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our algorithm were tested in Monte Carlo simulations and gave very good performance in terms of post-resolution conflicts. Computations times were high, partly because no attempt was made to optimize the implementation of the algorithms. Note also that the algorithm can provide a fairly accurate separation between “good” and “bad” maneuvers
(i.e. maneuvers that meet, or violate the constraints) relatively cheaply, using a low J. It is only when we try to find an optimal maneuver among these that the computational load really kicks in.
Current research concentrates on overcoming the sub-optimality imposed by the penalty formulation of the constrained optimization problem considered in Section 2. A possible way is to use the Monte Carlo Markov Chain procedure presented in Section 3 to obtain optimization parameters that satisfy the constraints and then to optimize over this set in a successive step. We are also working on sequential Monte Carlo implementations of the optimization algorithm [4]. This will allow considerable computational savings, since it will enable the re-use of simulations from one step of the procedure to the next. It will also introduce feedback to the process, since it will make it possible to repeat the optimization on line in a receding horizon manner. Finally, we are continuing to work on modeling and implementation in the simulator of typical ATC situation with a realistic parameterization of control actions and control objectives.
References
[1] H.A.P. Blom and G.J. Bakker. Conflict probability and incrossing probability in air traffic management. In IEEE Conference on Decision and Control, Las Vegas, Nevada, U.S.A., December 2002.
[2] EUROCONTROL Experimental Centre. Analysis of the current situation in the Paris, London and Frankfurt TMA. Technical Report Work Package 1: Final Project Report, FALBALA, April 27, 2004. Available from World Wide Web: http://www. eurocontrol.int/care/asas/falbala-forum/falbala-diss.htm.
[3] R.E. Cole, C. Richard, S. Kim, and D. Bailey. An assessment of the 60 km rapid update cycle (ruc) with near real-time aircraft reports. Technical Report NASA/A-1, MIT Lincoln Laboratory, July 15, 1998.
[4] A. Doucet, N de Freitas, and N. Gordon (eds). Sequential Monte Carlo Methods in Practice. Springer-Verlag, 2001.
[5] EUROCONTROL Experimental Centre. User Manual for the Base of Aircraft Data (BADA) — Revision 3.3. 2002. Available from World Wide Web: http://www.eurocontrol.fr/projects/bada/.
[6] EUROCONTROL Experimental Centre. Air-Traffic Control Familiarisation Course. 2004.
[7] E. Frazzoli, Z.H. Mao, J.H. Oh, and E. Feron. Aircraft conflict resolution via semi-definite programming. AIAA Journal of Guidance, Control, and Dynamics, 24(1):79– 86, 2001.
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[8] W. Glover and J. Lygeros. A stochastic hybrid model for air traffic control simulation. In R. Alur and G. Pappas, editors, Hybrid Systems: Computation and Control, number 2993 in LNCS, pages 372–386. Springer Verlag, 2004.
　
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