Jul 2026· IEEE Jordan Conference on Applied Electrical Engineering and Computing Technologies· pp. 191-196· 0 citations· 16 references
Abstract
The Koopman operator enables nonlinear systems to be represented in an approximately linear form for linear control design. However, Extended Dynamic Mode Decomposition with Control (EDMDc) is often limited by the closure problem when generic observables fail to capture the system dynamics. This paper addresses this issue using physicsinformed observables derived from Lie derivatives for nonlinear mechanical systems. The resulting lifted models accurately capture nonlinear dynamics and enable standard LQR design with improved performance over Jacobian-based LQR during large transients. Results further demonstrate that complete physics-informed lifting is essential to minimize closure errors. The main contributions are: (1) analysis of the closure problem, (2) a Lie-derivative-based observable selection framework, and (3) comparison of Koopman-based and Jacobian-based LQR for polynomial nonlinear systems.
State estimation for nonlinear dynamical systems remains a fundamental challenge, particularly when measurements are sparse and internal states are inaccessible. This work presents a KOOPMAN-based Linear State Observer (KOOPMAN-LSO) design framework that enables linear observer synthesis for nonlinear systems through K...
Mustapha Habib, Dario Aguiar, Esther Kieseritzky et al.· 0 citations
Finite-dimensional Koopman models enable efficient linear prediction and control of nonlinear robotic systems. However, models learned purely from trajectory data may violate the energetic structure of the underlying mechanics, producing predictions that exhibit artificial energy growth and diverge under recursive prop...
Rajpal Singh, Aditya Singh, J. Keshavan· 0 citations
This paper presents a data-efficient Koopman-based tracking model predictive control (MPC) scheme for nonlinear systems. Linear surrogate models are constructed online via a kernel extended dynamic mode decomposition (EDMD) framework in a reproducing kernel Hilbert space (RKHS), for which a proportional approximation e...
Hai-Ning Yan, Huai-Cheng Yan, Kai-Tian Chen et al.· IEEE Transactions on Automat...· 0 citations
Correlation-Basis enhanced DMD is introduced, a data-driven method whose goal is to learn an effective autonomous linear operator for periodic nonlinear dynamics, used to absorb nonlinear components that cannot be represented by the learned linear operator.
Paolo Climaco, J. Garcke, Xenia F. Gerloff· 0 citations
This work proposes a cascaded physics-informed neural network (PINN) framework to approximately solve partial differential equations (PDEs) and demonstrates that this approach can computationally discover effective feedback-linearizing representations of nonlinear systems for control tasks.
Pavlos Kallinikidis, Feng-Jun Yang, David Snyder et al.· 0 citations
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