Data-Driven State Observers for Measure-Preserving Systems

2025/09/24 by Wentao Tang, Tang, Wentao
Engineering · #37A05 #37C05 #37C40 #47A10 #47B20 #93B28 #93B53 #Advanced Control Systems Optimization #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Fault Detection and Control Systems #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2509.20596

openalex publication_date 2025/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The increasing use of data-driven control strategies gives rise to the problem of learning-based state observation. Motivated by this need, the present work proposes a data-driven approach for the synthesis of state observers for discrete-time nonlinear systems with measure-preserving dynamics. To this end, Kazantzis-Kravaris/Luenburger (KKL) observers are shown to be well-defined, where the observer design boils down to determining a nonlinear injective mapping of states and its pseudo-inverse. For its learning-based construction, the KKL observer is related to the Koopman and Perron-Frobenius operators, defined on a Sobolev-type reproducing kernel Hilbert space (RKHS) on which they are shown to be normal operators and thus have a spectral resolution. Hence, observer synthesis algorithms, based on kernel interpolation/regression routines for the desired injective mapping in the observer and its pseudo-inverse, have been proposed in various settings of available dataset -- (i) many orbits, (ii) single long orbit, and (iii) snapshots. Theoretical error analyses are provided, and numerical studies on a chaotic Lorenz system are demonstrated.

Citations

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Cited by

• EDMD-Based Robust Observer Synthesis for Nonlinear Systems

Related

• Synthesis of Data-Driven Nonlinear State Observers using Lipschitz-Bounded Neural Networks
• KKL Observer Synthesis for Nonlinear Systems via Physics-Informed Learning
• Data-Driven Nonlinear State Observation using Video Measurements
• Data-Driven Observer Synthesis for Autonomous Limit Cycle Systems through Estimation of Koopman Eigenfunctions
• Adaptive Meta-Learning-Based KKL Observer Design for Nonlinear Dynamical Systems