DISTRIBUTED STOCHASTIC HYBRID SYSTEMS (original) (raw)

Structured modeling of concurrent stochastic hybrid systems

… , Modelling and Analysis of Timed and …, 2004

We propose a modeling language for structured specification of interacting components with both hybrid and stochastic dynamics. The behavior of a stochastic hybrid agent is described using a hybrid automaton whose dynamics is specified by stochastic differential equations and probabilistic jumps. Stochastic hybrid agents interact with other agents using shared variables. The operations of parallel composition, instantiation and hiding are defined to allow hierarchical descriptions of complex agents. We report on a stochastic extension of the modeling environment Charon for hybrid systems, a simulation tool, and case studies using the tool.

Toward a General Theory of Stochastic Hybrid Systems

2008

In this chapter we set up a mathematical structure, called Markov string, to obtaining a very general class of models for stochastic hybrid systems. Markov Strings are, in fact, a class of Markov processes, obtained by a mixing mechanism of stochastic processes, introduced by Meyer. We prove that Markov strings are strong Markov processes with the càdlàg property. We then show how a very general class of stochastic hybrid processes can be embedded in the framework of Markov strings. This class, which is referred to as the General Stochastic Hybrid Systems (GSHS), includes as special cases all the classes of stochastic hybrid processes, proposed in the literature.

Functional Abstractions of Stochastic Hybrid Systems

Analysis and Design of Hybrid Systems 2006, 2006

The verification problem for stochastic hybrid systems is quite difficult. One method to verify these systems is stochastic reachability analysis. Concepts of abstractions for stochastic hybrid systems are needed to ease the stochastic reachability analysis. In this paper, we set up different ways to define abstractions for stochastic hybrid systems, which preserve the parameters of stochastic reachability. A new concept of stochastic bisimulation is introduced and its connection with equivalence of stochastic processes is established.

Approximate Abstractions of Stochastic Hybrid Systems

IEEE Transactions on Automatic Control, 2011

We present a constructive procedure for obtaining a finite approximate abstraction of a discrete-time stochastic hybrid system. The procedure consists of a partition of the state space of the system and depends on a controllable parameter. Given proper continuity assumptions on the model, the approximation errors introduced by the abstraction procedure are explicitly computed and it is shown that they can be tuned through the parameter of the partition. The abstraction is interpreted as a Markov set-Chain. We show that the enforcement of certain ergodic properties on the stochastic hybrid model implies the existence of a finite abstraction with finite error in time over the concrete model, and allows introducing a finite-time algorithm that computes the abstraction.

Towards Stochastic Formal Methods for Hybrid Systems

2000

This paper considers the issue of developing formal methods for stochastic hybrid systems. The stochastic continuous behaviour breaks many essential properties of hybrid automata. Therefore, it becomes very difficult to extend to the stochastic case the well-established formal methods for hybrid systems. We propose a radical approach of tailoring the basic foundations of formal methods for the stochastic case. Our

Modeling and analysis of networked control systems using stochastic hybrid systems

This paper aims at familiarizing the reader with Stochastic Hybrid Systems (SHSs) and enabling her to use these systems to model and analyze Networked Control Systems (NCSs). Towards this goal, we introduce two different models of SHSs and a set of theoretical tools for their analysis. In parallel with the presentation of the mathematical models and results, we provide a few simple examples that illustrate the use of SHSs to models NCSs.

A compositional modelling and analysis framework for stochastic hybrid systems

2012

Abstract The theory of hybrid systems is well-established as a model for real-world systems consisting of continuous behaviour and discrete control. In practice, the behaviour of such systems is also subject to uncertainties, such as measurement errors, or is controlled by randomised algorithms. These aspects can be modelled and analysed using stochastic hybrid systems.