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The minimum time-to-climb and fuel consumption problems and CAS/Mach procedure for aircraft

Abstract : 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 air slope 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. 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.
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Preprints, Working Papers, ...
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Contributor : Olivier Cots <>
Submitted on : Tuesday, November 27, 2018 - 12:02:39 PM
Last modification on : Saturday, June 13, 2020 - 3:45:48 AM
Long-term archiving on: : Thursday, February 28, 2019 - 2:22:43 PM


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  • HAL Id : hal-01936193, version 1


Olivier Cots, J Gergaud, D Goubinat. The minimum time-to-climb and fuel consumption problems and CAS/Mach procedure for aircraft. 2018. ⟨hal-01936193⟩



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