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Efficient Convexification of Flight Path Optimization Problems

  • Gottfried Sachs
  • Rainer Mehlhorn
  • Michael Dinkelmann
Conference paper
Part of the International Series of Numerical Mathematics book series (ISNM, volume 124)

Abstract

A problem in the optimization of flight paths concerns the modelling of the thrust force direction. This problem is addressed by considering various mathematical modellings of thrust force directions in a unified approach. When modelling the thrust force direction which is basically related to the vehicle attitude as a linear or non-linear function of angle of attack, higher order optimality conditions are generally not met for interior thrust settings. A convexification technique is developed for efficiently computing a solution. There may be interior arcs as the limiting case of chattering arcs which concern both controls thrust setting and angle of attack of the original system. A numerical example of hypersonic range flight is presented.

Keywords

Thrust Force Flight Path Hypersonic Vehicle Singular Control Aerodynamic Lift 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

CD

drag coefficient

CL

lift coefficient

D

drag

g

gravity acceleration

H

Hamiltonian

h

altitude

J

performance criterion

L

lift

M

Mach number

m

mass

mf

fuel mass consumed

re

radius of the Earth

S

reference area

S

switching function

s

range

T

thrust

t

time

tf

final time

u

control variables vector

V

speed

ϰ

state variables vector

α

angle of attack

αT

final time

γ

flight path angle

δT

throttle setting

εT

thrust inclination angle (relative to α)

ζ

control variable of modified system

λ

adjoint variables vector

ρ

atmopheric density

σ

specific fuel consumption

Φ

Mayer form of performance criterion

ωe

angular velocity of the Earth

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References

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Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • Gottfried Sachs
    • 1
  • Rainer Mehlhorn
    • 1
  • Michael Dinkelmann
    • 1
  1. 1.Institut für Flugmechanik und FlugregelungTechnische Universität MünchenGarchingGermany

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