论文标题
部分可观测时空混沌系统的无模型预测
Parametrized topological complexity of sphere bundles
论文作者
论文摘要
参数化运动计划算法具有高度的灵活性和普遍性，它们可以在各种外部条件下工作，这些条件被视为参数并构成算法输入的一部分。在本文中，我们分析了球体束的参数化运动计划问题。我们的主要结果为参数化拓扑复杂性提供了上限和下限。上限通常涉及相关振动的截面类别，并且下限是根据特征类及其特性给出的。我们在许多示例中明确计算了参数化的拓扑复杂性，并表明它可以任意较大的值。
Parametrized motion planning algorithms have high degree of flexibility and universality, they can work under a variety of external conditions, which are viewed as parameters and form part of the input of the algorithm. In this paper we analyse the parameterized motion planning problem in the case of sphere bundles. Our main results provide upper and lower bounds for the parametrized topological complexity; the upper bounds typically involve sectional categories of the associated fibrations and the lower bounds are given in terms of characteristic classes and their properties. We explicitly compute the parametrized topological complexity in many examples and show that it may assume arbitrarily large values.
