Abstract
This paper addresses the problem of formally describing hybrid sampled data systems. Using the techniques proposed in Duration Calculus, we first develop a formal calculus, called Accumulation Calculus, for specifying real valued step functions of time. The key idea is that such functions are described using their integrals in bounded closed intervals. The semantics of Accumulation Calculus formulae as well as a relatively complete axiom system are presented.
Sampled data are a particular type of step functions which change at regular periods only. Suitable axioms are introduced to capture this. Special formulae and modalities are introduced to describe such data. Some proof rules are proposed for these modalities and shown to be sound. Resulting system is called a calculus for hybrid sampled data systems. Well established representations of sampled data systems from control theory such as difference equations can be directly translated into such formulae. At the same time the calculus allows reasoning about asynchronous events and their effect on sampled data. A detailed case study of a heating system is given to illustrate the applicability of the calculus to hybrid sampled data systems.
This work is supported by the National Hi-Tech R&D Programme of China and UNU/IIST in the joint project DeTfoRS.
On leave from Department of Computer Science and Engineering, Jiaotong University, Shanghai 200030, P.R.China
On leave from Computer Science Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
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Huiqun, Y., Pandya, P.K., Yongqiang, S. (1994). A calculus for hybrid sampled data systems. In: Langmaack, H., de Roever, WP., Vytopil, J. (eds) Formal Techniques in Real-Time and Fault-Tolerant Systems. FTRTFT ProCoS 1994 1994. Lecture Notes in Computer Science, vol 863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58468-4_192
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DOI: https://doi.org/10.1007/3-540-58468-4_192
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