Learning Koopman operator under dissipativity constraints

Keita Hara, Masaki Inoue, Noboru Sebe

Research output: Contribution to journalConference articlepeer-review

1 Citation (Scopus)

Abstract

This paper addresses a learning problem for nonlinear dynamical systems with incorporating any specified dissipativity property. The nonlinear systems are described by the Koopman operator, which is a linear operator defined on the infinite-dimensional lifted state space. The problem of learning the Koopman operator under specified quadratic dissipativity constraints is formulated and addressed. The learning problem is in a class of the non-convex optimization problem due to nonlinear constraints and is numerically intractable. By applying the change of variable technique and the convex overbounding approximation, the problem is reduced to sequential convex optimization and is solved in a numerically efficient manner. Finally, a numerical simulation is given, where high modeling accuracy achieved by the proposed approach including the specified dissipativity is demonstrated.

Original languageEnglish
Pages (from-to)1169-1174
Number of pages6
JournalIFAC-PapersOnLine
Volume53
Issue number2
DOIs
Publication statusPublished - 2020
Event21st IFAC World Congress 2020 - Berlin, Germany
Duration: 2020 Jul 122020 Jul 17

Keywords

  • Dissipativity
  • Koopman operator
  • Learning
  • Linear matrix inequality

ASJC Scopus subject areas

  • Control and Systems Engineering

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