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Error-based control systems on Riemannian state manifolds: Properties of the principal pushforward map associated to parallel transport
Mathematical Control and Related Fields ( IF 1.2 ) Pub Date : 2020-06-13 , DOI: 10.3934/mcrf.2020031
Simone Fiori ,

The objective of the paper is to contribute to the theory of error-based control systems on Riemannian manifolds. The present study focuses on system where the control field influences the covariant derivative of a control path. In order to define error terms in such systems, it is necessary to compare tangent vectors at different points using parallel transport and to understand how the covariant derivative of a vector field along a path changes after such field gets parallely transported to a different curve. It turns out that such analysis relies on a specific map, termed principal pushforward map. The present paper aims at contributing to the algebraic theory of the principal pushforward map and of its relationship with the curvature endomorphism of a state manifold.

中文翻译:

黎曼状态流形上基于错误的控制系统:与并行传输相关的主前推映射的属性

本文的目的是为黎曼流形上基于误差的控制系统理论做出贡献。本研究集中于控制场影响控制路径协变量导数的系统。为了在此类系统中定义误差项,有必要使用并行传输比较不同点处的切向量,并了解矢量场的协方差导数在沿着这种路径并行传输到不同曲线之后如何变化。事实证明,这种分析依赖于称为主推前映射的特定映射。本文旨在为主要前推映射的代数理论及其与状态流形的曲率内同态的关系做出贡献。
更新日期:2020-06-13
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