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Adaptive Neural Observer Framework for Discrete-Time Non-Affine Nonlinear Systems with Uncertainty
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Adaptive Neural Observer
Discrete-Time Nonlinear
Systems
Non-Affine Systems
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Abstract
In modern control engineering, precise state estimation of nonlinear systems under uncertainty remains a significant challenge, particularly for discrete-time non-affine dynamics. This paper introduces an Adaptive Neural Observer Framework designed to address the limitations of classical observers when dealing with parametric uncertainties, unmodeled dynamics, and external disturbances. The proposed framework integrates recurrent neural networks (RNNs) with a sliding-mode observer architecture, providing robust state estimation while maintaining real-time adaptability. By employing Lyapunov-based stability analysis, the observer guarantees convergence of the estimation error, ensuring that the system’s states can be accurately tracked despite nonlinearities and uncertainties. Simulation studies are conducted on discrete-time models of induction motors and other representative nonlinear systems, comparing the proposed framework with classical Luenberger-like observers and baseline neural observers. Results demonstrate that the proposed approach significantly improves convergence speed, estimation accuracy, and disturbance rejection, achieving near-zero steady-state errors within a shorter time horizon. Furthermore, the adaptive mechanism allows the observer to compensate for parameter variations and unmodeled nonlinearities, offering superior performance in scenarios where traditional methods fail. The study also explores the theoretical underpinnings of neural observer design, including stability guarantees, convergence properties, and robustness considerations, while providing critical analysis of trade-offs such as computational complexity and real-time implementation constraints. This work not only extends the theoretical foundations of nonlinear observer design but also offers practical insights for applications in high-performance motor drives, robotics, and energy systems where precise state knowledge is essential. The findings suggest that the proposed adaptive neural observer framework is a robust, scalable, and practically implementable solution for discrete-time non-affine nonlinear systems, bridging the gap between classical control theory and modern machine learning-based estimation techniques. These contributions provide a significant step forward in advancing reliable, adaptive, and efficient state estimation methods for complex engineering systems.
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