We address the problem of online scheduling of the descent aircraft trajectory. The problem is considered in a general framework of the multiphase optimal control. First, we obtain solution of this problem using traditional approach. Next, we develop novel solution algorithm using two key components: (i) inference of the dynamical and control variables of the descending trajectory from the low dimensional flight profile and (ii) solution of the resulting low-dimensional optimization problem using efficient local search. We show that the developed algorithm is much faster than the traditional one and discuss its future application to the simultaneous optimization of the runway throughput and the descent trajectory for each aircraft in convective weather conditions.
How to Cite
mutiphase optimization, aircraft landing trajectory scheduling, vertical trajectory optimization
Becerra, V. M. (2010). Solving complex optimal control problems at no cost with PSOPT.
Betts, J. T. (1998). Survey of Numerical Methods for Trajectory Optimization. Journal of Guidance, Control, and Dynamics, 21(2), 193–207.
Betts, J. T., & Cramer, E. J. (1995, jan). Application of Direct Transcription to Commercial Aircraft Trajectory Optimization. Journal of Guidance, Control, and Dynamics, 18(1), 151–159.
Byrd, R. H., Gilbert, J. C., & Nocedal, J. (2000, Nov 01). A trust region method based on interior point techniques for nonlinear programming. Mathematical Programming, 89(1), 149–185.
Cate, K. (2013, jan). Challenges in Achieving Trajectory-Based Operations. In 51st aiaa aerospace sciences meeting including the new horizons forum and aerospace exposition. American Institute of Aeronautics and Astronautics.
de Jong, P. M. A. (2014). Continuous Descent Operations using Energy Principles (PhD Thesis). de Jong, P. M. A., Bussink, F. J. L., Verhoeven, R. P. M.,
de Gelder, N., van Paassen, M. M., & Mulder, M. (2017, jun). Time and Energy Management During Approach: A Human-in-the-Loop Study. Journal of
Aircraft, 54(1), 177–189.
de Jong, P. M. A., de Gelder, N., Verhoeven, R., Bussink, F. J. L., Kohrs, R., van Paassen, M. M., & Mulder, M. (2015). Time and Energy Management During Descent and Approach: Batch Simulation Study. Journal of Aircraft, 52(1), 190–203.
Fahroo, F., & Ross, I. M. (2000). Direct trajectory optimization by a chebyshev pseudospectral method. In Proceedings of the 2000 american control conference. acc (ieee cat. no.00ch36334) (Vol. 6, p. 3860-3864 vol.6).
Hargraves, C., & Paris, S. (1987). Direct trajectory optimization using nonlinear programming and collocation. AIAA Journal of Guidance, Control, and Dynamics, 10(4), 338–342.
Lombaerts, T., Schuet, S., Wheeler, K., Acosta, D., & Kaneshige, J. (2013, aug). Safe Maneuvering Envelope Estimation based on a Physical Approach. In
Aiaa guidance, navigation, and control (gnc) conference (pp. 1–20). American Institute of Aeronautics and Astronautics.
M. Kamgarpour,W. Zhang, & C.J. Tomlin. (2011). Modeling and optimization of terminal airspace and aircraft arrival subject to weather uncertainties. AIAA Guidance, Navigation, and Control Conference, 1–13.
Matlab optimization toolbox. (2016). (The MathWorks, Natick, MA, USA)
Miquel, T., & Suboptimal, T. M. (2015). Suboptimal longitudinal reference trajectory Computation for time based continuous descent operations longitudinal reference trajectory Computation for time based continuous descent operations. 34th Digital Avionics Systems Conference, 34, 1–12.
Park, S. G., & Clarke, J.-P. (2016, mar). Vertical Trajectory Optimization to Minimize Environmental Impact in the Presence ofWind. Journal of Aircraft, 53(3), 725–737.
Patterson, M. A., & Rao, A. V. (2015). GPOPS-II manul: A General-Purpose MATLAB Software for Solving Multiple-Phase Optimal Control Problems Version 2 . 1 (Tech. Rep. No. October).
