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References
B. Moore (1981). Principal Component analysis in linear systems: Controllability, Observability and model reduction, IEEE Transactions on Automatic Control, AC-26, 1, 17–31.
A.C. Antoulas, D.C. Sorensen and S. Gugercin (2001). A survey of model reduction methods for large-scale systems, Contemporary Mathematics, AMS Publications, Providence, RI.
C.A. Beattie and S. Gugercin (2007). Krylov-based minimization for optimal H2 model reduction, 46th IEEE Conference on Decision and Control, New Orleans.
J.R. Phillips (2003). Projection-based approaches for model reduction of weakly nonlinear, time-varying systems, IEEE Transactions on computer-aided design of integrated circuits and systems 22, 2, 171–187.
M. Condon and R. Ivanov (2005a). Nonlinear systems-Algebraic Gramians and Model Reduction, COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 24, 1, 202–219.
M. Condon and R. Ivanov (2005b). Balanced Model Reduction from a Perturbative Representation of Weakly Nonlinear Systems, NOLTA 2005, Bruges.
T. Veijola and L. Costa (1998). Combined electrical and thermal circuit simulation using APLAC, Circuit Theory Laboratory Report Series, No. CT-34, Helsinki University of Technology.
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Condon, M., Grahovski, G.G. (2009). Model Reduction of Weakly Nonlinear Systems. In: Ao, SI., Gelman, L. (eds) Advances in Electrical Engineering and Computational Science. Lecture Notes in Electrical Engineering, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2311-7_2
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