A Compositional Approach to the Design of Hybrid Systems

Jozef Hooman

Appeared in: Hybrid Systems, LNCS 736, Springer-Verlag, pages 121-148, 1993.


To specify and verify distributed real-time systems,classical Hoare triples are extended with timing primitives and the interpretation is modified to be able to specify non-terminating computations. For these modified triples a compositional proof system has been formulated. Compositionality supports top-down program derivation, and by using a dense time domain also hybrid systems with continuous components can be designed. This is illustrated by a process control example of a water level monitoring system. First we prove the correctness of a control strategy in terms of a continuous interface. Next, to obtain a discrete interface, a sensor and an actuator are introduced. Using their specifications only, a suitable specification of the control unit is derived. This reduces the design of the system to the conventional problem of deriving a program according to its specification. Finally the control unit is extended, in a modular way, with error detection features.