Neural-NPV Control: Learning Parameter-Dependent Controllers and Lyapunov Functions with Neural Networks
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914454770286592 |
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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 |