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By M. Mulder
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Additional info for Air Traffic Control
Our final target is introduction of stochastic hybrid systems (SHS). In deterministic model N* we will introduce probabilistic terms. An important work which has influenced the theory development for SHS is (Davis, 1993). In that reference the piecewise deterministic Markov processes are introduced. , 1997) has considered the optimal control for switching diffusions. This model describes the evolution of a process depending on a set of stochastic differential equations among which the process jumps according to state – dependent transitions intensities.
This scheme does not use the central controllers, but the information related to the planning of routing pattern is exchanged among the nodes. It has been primarily designed for use in the fully connected networks or nearly full connected networks and employs random search techniques in order to find the beneficial routing pattern. Since the problems of considering the dynamic routing increase with the number of possible network structures and they vary with the set limitations, the attention will be focused here on special network structure which is not fully connected, and it is imposed by the arrangement of sectors and organization of airspace.
The event times are then specified on the single trajectory and the sequence of these times varies depending on the single initial condition. The switching systems are characterized by event conditions that are a priori defined trough a sequence of jumping times t k kN . The hybrid models are more complicated then switched models. To prove properties of a hybrid system which is a simulation of it and contains all of its behaviors. Properties of hybrid systems are then proved on the simulation and translated back to the original hybrid model.