21,140 research outputs found
Probabilistic Reachability Analysis for Large Scale Stochastic Hybrid Systems
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
Multiobjective Tactical Planning under Uncertainty for Air Traffic Flow and Capacity Management
We investigate a method to deal with congestion of sectors and delays in the
tactical phase of air traffic flow and capacity management. It relies on
temporal objectives given for every point of the flight plans and shared among
the controllers in order to create a collaborative environment. This would
enhance the transition from the network view of the flow management to the
local view of air traffic control. Uncertainty is modeled at the trajectory
level with temporal information on the boundary points of the crossed sectors
and then, we infer the probabilistic occupancy count. Therefore, we can model
the accuracy of the trajectory prediction in the optimization process in order
to fix some safety margins. On the one hand, more accurate is our prediction;
more efficient will be the proposed solutions, because of the tighter safety
margins. On the other hand, when uncertainty is not negligible, the proposed
solutions will be more robust to disruptions. Furthermore, a multiobjective
algorithm is used to find the tradeoff between the delays and congestion, which
are antagonist in airspace with high traffic density. The flow management
position can choose manually, or automatically with a preference-based
algorithm, the adequate solution. This method is tested against two instances,
one with 10 flights and 5 sectors and one with 300 flights and 16 sectors.Comment: IEEE Congress on Evolutionary Computation (2013). arXiv admin note:
substantial text overlap with arXiv:1309.391
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