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Modeling and Validating Hybrid Systems Using VDM and Mathematica

Bernhard K. Aichernig·Reinhold Kainhofer
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Abstract

Hybrid systems are characterized by the hybrid evolution of their state: A part of the state changes discretely, the other part changes continuously over time. Typically, modern control applications belong to this class of systems, where a digital controller interacts with a physical environment. In this article we illustrate how a combination of the formal method VDM and the computer algebra system Mathematica can be used to model and simulate both aspects: the control logic and the physics involved. A new Mathematica package emulating VDM-SL has been developed that allows the integration of differential equation systems into formal specifications. The SAFER example from Kelly (1997) serves to demonstrate the new simulation capabilities Mathematica adds: After the thruster selection process, the astronaut's actual position and velocity is calculated by numerically solving Euler's and Newton's equations for rotation and translation. Furthermore, interactive validation is supported by a graphical user interface and data animation.

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Bernhard K. Aichernig, Reinhold Kainhofer. 2004-07-20. Modeling and Validating Hybrid Systems Using VDM and Mathematica. https://arxiv.org/abs/cs/0407050

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