Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems

• URL: http://arxiv.org/abs/2210.01476v2
• Date: Wed, 5 Apr 2023 15:00:56 GMT
• Title: Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems
• Authors: Muhammad Umar B. Niazi, John Cao, Xudong Sun, Amritam Das, Karl Henrik Johansson
• Abstract summary: Luenberger observers for nonlinear systems involve transforming the state to an alternate coordinate system. We propose a novel approach that uses supervised physics-informed neural networks to approximate both the transformation and its inverse. Our method exhibits superior robustness capabilities to contemporary methods and demonstrates to both neural network's approximation errors and system uncertainties.
• Score: 5.953597709282766
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Designing Luenberger observers for nonlinear systems involves the challenging task of transforming the state to an alternate coordinate system, possibly of higher dimensions, where the system is asymptotically stable and linear up to output injection. The observer then estimates the system's state in the original coordinates by inverting the transformation map. However, finding a suitable injective transformation whose inverse can be derived remains a primary challenge for general nonlinear systems. We propose a novel approach that uses supervised physics-informed neural networks to approximate both the transformation and its inverse. Our method exhibits superior generalization capabilities to contemporary methods and demonstrates robustness to both neural network's approximation errors and system uncertainties.

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