A formal description of hybrid systems

Zhou, Chunlin; Wang, Ji; Ravn, Anders P.

doi:10.1007/bfb0020972

Cited by 98 publications

(35 citation statements)

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“…Inspired by He [39], Zhou et al [12] presented a hybrid variant of CSP as a language for describing hybrid systems. They gave a semantics in extended duration calculus [60] but no verification technique.…”

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confidence: 99%

Differential Dynamic Logic for Hybrid Systems

2008

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Hybrid systems are models for complex physical systems and are defined as dynamical systems with interacting discrete transitions and continuous evolutions along differential equations. With the goal of developing a theoretical and practical foundation for deductive verification of hybrid systems, we introduce a dynamic logic for hybrid programs, which is a program notation for hybrid systems. As a verification technique that is suitable for automation, we introduce a free variable proof calculus with a novel combination of real-valued free variables and Skolemisation for lifting quantifier elimination for real arithmetic to dynamic logic. The calculus is compositional, i.e., it reduces properties of hybrid programs to properties of their parts. Our main result proves that this calculus axiomatises the transition behaviour of hybrid systems completely relative to differential equations. In a case study with cooperating traffic agents of the European Train Control System, we further show that our calculus is well-suited for verifying realistic hybrid systems with parametric system dynamics.

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confidence: 99%

Differential Dynamic Logic for Hybrid Systems

2008

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“…Here, for simplicity, we focus on message passing via explicit channels of the form defined in process algebras such as CSP ( [10]), i.e., both transmitting and receiving processes wait when ready to communicate. This model of communication is carried over to Hybrid CSP (HCSP) [1] through which much of our development is done. In HCSP, a channel ch, say, mediates between processes and carries values between them when both are willing to participate; a process's willingness to communicate is indicated through two predicates associated with the channel:…”

Section: A Phenomenal Modelsmentioning

confidence: 99%

“…In particular, we introduce the notion of a mechanism description language (mdl), a language for describing mechanisms. This relates back to Craver's model, although we do not limit ourselves to biological mechanisms: we wish to consider designed formal mechanisms as might, for instance, be expressed through HCSP [1], other dialects of Process Algebras [10,15], Petri Nets [12], Statecharts [9], programming languages, etc.…”

Section: Introductionmentioning

confidence: 99%

A Phenomenal Basis for Hybrid Modelling

Hall

Rapanotti

Markov

2017

2017 IEEE International Conference on Information Reuse and Integration (IRI)

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Abstract-This work in progress extends the new mechanical philosophy from science to engineering. Engineering is the practice of organising the design and construction of artifices that satisfy needs in real-world contexts. This work shows how artifices can be described in terms of their mechanisms and composed through their observable phenomena.Typically, the engineering of real system requires descriptions in many di↵erent languages: software components will be described in code; sensors and actuators in terms of their physical and electronic characteristics; plant in terms of di↵er-ential equations, perhaps. Another aspect of this work, then, to construct a formal framework so that diverse description languages can be used to characterise sub-mechanisms.The work is situated in Problem Oriented Engineering, a design theoretic framework engineering defined by the first two authors.

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“…For distributed hybrid systems, even giving a formal semantics is very challenging [3,22,12,27]! A formal semantics has been defined for a hybrid version of CSP [3] and a hybrid version of the π-calculus [22].…”

Section: Related Workmentioning

confidence: 99%

Quantified differential invariants

Platzer

2011

Proceedings of the 14th International Conference on Hybrid Systems: Computation and Control

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We address the verification problem for distributed hybrid systems with nontrivial dynamics. Consider air traffic collision avoidance maneuvers, for example. Verifying dynamic appearance of aircraft during an ongoing collision avoidance maneuver is a longstanding and essentially unsolved problem. The resulting systems are not hybrid systems and their state space is not of the form R n . They are distributed hybrid systems with nontrivial continuous and discrete dynamics in distributed state spaces whose dimension and topology changes dynamically over time. We present the first formal verification technique that can handle the complicated nonlinear dynamics of these systems. We introduce quantified differential invariants, which are properties that can be checked for invariance along the dynamics of the distributed hybrid system based on differentiation, quantified substitution, and quantifier elimination in real-closed fields. This gives a computationally attractive technique, because it works without having to solve the infinite-dimensional differential equation systems underlying distributed hybrid systems. We formally verify a roundabout maneuver in which aircraft can appear dynamically. Categories and Subject Descriptors KeywordsDistributed hybrid systems, verification logic, quantified differential equations, quantified differential invariants *

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A formal description of hybrid systems

Cited by 98 publications

References 10 publications

Differential Dynamic Logic for Hybrid Systems

Differential Dynamic Logic for Hybrid Systems

A Phenomenal Basis for Hybrid Modelling

Quantified differential invariants

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