Affiliation:
1. Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada H3A 0C3
Abstract
Approximating the Koopman operator from data is numerically challenging when many lifting functions are considered. Even low-dimensional systems can yield unstable or ill-conditioned results in a high-dimensional lifted space. In this paper, Extended Dynamic Mode Decomposition (DMD) and DMD with control, two methods for approximating the Koopman operator, are reformulated as convex optimization problems with linear matrix inequality constraints. Asymptotic stability constraints and system norm regularizers are then incorporated as methods to improve the numerical conditioning of the Koopman operator. Specifically, the
H
∞
norm is used to penalize the input–output gain of the Koopman system. Weighting functions are then applied to penalize the system gain at specific frequencies. These constraints and regularizers introduce bilinear matrix inequality constraints to the regression problem, which are handled by solving a sequence of convex optimization problems. Experimental results using data from an aircraft fatigue structural test rig and a soft robot arm highlight the advantages of the proposed regression methods.
Funder
Office of Naval Research
National Research Council Canada
Toyota Research Institute
National Science Foundation
Mitacs
Natural Sciences and Engineering Research Council of Canada
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
4 articles.
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