Design of Embedded Controllers for Safety Critical Systems

Project IST-2001-38314


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Hybrid System Modeling

Stochastic Control and Analysis of Hybrid Systems
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Stochastic Control and Analysis of Hybrid Systems

Home Work Plan Stochastic Control and Analysis of Hybrid Systems


Stochastic Control and Analysis of Hybrid Systems


Start month: 1

Duration:  24 months











Objectives: Hybrid systems will be used in COLUMBUS as a paradigm for modeling embedded systems with safety critical performance requirements. Embedded systems of this type have to operate in an uncertain and often adversarial environment. Stochastic analysis and control of hybrid systems is therefore essential to study and improve the performance of embedded systems in the presence of uncertainty. In this work package, we will address the theoretical foundations of this process for classes of stochastic hybrid systems.


Work Description: Safety constraints are naturally formulated as questions of reachability of certain sets in the state space. We will investigate probabilistic versions of such reachability questions starting with a class of systems known as piecewise deterministic Markov processes (PDMP) and working our way towards more general classes of stochastic hybrid systems. The work will be divided into a number of Tasks:

Task SHS1: Identify a number of safety critical situations from the motivating applications to power train, flight and air traffic control, to be treated as case studies for subsequent results. Formalize these safety problems as reachability questions for appropriate stochastic hybrid systems. Develop stochastic simulation structures for encoding and simulating these examples.

Task SHS2: Lay the foundations for reachability analysis of PDMP. Fundamental problems that will be addressed here include the development of appropriate measures on the space of trajectories of these systems to capture reachability questions and conceptual algorithms for computing the measure of reachability “events”.

Task SHS3: Establish classes of stochastic hybrid systems amenable to computational analysis. We envision that computational automation of reachability algorithms should be possible for stochastic extensions of timed and multi rate automata common in the hybrid systems literature. Natural extensions of these can be found within the class of PDMP.

Task SHS4: Extend the results for more general classes of stochastic hybrid systems, e.g. systems that allow diffusion in the continuous evolution. The full theoretical treatment of this problem is likely to be very difficult in general. If needed we will establish special cases amenable to theoretical manipulation ands resort to simulation for treating the more general case.



DSHS1: Report on safety critical case studies from the motivating applications.

DSHS2: Report on theoretical foundations.

DSHS3: Report on computable stochastic hybrid systems classes.

DSHS4: Contribution to the final deliverable.



Month 6:   DSHS1 report (public)

Month 18: DSHS2 report (public)

Month 24: DSHS3 report (public)

Month 24: DSHS4, contribution to the final project deliverable

Tasks SHS4 is not critical to the flow of the overall project and is somewhat open ended. Progress made in this task will be reported in DSHS2, together with the framework set out for Task SHS2.


Interrelation with other WPs

WPSHS will receive background input from all the partners about safety critical situations motivated by the applications. The deliverables of WPSHS will be used as input in WPDF.