Singular versus boundary arcs for aircraft trajectory optimization in climbing phase. (English) Zbl 1514.49013
Summary: 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.
MSC:
| 49K15 | Optimality conditions for problems involving ordinary differential equations |
| 49M05 | Numerical methods based on necessary conditions |
| 49S05 | Variational principles of physics |
| 93B27 | Geometric methods |
| 70Q05 | Control of mechanical systems |
Keywords:
optimal control with state constraints; singular arcs; geometric control; homotopy method; aircraft trajectory optimizationSoftware:
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