Trigonometric Embeddings in Polynomial Extended Mode Decomposition—Experimental Application to an Inverted Pendulum

Camilo Garcia-Tenorio, Gilles Delansnay, Eduardo Mojica-Nava and Alain Vande Wouwer
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Camilo Garcia-Tenorio: Departamento de Ingeniería Mecánica y Mecatrónica, Universidad Nacional de Colombia, Carrera 30 No. 45-03, Bogotá 111321, Colombia
Gilles Delansnay: Systems, Estimation, Control and Optimization (SECO), Université de Mons, 7000 Mons, Belgium
Eduardo Mojica-Nava: Departamento de Ingeniería Mecánica y Mecatrónica, Universidad Nacional de Colombia, Carrera 30 No. 45-03, Bogotá 111321, Colombia
Alain Vande Wouwer: Systems, Estimation, Control and Optimization (SECO), Université de Mons, 7000 Mons, Belgium

Mathematics, 2021, vol. 9, issue 10, 1-15

Abstract: The extended dynamic mode decomposition algorithm is a tool for accurately approximating the point spectrum of the Koopman operator. This algorithm provides an approximate linear expansion of non-linear discrete-time systems, which can be useful for system analysis and controller design. The accuracy of this algorithm depends heavily on the availability of a set of basis functions that provide the ability to capture the nonlinear dynamics of the underlying system. Recently, the use of orthogonal polynomials, along with reduction techniques for the dimension and maximum order of the polynomial basis, have been successfully used to approximate nonlinear systems with the additional benefit of using smaller datasets. This paper expands the current methods for selecting the set of observables for nonlinear systems with periodic behavior, which is prone to a representation in terms of trigonometric functions. The benefit of working with orthogonal polynomials is preserved by embedding the trigonometric functions into the orthogonal basis. The algorithm is illustrated with the data-driven modelling of an inverted pendulum in simulation and real-life experiments.

Keywords: extended dynamic mode decomposition; Koopman operator; orthogonal polynomials; mathematical modeling; dynamic systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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