利用状态变换提高混合单调可达集逼近的保真度
Improving the Fidelity of Mixed-Monotone Reachable Set Approximations via State Transformations
摘要：
混合单调系统可以通过分解函数分离成递增和递减分量，并且该分解函数允许将系统动态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用超矩形有效地过度逼近可达集，然而，与单调性属性不同，单调性属性可以应用于计算，例如，包含可达集的最紧超矩形，混合单调性性质的应用通常导致保守的可达集近似。在这项工作中，探讨保守性的方法，我们认为，特别是，嵌入系统是单调的替代偏序。这个交替嵌入系统是用一个相关系统的分解函数构造的，该分解函数是通过初始状态空间的线性变换形成的。我们展示了这些交替嵌入系统如何允许计算具有改进保真度的可达集，即，减少保守主义。
英文摘要：
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.
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