Sequential Monte Carlo Simulation of Rare Event Probability in Stochastic Hybrid Systems

Krystul, Jaroslav; Blom, H.A.P.

doi:10.3182/20050703-6-cz-1902.00382

Cited by 28 publications

(30 citation statements)

References 9 publications

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“…The good message is that in literature on sequential MC simulation, e.g., see [18], [19], [23], [35], [48], [52], complementary directions have been developed which remain to be explored for application to free flight collision risk estimation. These potential improvements of sequential MC simulation will be studied in follow-up research.…”

Section: Discussionmentioning

confidence: 99%

“…This method essentially consists of taking advantage of an appropriately nested sequence of closed subsets of [45], [47] extended this Interacting Particle System (IPS) approach to switching diffusions. For probabilistic reachability analysis of an air traffic design, this IPS approach is now further extended to the class of SHS the execution of which satisfies the strong Markov property as adressed in Chapter 2 of this volume.…”

Section: Risk Factorisation Using Multiple Conflict Levelsmentioning

confidence: 99%

See 1 more Smart Citation

Free Flight Collision Risk Estimation by Sequential MC Simulation

Blom¹,

Krystul²,

Bakker³

2006

Automation and Control Engineering

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Section: Discussionmentioning

confidence: 99%

Section: Risk Factorisation Using Multiple Conflict Levelsmentioning

confidence: 99%

Free Flight Collision Risk Estimation by Sequential MC Simulation

Blom¹,

Krystul²,

Bakker³

2006

Automation and Control Engineering

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“…In [14]- [16], hybrid versions of the baseline IPS algorithm [8]- [11] have been developed, which take into account that rare discrete modes may contribute significantly to the reach probability to be estimated. In [14], the hybrid IPS version simulates another, more frequent switching, M -valued process { } Q.E.D.…”

Section: Aggregation Of Modesmentioning

confidence: 99%

“…In [14], the hybrid IPS version simulates another, more frequent switching, M -valued process { } Q.E.D. The prediction of the x-part of the particle over time step h is done by drawing a sample from (.…”

Section: Aggregation Of Modesmentioning

confidence: 99%

Probabilistic reachability analysis for large scale stochastic hybrid systems

Blom

Bakker

Krystul

2007

2007 46th IEEE Conference on Decision and Control

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Abstract-This paper studies probabilistic reachability analysis for large scale stochastic hybrid systems (SHS) as a problem of rare event estimation. In literature, advanced rare event estimation theory has recently been embedded within a stochastic analysis framework, and this has led to significant novel results in rare event estimation for a diffusion process using sequential MC simulation. This paper presents this rare event estimation theory directly in terms of probabilistic reachability analysis of an SHS, and develops novel theory which allows to extend the novel results for application to a large scale SHS where a very huge number of rare discrete modes may contribute significantly to the reach probability. Essentially, the approach taken is to introduce an aggregation of the discrete modes, and to develop importance sampling relative to the rare switching between the aggregation modes. The practical working of this approach is demonstrated for the safety verification of an advanced air traffic control example.

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“…Theoretical solutions are based on martingale theory (see Bujorianu et al [2003] and ), Bayesian statistics (as in Bujorianu [2005]), and optimal control (Bujorianu et al [2008]). Numerical solutions are mainly based on interactive particle systems ( Blom et al [2007]), Monte Carlo simulations (Krystul et al [2005]), Markov chain approximations (Prandini et al [2006]), and dynamic programming (Koutsoukos et al [2008]). …”

Section: Introductionmentioning

confidence: 99%

State constrained reachability for stochastic hybrid systems

Bujorianu

2011

Nonlinear Analysis: Hybrid Systems

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The stochastic hybrid systems constitute well established classes of realistic models of hybrid discrete/continuous dynamics subject to random perturbations, autonomous uncontrollable transitions, nondeterminism or uncertainty. Stochastic reachability analysis is a key factor in the verification and deployment of stochastic hybrid systems. The encouraging recent progress prompts us to refine the problem to cover more realistic situations. We extend the so called constrained reachability problem from the probabilistic discrete case to stochastic hybrid systems. Then we define mathematically this problem, and we obtain the reach probabilities as solutions of a boundary value problem. The last problem is well studied and numerical, even symbolic solutions exist. This characterization is useful in stochastic control, in probabilistic path planning and for nano-systems.

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Sequential Monte Carlo Simulation of Rare Event Probability in Stochastic Hybrid Systems

Cited by 28 publications

References 9 publications

Free Flight Collision Risk Estimation by Sequential MC Simulation

Free Flight Collision Risk Estimation by Sequential MC Simulation

Probabilistic reachability analysis for large scale stochastic hybrid systems

State constrained reachability for stochastic hybrid systems

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