FTRTFT 1994, ProCoS 1994: Formal Techniques in Real-Time and Fault-Tolerant Systems pp 716-737

# A calculus for hybrid sampled data systems

• Yu Huiqun
• Paritosh K. Pandya
• Sun Yongqiang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 863)

## 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.

## Keywords

Difference Equation Hybrid System Boolean Function Heat System Predicate Symbol
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Yu Huiqun
• 1
• Paritosh K. Pandya
• 1
• Sun Yongqiang
• 2
1. 1.UNU/IISTMacau
2. 2.Department of Computer Science and EngineeringJiaotong UniversityShanghaiP.R.China