Hybrid systems are complex systems where a software controller interacts with a physical environment, usually named a plant, through sensors and actuators. The specification and design of such systems usually rely on the description of both continuous and discrete behaviours. From complex embedded systems to autonomous vehicles, these systems became quite common, including in safety critical domains. However, their formal verification and validation as a whole is still a challenge. To address this challenge, this article contributes to the definition of a reusable and tool supported formal framework handling the design and verification of hybrid system models that integrate both discrete (the controller part) and continuous (the plant part) behaviours. This framework includes the development of a process for defining a class of basic theories and developing domain theories and then the use of these theories to develop a generic model and system-specific models. To realise this framework, we present a formal proof tool chain, based on the Event-B correct-by-construction method and its integrated development environment Rodin, to develop a set of theories, a generic model, proof processes, and the required properties for designing hybrid systems in Event-B. Our approach relies on hybrid automata as basic models for such systems. Discrete and continuous variables model system states and behaviours are given using discrete state changes and continuous evolution following a differential equation. The proposed approach is based on refinement and proof using the Event-B method and the Rodin toolset. Two case studies borrowed from the literature are used to illustrate our approach. An assessment of the proposed approach is provided for evaluating its extensibility, effectiveness, scalability, and usability.

中文翻译：

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事件-B 杂交

混合系统是复杂系统，其中软件控制器通过传感器和执行器与物理环境（通常称为工厂）进行交互。此类系统的规范和设计通常依赖于对连续和离散行为的描述。从复杂的嵌入式系统到自动驾驶汽车，这些系统变得相当普遍，包括在安全关键领域。然而，它们作为一个整体的形式验证和验证仍然是一个挑战。为了应对这一挑战，本文有助于定义一个可重用和工具支持的正式框架，以处理集成离散（控制器部分）和连续（工厂部分）行为的混合系统模型的设计和验证。该框架包括开发定义一类基本理论和开发领域理论的过程，然后使用这些理论开发通用模型和系统特定模型。为了实现这个框架，我们提出了一个形式化的证明工具链，基于Event-B正确的构造方法及其集成开发环境Rodin，开发了一套理论、一个通用模型、证明过程和所需的属性用于在 Event-B 中设计混合系统。我们的方法依赖于混合自动机作为此类系统的基本模型。离散和连续变量模型系统状态和行为是使用离散状态变化和遵循微分方程的连续演化给出的。所提出的方法基于使用 Event-B 方法和罗丹工具集的改进和证明。从文献中借来的两个案例研究用于说明我们的方法。对提议的方法进行了评估，以评估其可扩展性、有效性、可扩展性和可用性。