Process Algebraic Approach to Hybrid Systems

Abstract

Process algebra is a theoretical framework for the modelling and analysis of the behaviour of concurrent discrete event systems that has been developed within computer science in past quarter century. It has generated a deeper understanding of the nature of concepts such as observable behaviour in the presence of nondeterminism, system composition by interconnection of concurrent component systems, and notions of behavioural equivalence of such systems. It has contributed fundamental concepts such as bisimulation, and has been succesfully used in a wide range of problems and practical applications in concurrent systems. We believe that the basic tenets of process algebra are highly compatible with the behavioural approach to dynamical systems. In our contribution we present an extension of classical process algebra that is suitable for the modelling and analysis of continuous and hybrid dynamical systems. It provides a natural framework for the concurrent composition of such systems, and can deal with nondeterministic behaviour that may arise from the occurrence of internal switching events. Standard process algebraic techniques lead to the characterization of the observable behaviour of such systems as equivalence classes under some suitably adapted notion of bisimulation.

Constitutive Hybrid Processes: a Process-Algebraic Semantics for Hybrid Bond Graphs

“…Other hybrid process algebras have been developed, such as ACP srt hs [24], hybrid [25] and the -calculus [26], but they all have a property inherited from hybrid automata theory [27,28] requiring that abstract actions are used to represent discontinuities in the physics. HyPA and BHPC [29] are the only hybrid process algebras that allow discontinuous behavior without explicit communication between actions. Finally, we chose HyPA over BHPC, because the latter was not available when the research presented in this paper began, but also because it allows us to prove statements about the general structure of constitutive processes using equational reasoning, which has not yet been developed for BHPC.…”

“…HyPA and BHPC [29] are the only hybrid process algebras that allow discontinuous behavior without explicit communication between actions. Finally, we chose HyPA over BHPC, because the latter was not available yet when the research presented in this paper started, but also because it allows us to prove statements about the general structure of constitutive processes using equational reasoning, which has not yet been developed for BHPC.…”

Modeling and Analysis of Radiation Therapy System with Respiratory Compensation Using Uppaal

“…process algebras [6], [11], [15], [16], [19], [22], timed automaton [2], hybrid automaton [1], SPIN [12] and Uppaal [3] tools and a lot more, see [5] for a wider overview. Successful application of formal techniques have been reported in different areas, such as the automotive industry [10], electronics [18], industrial devices control [17] and other.…”

Compositional Modelling of Stochastic Hybrid Systems

“…Automata approaches making distinction between active (or output) actions and passive (or input) actions are [JSvdS03] and [LSV01]. In the process algebraic approach [BKU05,Cui04], the processes are represented by algebraic formulas, which can be combined by using operators (like parallel composition operators) to form new algebraic formulas. In the Petri net approach [DA98], discrete state Petri nets are extended with continuous variables to form a hybrid Petri net.…”