Resolution of Con icts Involving Many Aircraft via Semide nite Programming
نویسندگان
چکیده
Aircraft con ict detection and resolution is currently attracting the interest of many air transportation service providers and is concerned with the following question: Given a set of airborne aircraft and their intended trajecto-ries, what control strategy should be followed by the pilots and the air traf c service provider to prevent the aircraft from coming too close to each other? This paper addresses this problem by presenting a resolution methodology whereby each aircraft proposes its desired heading while a centralized air traf c control authority resolves any con ict arising between aircraft, while minimizing the deviation between desired and con ict-free heading for each aircraft. The resolution methodology relies on a combination of convex programming and randomized searches: It is shown that a version of the planar, multiaircraft con ict resolution problem, accounting for all possible crossing patterns among aircraft, might be recast as a nonconvex, quadratically constrained quadratic program. For this type of problem, there exist ef cient numerical relaxations, based on semide nite programming, that provide lower bounds on the best achievable objective. These relaxations also lead to a random search technique to compute feasible, locally optimal, and con ict-free strategies. This approach is demonstrated on numerical examples and discussed.
منابع مشابه
Semideenite Programming
In semide nite programming one minimizes a linear function subject to the constraint that an a ne combination of symmetric matrices is positive semide nite. Such a constraint is nonlinear and nonsmooth, but convex, so semide nite programs are convex optimization problems. Semide nite programming uni es several standard problems (e.g., linear and quadratic programming) and nds many applications ...
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تاریخ انتشار 1999