Newest papers

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

Chinese

我们分析了对连续时间闭环动态的明示和暗示的欧莱尔分辨率,由一个非线性全状态系统为一个完全运行的非线性全状态系统所产生的连续时间闭环动态。定量连续时间的欧莱尔分辨率提供了对错误分析所需的紧凑性和规律性界限。对于明确的欧莱尔来说,一个可计算的上级步骤大小门槛保证了从隧道边界的全球节点距离。我们表明,在有限时间地平线上保持了第一个顺序的汇总,并且在一个 ~ dissipativity 条件下(一个 ~ 侧 Lipschitz 绑在隧道压缩支配的工厂上),在时间上均匀地保证了。对于默认的欧莱尔来说,每个步骤大小都存在一个允许的更新

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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