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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.11256 |
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| _version_ | 1866916008025915392 |
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| author | Villanueva, Mario Eduardo Oravec, Juraj Paulen, Radoslav Houska, Boris |
| author_facet | Villanueva, Mario Eduardo Oravec, Juraj Paulen, Radoslav Houska, Boris |
| contents | This paper introduces computationally efficient methods for synthesizing explicit piecewise affine (PWA) feedback laws for nonlinear discrete-time systems, ensuring robustness and performance guarantees. The approach proceeds by optimizing a configuration-constrained PWA approximation of the value function of an infinite-horizon min-max Hamilton-Jacobi-Bellman equation. Here, robustness and performance are maintained by enforcing the PWA approximation to be a generalized control Lyapunov function for the given nonlinear system. This enables the generation of feedback laws with configurable storage complexity and pre-determined evaluation times, based on a selected configuration template. The framework's effectiveness is demonstrated through a constrained Van der Pol oscillator case study, where an explicit PWA controller with certified ergodic performance and specified complexity is synthesized over a large operational domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11256 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Feedback Synthesis for Nonlinear Systems Via Convex Control Lyapunov Functions Villanueva, Mario Eduardo Oravec, Juraj Paulen, Radoslav Houska, Boris Optimization and Control This paper introduces computationally efficient methods for synthesizing explicit piecewise affine (PWA) feedback laws for nonlinear discrete-time systems, ensuring robustness and performance guarantees. The approach proceeds by optimizing a configuration-constrained PWA approximation of the value function of an infinite-horizon min-max Hamilton-Jacobi-Bellman equation. Here, robustness and performance are maintained by enforcing the PWA approximation to be a generalized control Lyapunov function for the given nonlinear system. This enables the generation of feedback laws with configurable storage complexity and pre-determined evaluation times, based on a selected configuration template. The framework's effectiveness is demonstrated through a constrained Van der Pol oscillator case study, where an explicit PWA controller with certified ergodic performance and specified complexity is synthesized over a large operational domain. |
| title | Feedback Synthesis for Nonlinear Systems Via Convex Control Lyapunov Functions |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2512.11256 |