Neural-NPV Control: Learning Parameter-Dependent Controllers and Lyapunov Functions with Neural Networks

Fuente: arXiv
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Main Authors: Niloy, MD Abul Kashem, Hallmark, Adam, Cheng, Yikun, Zhao, Pan
Format: Preprint
Published: 2026
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author Niloy, MD Abul Kashem
Hallmark, Adam
Cheng, Yikun
Zhao, Pan
author_facet Niloy, MD Abul Kashem
Hallmark, Adam
Cheng, Yikun
Zhao, Pan
contents Nonlinear parameter-varying (NPV) systems are a class of nonlinear systems whose dynamics explicitly depend on time-varying external parameters, making them suitable for modeling real-world systems with dynamics variations. Traditional synthesis methods for NPV systems, such as sum-of-squares (SOS) optimization, are only applicable to control-affine systems, face scalability challenges and often lead to conservative results due to structural restrictions. To address these limitations, we propose Neural-NPV, a two-stage learning-based framework that leverages neural networks to jointly synthesize a PD controller and a PD Lyapunov function for an NPV system under input constraints. In the first stage, we utilize a computationally cheap, gradient-based counterexample-guided procedure to synthesize an approximately valid PD Lyapunov function and a PD controller. In the second stage, a level-set guided refinement is then conducted to obtain a valid Lyapunov function and controller while maximizing the robust region of attraction (R-ROA). We demonstrate the advantages of Neural-NPV in terms of applicability, performance, and scalability compared to SOS-based methods through numerical experiments involving an simple inverted pendulum with one scheduling parameter and a quadrotor system with three scheduling parameters.
format Preprint
id arxiv_https___arxiv_org_abs_2603_17134
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Neural-NPV Control: Learning Parameter-Dependent Controllers and Lyapunov Functions with Neural Networks
Niloy, MD Abul Kashem
Hallmark, Adam
Cheng, Yikun
Zhao, Pan
Systems and Control
Optimization and Control
Nonlinear parameter-varying (NPV) systems are a class of nonlinear systems whose dynamics explicitly depend on time-varying external parameters, making them suitable for modeling real-world systems with dynamics variations. Traditional synthesis methods for NPV systems, such as sum-of-squares (SOS) optimization, are only applicable to control-affine systems, face scalability challenges and often lead to conservative results due to structural restrictions. To address these limitations, we propose Neural-NPV, a two-stage learning-based framework that leverages neural networks to jointly synthesize a PD controller and a PD Lyapunov function for an NPV system under input constraints. In the first stage, we utilize a computationally cheap, gradient-based counterexample-guided procedure to synthesize an approximately valid PD Lyapunov function and a PD controller. In the second stage, a level-set guided refinement is then conducted to obtain a valid Lyapunov function and controller while maximizing the robust region of attraction (R-ROA). We demonstrate the advantages of Neural-NPV in terms of applicability, performance, and scalability compared to SOS-based methods through numerical experiments involving an simple inverted pendulum with one scheduling parameter and a quadrotor system with three scheduling parameters.
title Neural-NPV Control: Learning Parameter-Dependent Controllers and Lyapunov Functions with Neural Networks
topic Systems and Control
Optimization and Control
url https://arxiv.org/abs/2603.17134