Alternative Method to Solve a Variational Inequality Applied to an Air Traffic Control Example

摘要

Some important problems of air traffic control, such as collision avoidance, can mathematically be formulated as problems of optimal stopping a diffusion. As shown, an optimal stopping policy can be characterized by a variational inequality (VI). To compute the solution of such a VI, a new iteration scheme is developed. The simplicity of this scheme is explicitly due to the assumption that the cost of stopping is a sufficiently smooth function of the state, which often holds for stopping problems. The scheme is applied to a simple example of air traffic control.