Abstract
Sequential quadratic programming is used to solve several minimum-fuel flight path optimization problems for a point-mass aircraft flying in a vertical plane. Each optimal control problem involves two control functions: a “steering” control and a “thrust” control. Range is the independent variable. Four dynamic models are examined. The usual point-mass model requires four states (speed, flight path angle, altitude, and mass) and angle of attack as the steering control. An intermediate model with three states (speed, altitude, and mass) neglects the flight path angle dynamics and uses flight path angle as the steering control. An energy-state approximation and a point-mass model including engine dynamics are also treated. Explicit function representations are used to model the aircraft's thrust, lift, and drag characteristics. Numerical solutions are presented for several fuel-optimal transition flight paths between specified states. A comparison of results for the various dynamic models is also given.
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