Real world systems of interest often feature interactions between discrete and continuous dynamics. Various hybrid system formalisms have been used to model and analyse this combination of dynamics, ranging from mathematical descriptions, e.g., using impulsive differential equations and switching, to automata-theoretic and language-based approaches. This paper bridges two such formalisms by showing how various classes of switched systems can be modeled using the language of hybrid programs from differential dynamic logic (dL). The resulting models enable the formal specification and verification of switched systems using dL and its existing deductive verification tools such as KeYmaera X. Switched systems also provide a natural avenue for the generalization of dL's deductive proof theory for differential equations. The completeness results for switched system invariants proved in this paper enable effective safety verification of those systems in dL.

中文翻译：

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交换系统作为混合程序

感兴趣的现实世界系统通常具有离散和连续动力学之间的相互作用。从数学描述（例如使用脉冲微分方程和切换）到自动机理论和基于语言的方法，各种各样的混合系统形式已被用于建模和分析动力学的这种组合。本文通过展示如何使用来自差分动态逻辑（dL）的混合程序语言来建模各种类型的交换系统，从而弥合了这两种形式主义。结果模型可以使用dL及其现有的演绎验证工具（例如KeYmaera X）对交换系统进行正式规范和验证。交换系统还为dL的微分方程演绎证明理论的推广提供了自然的途径。