论文标题
通过状态转换提高混合 - 孔酮可达到的近似值的忠诚度
Improving the Fidelity of Mixed-Monotone Reachable Set Approximations via State Transformations
论文作者
论文摘要
混合 - 单调系统可以通过分解函数分离成增加和减少组件，并且该分解函数允许将系统动力学嵌入高阶单调嵌入系统中。以这种方式嵌入系统动力学有助于使用超矩形的可触及套件的有效过度透射式过度对象，但是，与单调性属性不同，可以应用于计算，例如，最紧密的超旋转直角包含可触及的集合，包含可及的混合性属性的应用，通常在保守的触发范围中均可在保守范围内产生近似值。在这项工作中，探索方法中的保守主义，我们特别考虑的是，相对于替代部分秩序，它们是单调的。该替代嵌入系统是通过与初始状态空间的线性变换形成的相关系统的分解函数构建的。我们展示了这些替代嵌入系统如何允许以改善的保真度（即减少保守主义）计算可达集合。
Mixed-monotone systems are separable via a decomposition function into increasing and decreasing components, and this decomposition function allows for embedding the system dynamics in a higher-order monotone embedding system. Embedding the system dynamics in this way facilitates the efficient over-approximation of reachable sets with hyperrectangles, however, unlike the monotonicity property, which can be applied to compute, e.g., the tightest hyperrectangle containing a reachable set, the application of the mixed-monotonicity property generally results in conservative reachable set approximations. In this work, explore conservatism in the method and we consider, in particular, embedding systems that are monotone with respect to an alternative partial order. This alternate embedding system is constructed with a decomposition function for a related system, formed via a linear transformation of the initial state-space. We show how these alternate embedding systems allow for computing reachable sets with improved fidelity, i.e., reduced conservatism.
