Manuela L. Bujorianu

Reachability questions in piecewise deterministic Markov processes

We formulate a stochastic hybrid system model that allows us to capture a class of Markov processes known as piecewise deterministic Markov processes (PDMPs). For this class of stochastic processes we formulate a probabilistic reachability problem. Basic properties of PDMPs are reviewed and used to show that the reachability question is indeed well defined. Possible methods for computing the reach probability are then concerned.

Extended stochastic hybrid systems and their reachability problem

In this paper we generalize a model for stochastic hybrid systems. First, we prove that this model is a right Markov process and it satisfies some mathematical properties. Second, we propose a method based on the theory of Dirichlet forms to study the reachability problem associated with these systems.

Stochastic Hybrid Models: An Overview

Abstract An overview of Stochastic Hybrid Models developed in the literature is presented. Attention is concentrated on three classes of models: Piecewise Deterministic Markov Processes, Switching Diffusion Processes and Stochastic Hybrid Systems. The descriptive power of the three classes is compared and conditions under which the classes coincide are developed. The theoretical analysis is motivated by modelling problelns in Air Traffic Management.

General stochastic hybrid systems: modelling and optimal control

We develop a model for general stochastic hybrid systems (GSHS) which is a generalization of piecewise-deterministic Markov processes (PDMP), introduced by Davis and stochastic hybrid systems proposed by Hu, Lygeros and Sastry. This model possesses certain desirable properties, as the strong Markov property and the cadlag property. Extending results available for PDMP, we develop the extended generator formula and the differential formula for GSHS. Then we investigate the dynamic programming for GSHS, using the differential formula.

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.

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.

Functional abstractions of stochastic hybrid systems

Abstract 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

An auxiliary, safety, wide-angle, convex mirror for ready and simple association with a vehicle-mounted outside rearview mirror which has a reflective glass mounted within the peripheral lip of an outer housing, the auxiliary mirror being secured in a position wholly outboard of the rearview mirror by a bracket having a surface adhesively secured to the face of the rearview-mirror glass.

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.