Prats, X., Pérez-Batlle, M., Barrado, C., Vilardaga, S., Bas, I., Birling, F., . . . Marsman, A. (2014). Enhancement of a time and energy management algorithm for continuous descent operations. In 14th aiaa aviation technology, integration, and operations conference, aiaa aviation and aeronautics forum and exposition 2014 (pp. 1–11). Alanta.
Rao, A. V. (2014). Trajectory optimization: A survey. In H.Waschl, I. Kolmanovsky, M. Steinbuch, & L. del Re (Eds.), Optimization and optimal control in automotive systems (pp. 3–21). Cham: Springer International Publishing.
Rao, A. V., Benson, D. A., Darby, C., Patterson, M. A., Francolin, C., Sanders, I., & Huntington, G. T. (2010, apr). Algorithm 902: GPOPS, A MATLAB Software for Solving Multiple-phase Optimal Control Problems Using the Gauss Pseudospectral Method. ACM Trans. Math. Softw., 37(2), 22:1—-22:39.
Schuet, S., Lombaerts, T., Acosta, D., Wheeler, K., & Kaneshige, J. (2014, jan). An Adaptive Nonlinear Aircraft Maneuvering Envelope Estimation Approach for Online Applications. In Aiaa guidance, navigation, and control conference (pp. 1–22). American Institute of Aeronautics and Astronautics.
Shish, K., Kaneshige, J., Acosta, D., Schuet, S., Lombaerts, T., Martin, L., & Madavan, A. N. (2016, aug). Aircraft Mode and Energy-State Prediction, Assessment, and Alerting. Journal of Guidance, Control, and Dynamics, 0.
Shish, K. H., Kaneshige, J. T., Acosta, D. M., Schuet, S., Lombaerts, T., Martin, L., & Madavan, A. N. (2015, jan). Trajectory Prediction and Alerting for Aircraft Mode and Energy State Awareness. In Aiaa infotech@ aerospace (pp. 1–19). American Institute of Aeronautics and Astronautics.
Tomlin, C., Lygeros, J., & Sastry, S. (2000). A game theoretic approach to controller design for hybrid systems. Proceedings of the IEEE, 88(7), 949–970.
Tomlin, C. J., Mitchell, I., Bayen, A. M., & Oishi, M. (2003, July). Computational techniques for the verification of hybrid systems. Proceedings of the IEEE, 91(7), 986-1001.
Vinh, N. X. (1981). Optimal Trajectories in Atmospheric Flight. Elsevier Scientific Software.
Young, S., Uijt De Haag, M., Daniels, T., Evans, K., E.and Shish, Schuet, S., Etherington, T., & Kiggins, D. (2016, jan). Evaluating Technologies for Improved Airplane State Awareness and Prediction. In Aiaa infotech @ aerospace (pp. 1–12). American Institute of Aeronautics and Astronautics.
Zhao, Y. (2012). Efficient and robust aircraft landing trajectory optimization. ProQuest Dissertations and Theses, 227.
The Prognostic and Health Management Society advocates open-access to scientific data and uses a Creative Commons license for publishing and distributing any papers. A Creative Commons license does not relinquish the author’s copyright; rather it allows them to share some of their rights with any member of the public under certain conditions whilst enjoying full legal protection. By submitting an article to the International Conference of the Prognostics and Health Management Society, the authors agree to be bound by the associated terms and conditions including the following:
As the author, you retain the copyright to your Work. By submitting your Work, you are granting anybody the right to copy, distribute and transmit your Work and to adapt your Work with proper attribution under the terms of the Creative Commons Attribution 3.0 United States license. You assign rights to the Prognostics and Health Management Society to publish and disseminate your Work through electronic and print media if it is accepted for publication. A license note citing the Creative Commons Attribution 3.0 United States License as shown below needs to be placed in the footnote on the first page of the article.
First Author et al. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 United States License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.