基于约束zonotope的非线性离散时间系统集值状态估计保证方法
Guaranteed methods based on constrained zonotopes for set-valued state estimation of nonlinear discrete-time systems
AI总结：
本文提出基于均值扩展和一阶Taylor扩展的约束zonotope方法，用于非线性离散时间系统的集值状态估计，在保留计算优势的同时实现了更紧的预测和更新包络。
摘要：
本文提出了针对具有未知但有界不确定性的非线性离散时间系统进行集值状态估计的新方法。单个时间步包括通过非线性动力学传播系统状态的包络（预测），然后将该集合与有界误差测量的交集进行包络（更新）。当这些包络由区间、椭球、平行多面体和zonotope等简单集合表示时，某些集合运算可能非常保守。然而，使用一般凸多面体的计算要求要高得多。为了解决这个问题，本文提出了两种新方法，即均值扩展和一阶Taylor扩展，用于通过非线性映射高效地传播约束zonotope。这些方法以一致的方式扩展了现有的zonotope方法。示例表明，与zonotopic估计方法相比，这些扩展产生了更紧的预测包络，同时在很大程度上保留了zonotope的计算优势。此外，它们能够实现更紧的更新包络，因为约束zonotope比zonotope能更准确地表示交集。
英文摘要：
This paper presents new methods for set-valued state estimation of nonlinear discrete-time systems with unknown-but-bounded uncertainties. A single time step involves propagating an enclosure of the system states through the nonlinear dynamics (prediction), and then enclosing the intersection of this set with a bounded-error measurement (update). When these enclosures are represented by simple sets such as intervals, ellipsoids, parallelotopes, and zonotopes, certain set operations can be very conservative. Yet, using general convex polytopes is much more computationally demanding. To address this, this paper presents two new methods, a mean value extension and a first-order Taylor extension, for efficiently propagating constrained zonotopes through nonlinear mappings. These extend existing methods for zonotopes in a consistent way. Examples show that these extensions yield tighter prediction enclosures than zonotopic estimation methods, while largely retaining the computational benefits of zonotopes. Moreover, they enable tighter update enclosures because constrained zonotopes can represent intersections much more accurately than zonotopes.
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