32,624 research outputs found
Statistical Model Checking for Stochastic Hybrid Systems
This paper presents novel extensions and applications of the UPPAAL-SMC model
checker. The extensions allow for statistical model checking of stochastic
hybrid systems. We show how our race-based stochastic semantics extends to
networks of hybrid systems, and indicate the integration technique applied for
implementing this semantics in the UPPAAL-SMC simulation engine. We report on
two applications of the resulting tool-set coming from systems biology and
energy aware buildings.Comment: In Proceedings HSB 2012, arXiv:1208.315
Different Approaches on Stochastic Reachability as an Optimal Stopping Problem
Reachability analysis is the core of model checking of time systems. For
stochastic hybrid systems, this safety verification method is very little supported mainly
because of complexity and difficulty of the associated mathematical problems. In this
paper, we develop two main directions of studying stochastic reachability as an optimal
stopping problem. The first approach studies the hypotheses for the dynamic programming
corresponding with the optimal stopping problem for stochastic hybrid systems.
In the second approach, we investigate the reachability problem considering approximations
of stochastic hybrid systems. The main difficulty arises when we have to prove the
convergence of the value functions of the approximating processes to the value function
of the initial process. An original proof is provided
Model checking stochastic hybrid systems
The interplay of random phenomena with discrete-continuous dynamics deserves increased attention in many systems of growing importance. Their verification needs to consider both stochastic behaviour and hybrid dynamics. In the verification of classical hybrid systems, one is often interested in deciding whether unsafe system states can be reached. In the stochastic setting, we ask instead whether the probability of reaching particular states is bounded by a given threshold. In this thesis, we consider stochastic hybrid systems and develop a general abstraction framework for deciding such problems. This gives rise to the first mechanisable technique that can, in practice, formally verify safety properties of systems which feature all the relevant aspects of nondeterminism, general continuous-time dynamics, and probabilistic behaviour. Being based on tools for classical hybrid systems, future improvements in the effectiveness of such tools directly carry over to improvements in the effectiveness of our technique.
We extend the method in several directions. Firstly, we discuss how we can handle continuous probability distributions. We then consider systems which we are in partial control of. Next, we consider systems in which probabilities are parametric, to analyse entire system families at once. Afterwards, we consider systems equipped with rewards, modelling costs or bonuses. Finally, we consider all orthogonal combinations of the extensions to the core model.In vielen Systemen wachsender Bedeutung tritt zufallsabhaÌngiges Verhalten gleichzeitig mit diskret-kontinuierlicher Dynamik auf. Um solche Systeme zu verifizieren, muÌssen sowohl ihr stochastisches Verhalten als auch ihre hybride Dynamik betrachtet werden. In der Analyse klassischer hybrider Systeme ist eine wichtige Frage, ob unsichere ZustaÌnde erreicht werden koÌnnen. Im stochastischen Fall fragen wir stattdessen nach garantierten Wahrscheinlichkeitsschranken. In dieser Arbeit betrachten wir stochastische hybride Systeme und entwickeln eine allgemeine Abstraktionsmethode um Probleme dieser Art zu entscheiden. Dies ermoÌglicht die erste automatische und praktisch anwendbare Methode, die Sicherheitseigenschaften von Systeme beweisen kann, in denen Nichtdeterminismus, komplexe Dynamik und probabilistisches Verhalten gleichzeitig auftreten. Da die Methode auf Analysetechniken fuÌr nichtstochastische hybride Systeme beruht, profitieren wir sofort von zukuÌnftigen Verbesserungen dieser Verfahren.
Wir erweitern diese Grundmethode in mehrere Richtungen: ZunaÌchst ergaÌnzen wir das Modell um kontinuierliche Wahrscheinlichkeitsverteilungen. Dann betrachten wir partiell kontrollierbare Systeme. Als naÌchstes untersuchen wir parametrische Systeme, um eine Klasse aÌhnlicher Modelle gleichzeitig behandeln. AnschlieĂend betrachten wir Eigenschaften, die auf der AbwaÌgung von Kosten und Nutzen beruhen. SchlieĂlich zeigen wir, wie diese Erweiterungen orthogonal kombiniert werden koÌnnen
Exact and Approximate Abstraction for Classes of Stochastic Hybrid Systems
A stochastic hybrid system contains a collection of interacting discrete and continuous components, subject to random behaviour. The formal verification of a stochastic hybrid system often comprises a method for the generation of a finite-state probabilistic system which either represents exactly the behaviour of the stochastic hybrid system, or which approximates conservatively its behaviour. We extend such abstraction-based formal verification of stochastic hybrid systems in two ways. Firstly, we generalise previous results by showing how bisimulation-based abstractions of non-probabilistic hybrid automata can be lifted to the setting of probabilistic hybrid automata, a subclass of stochastic hybrid systems in which probabilistic choices can be made with respect to finite, discrete alternatives only. Secondly, we consider the problem of obtaining approximate abstractions for discrete-time stochastic systems in which there are continuous probabilistic choices with regard to the slopes of certain system variables. We restrict our attention to the subclass of such systems in which the approximate abstraction of such a system, obtained using the previously developed techniques of Fraenzle et al., results in a probabilistic rectangular hybrid automaton, from which in turn a finite-state probabilistic system can be obtained. We illustrate this technique with an example, using the probabilistic model checking tool PRISM
Learning and testing stochastic discrete event
Dissertação de mestrado em Engenharia de InformĂĄticaSistemas de eventos discretos (DES) sĂŁo uma importante subclasse de sistemas (Ă luz da teoria dos sistemas). Estes tĂȘm sido usados, particularmente na indĂșstria para analisar e modelar um vasto conjunto de sistemas reais, tais como, sistemas de produção, sistemas de computador, sistemas de controlo de trĂĄfego e sistemas hĂbridos.
