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arXiv · 2512.11256

Feedback Synthesis for Nonlinear Systems Via Convex Control Lyapunov Functions

Mario Eduardo Villanueva·Juraj Oravec·Radoslav Paulen·Boris Houska
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Abstract

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.

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BibTeXRIS

Mario Eduardo Villanueva, Juraj Oravec, Radoslav Paulen, Boris Houska. 2025-12-12. Feedback Synthesis for Nonlinear Systems Via Convex Control Lyapunov Functions. https://arxiv.org/abs/2512.11256

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