## Singular perturbation techniques for real time aircraft trajectory optimization and controlAnthony J. Calise, Daniel D. Moerder, Langley Research Center, United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch, Drexel University. Dept. of Mechanical Engineering & Mechanics National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1982 - Mathematics - 103 pages |

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### Contents

Section Page | 1 |

Figure Page | 8 |

Second Boundary Layer Altitude Solution as a Function | 16 |

20 other sections not shown

### Common terms and phrases

actual flight path aircraft altitude algorithm altitude and flight Altitude versus velocity angle of attack approximation arg max asymptotic bank angle profile boundary layer Hamiltonian boundary layer optimal boundary layer solution Calise climb and descent climb path Command and actual computed constraint boundary control law control solution cruise energy level cruise point damping ratio descent path drag coefficient eigenvalues energy and heading equations F-8 aircraft flight path angle fourth boundary layer function Ground track heading dynamics horizontal lift indeterminate form intercept problem layer Hamiltonian evaluated lift and bank Mach numbers minimum time intercept necessary conditions Note obtained on-line optimal control optimal cruise optimal heading outer solution parameters path angle dynamics proportional control proportional vertical lift pseudo cruise energy range matching reference altitude second boundary layer Shinar singular perturbation methods Table target third boundary layer TIME(SEC TME SEC Trajectory Optimization values VT cos yt