Title: Responding to Unforeseen Events: Stable-by-Design Neural Feedback Control and the Youla-REN

Abstract

This paper investigates parameterizations for stabilizing nonlinear policies within the realm of learning-based control. We introduce a framework that merges a nonlinear adaptation of the Youla-Kucera parameterization with robust neural architectures, specifically the Recurrent Equilibrium Network (REN). This approach yields unconstrained parameterizations, enabling the use of first-order optimization techniques for search while guaranteeing closed-loop stability through structural design.

Our analysis addresses the interplay of three key factors: nonlinear system dynamics, partial observability, and incremental closed-loop stability constraints—specifically contraction and Lipschitz continuity. We demonstrate that when incremental stability requirements are paired with either nonlinear dynamics or partial observation, a Youla parameter that is both contracting and Lipschitz ensures the resulting closed-loop system retains these properties. However, when all three conditions coexist, incremental stability may be compromised in the presence of exogenous disturbances. In such cases, a more relaxed condition, termed "d-tube contraction and Lipschitzness," is preserved.

Furthermore, we establish converse results indicating that our proposed parameterization encompasses all contracting and Lipschitz closed-loop systems for specific classes of nonlinear dynamics. Numerical simulations highlight the practical advantages of this parameterization in scenarios requiring built-in stability guarantees during controller learning, including cases involving: (i) "economic" reward structures that lack inherent stabilizing properties; (ii) abbreviated training periods; and (iii) systems subject to uncertainty.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC