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Computer Science

A Compositional Approach to the Verification of Hybrid Systems

Profile image of Lacramioara AstefanoaeiLacramioara Astefanoaei

2016, Lecture Notes in Computer Science

https://doi.org/10.1007/978-3-319-30734-3_8
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16 pages

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Abstract

The increase of complexity in modelling systems and the chances of success when model-checking them tend to be inversely proportional. This mere observation justifies plainly the need to investigate alternative ways for verification. In this paper we present such an alternative which uses a compositional verification rule. The basic idea is to automatically compute local properties and combine them such that together they are strong enough to prove global safety properties of systems. In we showed how such a rule works in the framework of timed systems with a fixed number of components and in [3] how the whole approach can be extended to the parameterised case. The application of the compositional verification rule can be pushed even further with respect to two directions: (1) hybrid and (2) parametric systems. This is the subject of the present paper.

Figures (3)
Fig. 1. Temperature Controller System
Fig. 1. Temperature Controller System
Fig. 3. Illustrating Components with History Clocks for (Inter) Actions Adding History Clocks. History clocks are associated with actions and in- teractions. For a component B we use B” to denote its extension with history clocks. The extension of the system is obtained from the extensions of the com- ponents alone together with the history clocks for interactions. As an illustration, Figure 3 shows the extension of the system in Figure 1. The mechanism of history clocks can be understood as follows. When an in- teraction a takes place, the history clocks h, and h, associated to a and to any action a € a are reset. Thus they measure the time passed from the last occur- rence of a, respectively of a. We note that, since there is no timing constraint involving history clocks, the behaviour of the components is not changed by the addition of history clocks.
Fig. 3. Illustrating Components with History Clocks for (Inter) Actions Adding History Clocks. History clocks are associated with actions and in- teractions. For a component B we use B” to denote its extension with history clocks. The extension of the system is obtained from the extensions of the com- ponents alone together with the history clocks for interactions. As an illustration, Figure 3 shows the extension of the system in Figure 1. The mechanism of history clocks can be understood as follows. When an in- teraction a takes place, the history clocks h, and h, associated to a and to any action a € a are reset. Thus they measure the time passed from the last occur- rence of a, respectively of a. We note that, since there is no timing constraint involving history clocks, the behaviour of the components is not changed by the addition of history clocks.
Fig. 4. Parametric Temperature Controller System Returning to the temperature controller example, we recall that the constants used in the system are values for minimum and maximum bounds, recovering times for rods, temperature increase and decrease rates. If we see all these as parameters, the corresponding system is the one illustrated in Figure 4.
Fig. 4. Parametric Temperature Controller System Returning to the temperature controller example, we recall that the constants used in the system are values for minimum and maximum bounds, recovering times for rods, temperature increase and decrease rates. If we see all these as parameters, the corresponding system is the one illustrated in Figure 4.

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