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首页> 外文期刊>Automatic Control, IEEE Transactions on >Computing Abstractions of Nonlinear Systems
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Computing Abstractions of Nonlinear Systems

机译：非线性系统的抽象计算

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摘要

Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid systems and to design finite state controllers that provably enforce predefined specifications. We present a novel algorithm to compute such finite state models for nonlinear discrete-time and sampled systems which depends on quantizing the state space using polyhedral cells, embedding these cells into suitable supersets whose attainable sets are convex, and over-approximating attainable sets by intersections of supporting half-spaces. We prove a novel recursive description of these half-spaces and propose an iterative procedure to compute them efficiently. We also provide new sufficient conditions for the convexity of attainable sets which imply the existence of the aforementioned embeddings of quantizer cells. Our method yields highly accurate abstractions and applies to nonlinear systems under mild assumptions, which reduce to sufficient smoothness in the case of sampled systems. Its practicability in the design of discrete controllers for nonlinear continuous plants under state and control constraints is demonstrated by an example.
机译：足够准确的有限状态模型（也称为符号模型或离散抽象），使人们可以应用最初为纯粹离散系统开发的全自动方法，正式考虑连续系统和混合系统，并设计可证明强制执行预定义规范的有限状态控制器。我们提出了一种新颖的算法来计算此类非线性离散时间和采样系统的有限状态模型，该算法依赖于使用多面体单元对状态空间进行量化，将这些单元嵌入到其可达到的集合为凸的合适超集中，并通过相交来过度逼近可实现的集合支持半空间。我们证明了这些半空间的新颖递归描述，并提出了一个迭代过程来有效地计算它们。我们还为可​​达到的集合的凸性提供了新的充分条件，这意味着存在上述量化单元的嵌入。我们的方法产生了高度准确的抽象，并适用于在温和假设下的非线性系统，在采样系统的情况下，这种方法会降低到足够的平滑度。通过实例证明了其在非线性连续工厂离散控制器设计中在状态和控制约束下的实用性。

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