Closed-Loop Koopman Operator Approximation

• URL: http://arxiv.org/abs/2303.15318v3
• Date: Wed, 1 May 2024 17:34:26 GMT
• Title: Closed-Loop Koopman Operator Approximation
• Authors: Steven Dahdah, James Richard Forbes,
• Abstract summary: This paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller. The advantages of the proposed closed-loop Koopman operator approximation method are demonstrated in simulation and experimentally.
• Score: 5.317624228510749
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller. The Koopman operator allows a nonlinear system to be rewritten as an infinite-dimensional linear system by viewing it in terms of an infinite set of lifting functions. A finite-dimensional approximation of the Koopman operator can be identified from data by choosing a finite subset of lifting functions and solving a regression problem in the lifted space. Existing methods are designed to identify open-loop systems. However, it is impractical or impossible to run experiments on some systems, such as unstable systems, in an open-loop fashion. The proposed method leverages the linearity of the Koopman operator, along with knowledge of the controller and the structure of the closed-loop system, to simultaneously identify the closed-loop and plant systems. The advantages of the proposed closed-loop Koopman operator approximation method are demonstrated in simulation using a Duffing oscillator and experimentally using a rotary inverted pendulum system. An open-source software implementation of the proposed method is publicly available, along with the experimental dataset generated for this paper.

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