Temporal Forward–Backward Consistency, Not Residual Error, Measures the Prediction Accuracy of Extended Dynamic Mode Decomposition

Haseli, Masih; Cortés, Jorge

doi:10.1109/lcsys.2022.3214476

Cited by 7 publications

(2 citation statements)

References 28 publications

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“…The Koopman operator is a linear transformation that transfers the dynamics from state space to an infinite-dimensional observable space, where these observables can evolve linearly over time. However, working with an infinite-dimensional operator is impractical; thus, obtaining a finite-dimensional representation of the Koopman operator has been of great importance, and several methods have been introduced in the literature, such as extended dynamic mode decomposition (EDMD) [29][30][31][32][33] and the methods based on deep learning [34][35][36][37] to achieve this.…”

Section: Introductionmentioning

confidence: 99%

Koopman fault‐tolerant model predictive control

Bakhtiaridoust,

Yadegar,

Jahangiri

2024

IET Control Theory & Appl

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This paper introduces a novel data‐driven approach to develop a fault‐tolerant model predictive controller (MPC) for non‐linear systems. By adopting a Koopman operator‐theoretic perspective, the proposed method leverages historical data from the system to construct a data‐driven model that captures the non‐linear behaviour and fault characteristics. The fault influence is addressed through an online estimation of a time‐varying Koopman predictor, which allows for adjusting the MPC control law to counteract the fault effects. This estimation is performed in a higher dimensional Koopman feature space, where the dynamics behave linearly. As a result, the non‐linear fault‐tolerant MPC optimization problem can be replaced with a more practical and feasible linear time‐varying one using the approximated Koopman predictor. Moreover, by incorporating the online update procedure, the time‐varying Koopman predictor can represent the dynamics of the faulty system. Hence, the controller can adapt and compensate for the faults in real‐time, integrating the fault diagnosis module in the MPC framework and eliminating the need for a separate fault detection unit. Finally, the efficacy of the proposed approach is demonstrated through case study results, which highlight the ability of the controller to mitigate faults and maintain desired system behaviour.

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Section: Introductionmentioning

confidence: 99%

Koopman fault‐tolerant model predictive control

Bakhtiaridoust,

Yadegar,

Jahangiri

2024

IET Control Theory & Appl

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“…Almost 75 years after Koopman's seminal work in 1931, Mezić (2005 revive the Koopman operator and propose its use for prediction and control. In the following decade, a number of contributions have been made, including the analysis of global stability properties (Mauroy and Mezić, 2016), estimation (Netto and Mili, 2018), and numerical methods for approximating the Koopman action based on data, such as extended dynamic mode decomposition (EDMD) (Williams et al, 2015) and its analysis (Korda and Mezić, 2018b;Haseli and Cortés, 2022). While the Koopman theory was originally developed for autonomous systems, the literature also contains extensions to controlled systems, e.g., model predictive control (Korda and Mezić, 2018a), linear-quadratic regulation (Brunton et al, 2016), and Lian et al (2021) provide a Koopman perspective on the work by Willems et al (2005).…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics

Strässer

Berberich

Allgöwer

2021

2021 60th IEEE Conference on Decision and Control (CDC)

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Data-driven analysis and control of dynamical systems have gained a lot of interest in recent years. While the class of linear systems is well studied, theoretical results for nonlinear systems are still rare. In this paper, we present a data-driven controller design method for discretetime control-affine nonlinear systems. Our approach relies on the Koopman operator, which is a linear but infinite-dimensional operator lifting the nonlinear system to a higher-dimensional space. Particularly, we derive a linear fractional representation of a lifted bilinear system representation based on measured data. Further, we restrict the lifting to finite dimensions, but account for the truncation error using a finite-gain argument. We derive a linear matrix inequality based design procedure to guarantee robust local stability for the resulting bilinear system for all error terms satisfying the finite-gain bound and, thus, also for the underlying nonlinear system. Finally, we apply the developed design method to the nonlinear Van der Pol oscillator.

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Optimal control of a MEMS gyroscope based on the Koopman theory

Rahmani

Redkar

2023

Int. J. Dynam. Control

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Temporal Forward–Backward Consistency, Not Residual Error, Measures the Prediction Accuracy of Extended Dynamic Mode Decomposition

Cited by 7 publications

References 28 publications

Koopman fault‐tolerant model predictive control

Koopman fault‐tolerant model predictive control

Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics

Optimal control of a MEMS gyroscope based on the Koopman theory

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