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Euler Time-Discretization of Funnel-Controlled Dynamics

Thomas Berger, Hannes Gernandt, Pushya Mitra · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27185 · cited by 0 works (OpenAlex) · open-access PDF

Spanish

Analizamos las discretizaciones explícitas e implícitas de Euler de la dinámica de circuito cerrado en tiempo continuo generada por un controlador de túnel para un sistema de estado completo no lineal de grado relativo con ganancia de entrada positiva escalar. Un margen de túnel continuo cuantitativo proporciona los límites de compacidad y regularidad necesarios para el análisis de error. Para Euler explícito, un umbral de tamaño de paso superior computable garantiza una distancia global en nodo hacia el límite del túnel. Mostramos que la convergencia de primer orden se mantiene en horizontes de tiempo finitos y, bajo una condición de disipatividad (un Lipschitz de un lado vinculado a la planta dominada por el amortecimiento del túnel), uniformemente en el tiempo. Para Euler implícito

Machine translation (Meta M2M100); the English original follows.

Abstract

We analyze explicit and implicit Euler discretizations of the continuous-time closed-loop dynamics generated by a funnel controller for a fully actuated nonlinear full-state system of relative degree one with scalar positive input gain. A quantitative continuous-time funnel margin provides the compactness and regularity bounds needed for the error analysis. For explicit Euler, a computable upper step-size threshold guarantees a global nodewise distance from the funnel boundary. We show that first-order convergence holds on finite time horizons and, under a~dissipativity condition (a~one-sided Lipschitz bound on the plant dominated by the funnel damping), uniformly in time. For implicit Euler, an admissible update exists for every step size and every trajectory initialized in the funnel retains a step-size-independent nodal margin. Under dissipativity, the admissible root is unique for every step size, the discrete flow is contractive, and the first-order error bound is uniform in time.

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Topics: Funnel, Mathematics, Lipschitz continuity, Scalar (mathematics), Compact space, Convergence (economics)

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