Thomas Berger, Hannes Gernandt, Pushya Mitra · 2026 · arXiv
DOI: 10.48550/arXiv.2610.27185 · open-access PDF
Kami menganalisis diskretisasi Euler eksplisit dan implisit dari dinamisme loop tertutup berkelanjutan yang dihasilkan oleh kontroler funnel untuk sistem full-state nonlinear yang sepenuhnya dioperasikan dari tingkat relatif satu dengan kenaikan input positif skalar. Margin funnel berkelanjutan kuantitatif memberikan batas kompaksi dan regularitas yang diperlukan untuk analisis kesalahan. Untuk Euler eksplisit, ambang batas step-size atas yang dapat dihitung menjamin jarak nodus global dari batas funnel. Kami menunjukkan bahwa konvergensi urutan pertama memegang pada cakrawala waktu yang terbatas dan, di bawah kondisi dissipatifitas (a~one-sided
Machine translation (Meta M2M100); the English original follows.
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
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