Marius C. Bujorianu

Bisimulation for general stochastic hybrid systems

In this paper we define a bisimulation concept for some very general models for stochastic hybrid systems (general stochastic hybrid systems). The definition of bisimulation builds on the ideas of Edalat and of Larsen and Skou and of Joyal, Nielsen and Winskel. The main result is that this bisimulation for GSHS is indeed an equivalence relation. The secondary result is that this bisimulation relation for the stochastic hybrid system models used in this paper implies the same kind of bisimulation for their continuous parts and respectively for their jumping structures.

Integration of Specification Languages Using Viewpoints

This work provides a general integration mechanism for specification languages motivated by partial specification. We use category theory to formalise specification languages and define a relational semantic framework. We show some inherent limits of the approach, and propose a solution inspired from Z semantics to overcome it. An integration of Z and CCS is considered as an example.

An Integrated Specification Framework for Embedded Systems

In this paper, we address the complex issue of representation of continuous behaviour of the environment of the embedded controllers. In our approach, we propose two novel ideas. One is to consider the weak solutions to describe the evolution of the dynamical systems. The second novelty is to make available, at the design stage, the information about concurrent evolutions of the environment. We propose a new logic called the Hilbertian logic for representing continuous behaviours. Then, we use the causal order relations to integrate this logic with a probabilistic process algebra. For the resulting specification framework, we construct a denotational semantics rich in mathematical properties.

DISTRIBUTED STOCHASTIC HYBRID SYSTEMS

Abstract We consider a theoretical, but very general mathematical model of control systems, namely stochastic hybrid systems. Then we study how to define concurrency for these systems.

Contingent Hybrid Systems

Abstract This work proposes the first steps for studying resilient control for uncertain hybrid systems. We take a rather radical approach and consider the situations of severe uncertainty. This requires the replacement of classical Kolmogorov probabilities with special concepts from the generalized measure theory. To achieve this goal, we need a rigorous and carefully developed mathematical framework, which constitutes the major contribution of this paper. Technically, the resilience framework of hybrid systems is defined in two steps. First, we introduce the contingent hybrid system that is a mathematical model where uncertainty is quantized using both probabilities and generalized measures. Then, the concept of lithe decision is introduced for this model. The new method combines decision theory with model predictive control and statistics for uncertainty measures.

Model checking for a class of performance properties of fluid stochastic models

Recently, there is an explosive development of fluid approa- ches to computer and distributed systems. These approaches are inherently stochastic and generate continuous state space models. Usually, the performance measures for these systems are defined using probabilities of reaching certain sets of the state space. These measures are well understood in the discrete context and many efficient model checking procedures have been developed for specifications involving them. The continuous case is far more complicated and new methods are necessary. In this paper we propose a general model checking strategy founded on advanced concepts and results of stochastic analysis. Due to the problem complexity, in this paper, we achieve the first necessary step of characterizing mathematically the problem. We construct upper bounds for the performance measures using Martin capacities. We introduce a concept of bisimulation that preserves the performance measures and a metric that characterizes the bisimulation

Viewpoint Development of Stochastic Hybrid Systems

Nowadays, due to the explosive spreading of networked and highly distributed systems, mastering system complexity becomes a critical issue. Two development and verification paradigms have become more popular: viewpoints and randomisation. The viewpoints offer large freedom and introduce concurrency and compositionality in the development process. Randomisation is now a traditional method for reducing complexity (comparing with deterministic models) and it offers finer analytical analysis tools (quantification over non-determinism, multi-valued logics, etc). In this paper, we propose a combination of these two paradigms introducing a viewpoint methodology for systems with stochastic behaviours

True Concurrent Stochastic Processes

Abstract In this work we present an algebraic framework for true concurrent stochastic processes. Concurrency is modelled using partial order relations. Markov processes are considered using an abstraction given by their excessive functions. Applications include embedded systems, as cardiac stimulators, encephalogram analysers and air traffic control systems.

Towards Correspondence Carrying Specifications

In this work we study the unification of heterogeneous partial specifications using category theory. We propose an alternative to institution morphisms, which we call (abstract) correspondences carrying specifications. Our methodology is illustrated using a categorical specification style inspired by the state-and-operations style of Z as well as a categorical unification procedure.

An Interpretation of Concurrent Hybrid Time Systems over Multi-clock Systems

In this paper, we present a multiclock model for real time abstractions of hybrid systems. We call Hybrid Time systems the resulting model, which is constructed using category theory. Such systems are characterized by heterogeneous timing, some components having discrete time and others continuous time. We define a timed (or clock) system as a functor from a category of states to a category of time values. We further define concurrent composition operators and bisimulation.