O nosso trabalho explora uma extensĂŁo de DES com ĂȘnfase nos processos estocĂĄsticos, comummente chamado como sistemas de eventos discretos estocĂĄsticos (SDES). Existe assim a necessidade de estabelecer uma abstração estocĂĄstica atravĂ©s do uso de processos semi-Markovianos generalizados (GSMP) para SDES.
Assim, o objetivo do nosso trabalho Ă© propor uma metodologia e um conjunto de algoritmos para aprendizagem de GSMP, usar tĂ©cnicas de model-checking estatĂstico para a verificação e propor duas novas abordagens para teste de DES e SDES (respetivamente, nĂŁo estocasticamente e estocasticamente).
Este trabalho tambĂ©m introduz uma noção de modelação, analise e verificação de sistemas contĂnuos e modelos de perturbação no contexto da verificação por model-checking estatĂstico.Discrete event systems (DES) are an important subclass of systems (in systems theory). They have been used, particularly in industry, to analyze and model a wide variety of real systems, such as production systems, computer systems, traffic systems, and hybrid systems. Our work explores an extension of DES with an emphasis on stochastic processes, commonly called stochastic discrete event systems (SDES). There was a need to establish a stochastic abstraction for SDES through generalized semi-Markov processes (GSMP). Thus, the aim of our work is to propose a methodology and a set of algorithms for GSMP learning, using model checking techniques for verification, and to propose two new approaches for testing DES and SDES (non-stochastically and stochastically). This work also introduces a notion of modeling, analysis, and verification of continuous systems and disturbance models in the context of verifiable statistical model checking
Stochastic hybrid system : modelling and verification
Hybrid systems now form a classical computational paradigm unifying discrete and continuous system aspects. The modelling, analysis and verification of these systems are very difficult.
One way to reduce the complexity of hybrid system models is to consider randomization. The need for stochastic models has actually multiple motivations. Usually, when building models complete information is not available and we have to consider stochastic versions. Moreover, non-determinism and uncertainty are inherent to complex systems. The stochastic approach can be thought of as a way of quantifying non-determinism (by assigning a probability to each
possible execution branch) and managing uncertainty. This is built upon to the - now classical - approach in algorithmics that provides polynomial complexity algorithms via randomization.
In this thesis we investigate the stochastic hybrid systems, focused on modelling and analysis.
We propose a powerful unifying paradigm that combines analytical and formal methods. Its
applications vary from air traffic control to communication networks and healthcare systems.
The stochastic hybrid system paradigm has an explosive development. This is because of its
very powerful expressivity and the great variety of possible applications. Each hybrid system model can be randomized in different ways, giving rise to many classes of stochastic hybrid systems.
Moreover, randomization can change profoundly the mathematical properties of discrete and continuous aspects and also can influence their interaction. Beyond the profound foundational and semantics issues, there is the possibility to combine and cross-fertilize techniques from analytic mathematics (like optimization, control, adaptivity, stability, existence and uniqueness of trajectories, sensitivity analysis) and formal methods (like bisimulation, specification, reachability
analysis, model checking). These constitute the major motivations of our research. We
investigate new models of stochastic hybrid systems and their associated problems. The main difference from the existing approaches is that we do not follow one way (based only on continuous or discrete mathematics), but their cross-fertilization. For stochastic hybrid systems we introduce concepts that have been defined only for discrete transition systems. Then, techniques
that have been used in discrete automata now come in a new analytical fashion. This is partly explained by the fact that popular verification methods (like theorem proving) can hardly work even on probabilistic extensions of discrete systems. When the continuous dimension is added, the idea to use continuous mathematics methods for verification purposes comes in a natural
way.
The concrete contribution of this thesis has four major milestones:
1. A new and a very general model for stochastic hybrid systems;
2. Stochastic reachability for stochastic hybrid systems is introduced together with an approximating method to compute reach set probabilities;
3. Bisimulation for stochastic hybrid systems is introduced and relationship with reachability analysis is investigated.
4. Considering the communication issue, we extend the modelling paradigm
Abstractions of stochastic hybrid systems
Many control systems have large, infinite state space that can not be easily abstracted. One method to analyse and verify these systems is reachability analysis. It is frequently used for air traffic control and power plants. Because of lack of complete information about the environment or unpredicted changes, the stochastic approach is a viable alternative. In this paper, different ways of introducing rechability under uncertainty are presented. A new concept of stochastic bisimulation is introduced and its connection with the reachability analysis is established. The work is mainly motivated by safety critical situations in air traffic control (like collision detection and avoidance) and formal tools are based on stochastic analysis
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