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EDMD-Based Robust Observer Synthesis for Nonlinear Systems
arXiv:2509.09812v2 Announce Type: replace
Abstract: This paper presents a data-driven Koopman operator-based approach for designing robust state observers for nonlinear systems. Based on a finite-dimensional surrogate of the Koopman generator, identified via an extended dynamic mode decomposition (EDMD) procedure, a tractable formulation of the observer design problem is enabled on the data-driven model with conic uncertainties. The resulting problem is cast as a semidefinite program (SDP) with linear matrix inequalities (LMIs), guaranteeing exponential convergence of the observer with a predetermined rate in a probabilistic sense. The approach bridges the gap between statistical error tolerance and observer convergence certification, and enables an explicit use of linear systems theory for nonlinear observation in a data-driven framework. Numerical studies demonstrate the effectiveness and flexibility of the proposed method.
Abstract: This paper presents a data-driven Koopman operator-based approach for designing robust state observers for nonlinear systems. Based on a finite-dimensional surrogate of the Koopman generator, identified via an extended dynamic mode decomposition (EDMD) procedure, a tractable formulation of the observer design problem is enabled on the data-driven model with conic uncertainties. The resulting problem is cast as a semidefinite program (SDP) with linear matrix inequalities (LMIs), guaranteeing exponential convergence of the observer with a predetermined rate in a probabilistic sense. The approach bridges the gap between statistical error tolerance and observer convergence certification, and enables an explicit use of linear systems theory for nonlinear observation in a data-driven framework. Numerical studies demonstrate the effectiveness and flexibility of the proposed method.
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