论文标题
具有键入符号的功能集：混合的编量性和多种发音性，用于混合非线性可及性和过滤
Functional sets with typed symbols : Mixed zonotopes and Polynotopes for hybrid nonlinear reachability and filtering
论文作者
论文摘要
网络物理系统（CPS）的验证和合成具有挑战性，到目前为止仍然提出了许多问题。在本文中，基于定义为符号类型域的功能图像的新概念，提出了一种结合渴望和懒惰评估的组成方法。语法和语义是明确区分的。连续（间隔）和离散（签名，布尔）符号类型均用于通过线性和多项式函数对依赖性进行建模，从而导致混合的ZONOTOPIC和多功能值集。多头发形用键入的符号扩展了稀疏的多项式编织。多头发形既可以传播间隔的混合编码，又可以描述逻辑门的行为。给出了功能完整性结果，以及基本非线性和切换功能的包含方法。然后提出了多重发射的卡尔曼滤波器（PKF），作为杂种非线性延伸，是杂种非线性延伸器（ZKF）。简要概述了具有随机不确定性范式的桥梁。最后，包括比较在内的几个离散，连续和混合的数值示例说明了理论结果的有效性。
Verification and synthesis of Cyber-Physical Systems (CPS) are challenging and still raise numerous issues so far. In this paper, based on a new concept of mixed sets defined as function images of symbol type domains, a compositional approach combining eager and lazy evaluations is proposed. Syntax and semantics are explicitly distinguished. Both continuous (interval) and discrete (signed, boolean) symbol types are used to model dependencies through linear and polynomial functions, so leading to mixed zonotopic and polynotopic sets. Polynotopes extend sparse polynomial zonotopes with typed symbols. Polynotopes can both propagate a mixed encoding of intervals and describe the behavior of logic gates. A functional completeness result is given, as well as an inclusion method for elementary nonlinear and switching functions. A Polynotopic Kalman Filter (PKF) is then proposed as a hybrid nonlinear extension of Zonotopic Kalman Filters (ZKF). Bridges with a stochastic uncertainty paradigm are briefly outlined. Finally, several discrete, continuous and hybrid numerical examples including comparisons illustrate the effectiveness of the theoretical results.
