Title: AFAS - adaptive fast approximate simulation for non-linear model reduction

Authors: Shahkar Ahmad Nahvi; Mashuq-un-Nabi; S. Janardhanan

Addresses: Department of Electrical Engineering, Indian Institute of Technology, New Delhi, 110016, India ' Department of Electrical Engineering, Indian Institute of Technology, New Delhi, 110016, India ' Department of Electrical Engineering, Indian Institute of Technology, New Delhi, 110016, India

Abstract: In this work, we examine the problem of selecting linearisation points for trajectory piecewise linear (TPWL) approximation of non-linear dynamical systems. Linearisation point selection is a crucial step in the TPWL process, the quality and complexity of the approximation rests on it. In contrast to the popular approaches wherein linearisations are done at constant, pre-selected Euclidean distances in the state-space, we propose a new and simple error measure that helps in assessing the linearisation point requirement at different points on the non-linear system trajectory. Based on this error measure a new scheme to simulate the non-linear system, create linearisations at viable points and obtain a better TPWL approximation is presented. Finally, we substantiate our observations and propositions by detailed numerical tests on two non-linear circuits.

Keywords: large dynamical systems; model order reduction; MOR; nonlinear systems; approximate simulation; modelling; trajectory piecewise linear; TPWL; linearisation point selection; trajectory sampling; error analysis; nonlinear circuits.

DOI: 10.1504/IJMIC.2013.054315

International Journal of Modelling, Identification and Control, 2013 Vol.19 No.2, pp.113 - 124

Published online: 04 Jun 2013 *

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