Feedback Synthesis for Nonlinear Systems Via Convex Control Lyapunov Functions
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.
Cite
@article{arxiv.2512.11256,
title = {Feedback Synthesis for Nonlinear Systems Via Convex Control Lyapunov Functions},
author = {Mario Eduardo Villanueva and Juraj Oravec and Radoslav Paulen and Boris Houska},
journal= {arXiv preprint arXiv:2512.11256},
year = {2026}
}