Characterization of Gradient Control Systems
Characterization of Gradient Control Systems
复制标题
梯度控制系统的表征
DOI：
10.1137/s0363012903425568
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
P. Crouch
中科院分区：
文献类型：
--
作者：
J. Cortés;A. Schaft;P. Crouch
给出了一个一般的具有输出的非线性仿射控制系统及其状态空间上定义的一个无扭仿射连接，我们研究了该系统的梯度实现问题：我们给出了控制系统可以写成一个对应于某个伪黎曼度量且Levi-Civita连接等于给定仿射连接的梯度控制系统的充要条件。结果依赖于系统关于给定仿射连接的适当的相容概念，以及延长系统和梯度扩张的输出行为。与仿射联络相关的对称乘积在整个讨论中起着关键作用。
Given a general nonlinear affine control system with outputs and a torsion-free affine connection defined on its state space, we investigate the gradient realization problem: we give necessary and sufficient conditions under which the control system can be written as a gradient control system corresponding to some pseudo-Riemannian metric whose Levi-Civita connection is equal to the given affine connection. The results rely on a suitable notion of compatibility of the system with respect to the given affine connection, and on the output behavior of the prolonged system and the gradient extension. The symmetric product associated with an affine connection plays a key role throughout the discussion.