EDMD-Based Robust Observer Synthesis for Nonlinear Systems

2025/09/11 by Ye, Xiuzhen, Tang, Wentao · 2 citations
#FOS: Electrical engineering #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2509.09812

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.

Citations

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• Выпуклая оптимизация

Cited by

• Data-Driven State Observers for Measure-Preserving Systems
• Data-Driven Observer Synthesis for Autonomous Limit Cycle Systems through Estimation of Koopman Eigenfunctions

Related

• Uncertainty Modelling and Robust Observer Synthesis using the Koopman Operator
• An overview of Koopman-based control: From error bounds to closed-loop guarantees
• A Dual Koopman Approach to Observer Design for Nonlinear Systems
• SafEDMD: A Koopman-based data-driven controller design framework for nonlinear dynamical systems
• Koopman Operator Theory for Nonlinear Dynamic Modeling using Dynamic Mode Decomposition