Verification and Control of Probabilistic Rectangular Hybrid Automata

Abstract

Abstract. Hybrid systems are characterised by a combination of discrete and continuous components. In many application areas for hybrid systems, such as vehicular control and systems biology, stochastic behaviour is intrinsic. This has led to the development of stochastic extensions of formalisms, such as hybrid automata, for the modelling of hybrid systems, together with their associated verification and controller synthesis algorithms, in order to allow reasoning about quantitative properties such as "the vehicle's speed will reach 50kph within 10 seconds with probability at least 0.99". We consider probabilistic rectangular hybrid automata, which generalise the well-known class of rectangular hybrid automata with the possibility of representing random behavior of the discrete components of the system, permitting the modeling of the likelihood of faults, choices in randomised algorithms and message losses. We highlight the differences between verification and control problems for probabilistic rectangular hybrid automata and the corresponding problems for non-probabilistic rectangular hybrid automata. Furthermore, we will describe the effect of assumptions on the underlying model of time (discrete or continuous) on the considered verification and control problems. Finally, we will also consider how probabilistic rectangular hybrid automata can be used as abstract models for more general classes of stochastic hybrid systems.

Comparing Two Approaches to Include Stochasticity in Hybrid Automata

“…For example discrete probability distributions have been added to decidable subclasses of hybrid automata [21,22], which can be analyzed e.g. with the SISAT tool using abstraction [23].…”