@article{59504,
  abstract     = {{<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>}},
  author       = {{Cots, Olivier and Gergaud, Joseph and Goubinat, Damien and Wembe, Boris}},
  issn         = {{2822-7840}},
  journal      = {{ESAIM: Mathematical Modelling and Numerical Analysis}},
  number       = {{2}},
  pages        = {{817--839}},
  publisher    = {{EDP Sciences}},
  title        = {{{Singular <i>versus</i> boundary arcs for aircraft trajectory optimization in climbing phase}}},
  doi          = {{10.1051/m2an/2022101}},
  volume       = {{57}},
  year         = {{2022}},
}