[{"language":[{"iso":"eng"}],"user_id":"95394","_id":"59504","status":"public","abstract":[{"lang":"eng","text":"<jats:p>In this article, we are interested in optimal aircraft trajectories in climbing phase. We consider the cost index criterion which is a convex combination of the time-to-climb and the fuel consumption. We assume that the thrust is constant and we control the flight path angle of the aircraft. This optimization problem is modeled as a Mayer optimal control problem with a single-input affine dynamics in the control and with two pure state constraints, limiting the Calibrated AirSpeed (CAS) and the Mach speed. The candidates as minimizers are selected among a set of extremals given by the maximum principle. We first analyze the minimum time-to-climb problem with respect to the bounds of the state constraints, combining small time analysis, indirect multiple shooting and homotopy methods with monitoring. This investigation emphasizes two strategies: the common CAS/Mach procedure in aeronautics and the classical Bang-Singular-Bang policy in control theory. We then compare these two procedures for the cost index criterion.</jats:p>"}],"publication":"ESAIM: Mathematical Modelling and Numerical Analysis","type":"journal_article","doi":"10.1051/m2an/2022101","title":"Singular <i>versus</i> boundary arcs for aircraft trajectory optimization in climbing phase","volume":57,"date_created":"2025-04-10T14:34:18Z","author":[{"full_name":"Cots, Olivier","last_name":"Cots","first_name":"Olivier"},{"full_name":"Gergaud, Joseph","last_name":"Gergaud","first_name":"Joseph"},{"first_name":"Damien","last_name":"Goubinat","full_name":"Goubinat, Damien"},{"first_name":"Boris","full_name":"Wembe, Boris","last_name":"Wembe"}],"date_updated":"2025-04-10T14:39:50Z","publisher":"EDP Sciences","intvolume":"        57","page":"817-839","citation":{"bibtex":"@article{Cots_Gergaud_Goubinat_Wembe_2022, title={Singular <i>versus</i> boundary arcs for aircraft trajectory optimization in climbing phase}, volume={57}, DOI={<a href=\"https://doi.org/10.1051/m2an/2022101\">10.1051/m2an/2022101</a>}, number={2}, journal={ESAIM: Mathematical Modelling and Numerical Analysis}, publisher={EDP Sciences}, author={Cots, Olivier and Gergaud, Joseph and Goubinat, Damien and Wembe, Boris}, year={2022}, pages={817–839} }","mla":"Cots, Olivier, et al. “Singular <i>versus</i> Boundary Arcs for Aircraft Trajectory Optimization in Climbing Phase.” <i>ESAIM: Mathematical Modelling and Numerical Analysis</i>, vol. 57, no. 2, EDP Sciences, 2022, pp. 817–39, doi:<a href=\"https://doi.org/10.1051/m2an/2022101\">10.1051/m2an/2022101</a>.","short":"O. Cots, J. Gergaud, D. Goubinat, B. Wembe, ESAIM: Mathematical Modelling and Numerical Analysis 57 (2022) 817–839.","apa":"Cots, O., Gergaud, J., Goubinat, D., &#38; Wembe, B. (2022). Singular <i>versus</i> boundary arcs for aircraft trajectory optimization in climbing phase. <i>ESAIM: Mathematical Modelling and Numerical Analysis</i>, <i>57</i>(2), 817–839. <a href=\"https://doi.org/10.1051/m2an/2022101\">https://doi.org/10.1051/m2an/2022101</a>","ieee":"O. Cots, J. Gergaud, D. Goubinat, and B. Wembe, “Singular <i>versus</i> boundary arcs for aircraft trajectory optimization in climbing phase,” <i>ESAIM: Mathematical Modelling and Numerical Analysis</i>, vol. 57, no. 2, pp. 817–839, 2022, doi: <a href=\"https://doi.org/10.1051/m2an/2022101\">10.1051/m2an/2022101</a>.","chicago":"Cots, Olivier, Joseph Gergaud, Damien Goubinat, and Boris Wembe. “Singular <i>versus</i> Boundary Arcs for Aircraft Trajectory Optimization in Climbing Phase.” <i>ESAIM: Mathematical Modelling and Numerical Analysis</i> 57, no. 2 (2022): 817–39. <a href=\"https://doi.org/10.1051/m2an/2022101\">https://doi.org/10.1051/m2an/2022101</a>.","ama":"Cots O, Gergaud J, Goubinat D, Wembe B. Singular <i>versus</i> boundary arcs for aircraft trajectory optimization in climbing phase. <i>ESAIM: Mathematical Modelling and Numerical Analysis</i>. 2022;57(2):817-839. doi:<a href=\"https://doi.org/10.1051/m2an/2022101\">10.1051/m2an/2022101</a>"},"year":"2022","issue":"2","publication_identifier":{"issn":["2822-7840","2804-7214"]},"publication_status":"published"}]