Titlebook: Stochastic Hybrid Systems; Theory and Safety Cr Henk A. P. Blom,John Lygeros Book 2006 Springer-Verlag Berlin Heidelberg 2006 Approximation

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Branching and Interacting Particle Interpretations of Rare Event Probabilities, as well as in ruin type estimation problems. We also provide a rather detailed presentation of the asymptotic theory of these particle algorithms, including exponential extinction probabilities, .-mean error bounds, central limit theorem, and fluctuation variance comparaisons.

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ethnology

Critical Observability of a Class of Hybrid Systems and Application to Air Traffic Management,te is reached. We apply our results to the runway crossing control problem, i.e., the control of aircraft that cross landing or take-off runways. In the hybrid model of the system, five agents are present; four are humans, each modeled as hybrid systems, subject to situation awareness errors.

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A Sequential Particle Algorithm that Keeps the Particle System Alive,ts, a central limit theorem is proved by induction, based on the result of Rényi (1957) for sums of a random number of independent random variables. An alternate proof is also given, based on an original central limit theorem for triangular arrays of martingale increments spread across generations with different random sizes.

HOWL

A Stochastic Approximation Method for Reachability Computations, probability that two aircraft flying in the same region of the airspace get closer than a certain safety distance and that an aircraft enters a forbidden airspace area. In this context, the target set is the set of unsafe configurations for the system, and we are estimating the probability that an unsafe situation occurs.