Uncertainty Modelling and Robust Observer Synthesis using the Koopman Operator

• URL: http://arxiv.org/abs/2410.01057v1
• Date: Tue, 1 Oct 2024 20:31:18 GMT
• Title: Uncertainty Modelling and Robust Observer Synthesis using the Koopman Operator
• Authors: Steven Dahdah, James Richard Forbes,
• Abstract summary: The Koopman operator allows nonlinear systems to be rewritten as infinite-dimensional linear systems. A finite-dimensional approximation of the Koopman operator can be identified directly from data. A population of several dozen motor drives is used to experimentally demonstrate the proposed method.
• Score: 5.317624228510749
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper proposes a robust nonlinear observer synthesis method for a population of systems modelled using the Koopman operator. The Koopman operator allows nonlinear systems to be rewritten as infinite-dimensional linear systems. A finite-dimensional approximation of the Koopman operator can be identified directly from data, yielding an approximately linear model of a nonlinear system. The proposed observer synthesis method is made possible by this linearity that in turn allows uncertainty within a population of Koopman models to be quantified in the frequency domain. Using this uncertainty model, linear robust control techniques are used to synthesize robust nonlinear Koopman observers. A population of several dozen motor drives is used to experimentally demonstrate the proposed method. Manufacturing variation is characterized in the frequency domain, and a robust Koopman observer is synthesized using mixed $\mathcal{H}_2$-$\mathcal{H}_\infty$ optimal control.

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