混杂系统是一种实时嵌入式系统，广泛存在于航空航天、自动驾驶、交通运输、工业控制等安全性需求较高的复杂软件系统中，如何建立高效实用的混杂系统模型以确保复杂软件系统设计的正确性和可靠性是当前软件工程领域的挑战之一。.本课题拟通过微分半代数系统、符号计算与数值混合计算方法的交叉融合，构建微分半代数混杂系统模型及细化理论。具体包括:(1)采用微分代数进程代数语言及带微分半代数方程组状态转移标记的混杂变迁系统定义微分半代数混杂系统模型，构建其语法语义，在此基础上建立模型的等价关系；(2)通过符号和数值混合计算研究等价关系的判定及计算方法，根据等价关系的计算方法，实现等价关系的可判定性；(3)采用微分半代数变迁系统研究微分半代数混杂系统模型的细化理论，及行为等价在细化后的可保持性。最后构建复杂软件系统模型实例，验证所构建的模型及理论在实际复杂软件系统设计中的应用，以提高软件系统安全性及可靠性。

Hybrid system is a kind of real-time embedded systems, which is widely used in complex software systems with high security requirements, such as aerospace, autonomous driving, transportation and industrial control. How to establish efficient and practical hybrid system model to ensure the correctness and reliability of complex software system design is one of the challenges of software engineering..In this paper, the hybrid system model and refinement theory on differential semi-algebraic hybrid system are constructed by integrating of differential semi-algebraic hybrid system, symbolic computation and numerical computation. Specifically, it includes, (1) Using the differential algebra process algebra language and the hybrid transition system with the state transition mark of the differential semi-algebraic equations to define the differential semi-algebraic hybrid system model, constructing its syntax and semantics, and establishing the equivalence relation of the model. (2) Studying the judgment and calculation method of equivalence through symbolic calculation and numerical computation, and realizing the decidability of the equivalence relation according to the calculation of equivalence. (3) Using the differential algebra transition system to research the refinement theory and the maintainability of behavioral equivalence after refinement. Finally, an example of complex software system model is built to verify the application of the model and theory in the design of complex software system, so as to improve the software security and reliability.