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Logical Analysis of Hybrid Systems

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Abstract

Ensuring correct functioning of complex physical systems is among the most challenging and most important problems in computer science, mathematics, and engineering. In addition to nontrivial underlying physical system dynamics, the behaviour of complex systems is determined increasingly by computerised control and automatic analog or digital decision-making, e.g., in aviation, railway, and automotive applications. At the same time, correct decisions and control of these systems are becoming increasingly important, because more and more safety-critical processes are regulated using automatic or semiautomatic controllers, including the European Train Control System [117], collision avoidance manoeuvres in air traffic control [293, 196, 104, 238, 129, 171], car platooning technology for highways following the California PATH project [166], recent driverless vehicle technology [64], and biomedical applications like automatic glucose regulation for diabetes patients [223]. As a more general phenomenon of complex physical systems that are exemplified in these scenarios, correct system behaviour depends on correct functioning of the interaction of control with physical system dynamics and is not just an isolated property of only the control logic or only the physical system dynamics. These interactions of computation and control are more difficult to understand and get right than isolated systems. Even if the control software does not crash, the system may still malfunction, because the control software could issue unsafe control actions to the physical process. And even if the pure physics of the process is well understood, an attempt to control the process may still become unsafe, e.g., when the controller reacts to situation changes too slowly because computations take too long, or when sensor values are already outdated once the control actions finally take effect. It is the interaction of computation and control that must be taken into account. Systems with such an interaction of discrete dynamics and continuous dynamics are called hybrid dynamical systems, or just hybrid systems for short.

Time is defined so that motion looks simple [209, p. 23]

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Platzer, A. (2010). Introduction. In: Logical Analysis of Hybrid Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14509-4_1

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  • DOI: https://doi.org/10.1007/978-3-642-14509-4_1

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