A nonlinear programming approach for optimizing two-stage lifting vehicle ascent to orbit

Kamm, James L.; Johnson, I. L.

doi:10.1016/0005-1098(73)90030-7

Cited by 4 publications

(1 citation statement)

References 1 publication

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“…(1) and (4) and the inequality constraints on dynamic pressure, axial acceleration, and maximum thrust. ,iZ + a 2i z 2 + a 3i z 3 (7) where z= (t-t f ) I (t i+1 -t i ) 9 t 1 =15, t 2 =20,t 3 =25, t 4 …”

Section: Problem Definitionmentioning

confidence: 99%

Optimization of the Solid-Rocket Assisted Space Shuttle Ascent Trajectory

Johnson

1975

Journal of Spacecraft and Rockets

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Optimal solid-rocket assisted space shuttle ascent trajectories are investigated. Solid-rocket thrust profiles are simulated by using third-degree spline functions, with the values of the thrust ordinates defined as parameters. The trajectories are optimized parametrically-with use of the Davidon-Fletcher-Powell, penalty function method-by minimizing propellant weight subject to state and control inequality constraints and terminal boundary conditions. This study shows that optimizing a control variable parametrically by using third-degreespline-function interpolation allows the control to be shaped so that inequality constraints are strictly adhered to and all corners are eliminated. The absence of corners makes this method attractive from the viewpoint of solidrocket grain design limitations. Nomenclaturea a = axial acceleration dji = spline function coefficients bi = coefficients for cubic polynomial during tailoff C n = aerodynamic normal force coefficient D = drag force e =e } +e 2 + ... +e f e { = error functions gj = /th point equality constraint go = gravitational constant hi = /th point inequality constraint Ap = specific impulse kj = weight constants or penalty constants for point equality constraints gj = weight constants or penalty constants for point inequality constraints m = mass n g = number of point equality constraints n h = number of point inequality constraints Q = dynamic pressure Sj = state and control inequality constraints= angle of attack p = atmospheric density Subscripts i = /th value max = maximum min = minimum spin = spline curve fit of stage = evaluated at staging steer = evaluated at time when optimal steering begins tail = during tailoff Superscripts (') =d/dt

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Section: Problem Definitionmentioning

confidence: 99%

Optimization of the Solid-Rocket Assisted Space Shuttle Ascent Trajectory

Johnson

1975

Journal of Spacecraft and Rockets

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An active‐constraint logic for non‐linear programming

Das

Cliff

Kelley

1984

Optim Control Appl Methods

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Active‐constraint logic for non‐linear programming processes is sought such that the constraints in the active set possess positive projection multipliers and the resulting step does not violate the linear approximations to any of the constraints satisfied as equalities but considered inactive. Active‐constraint logic which has the desired properties is given for the cases of two and three constraints. For the general case featuring more than three constraints satisfied as equalities, an active‐set logic is suggested. The efficiency of the proposed logic is tested computationally on some quadratic programming problems in comparison with three existing active‐set strategies.

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On Converting Optimal Control Problems into Nonlinear Programming Problems

Kraft¹

1985

Computational Mathematical Programming

149

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A nonlinear programming approach for optimizing two-stage lifting vehicle ascent to orbit

Cited by 4 publications

References 1 publication

Optimization of the Solid-Rocket Assisted Space Shuttle Ascent Trajectory

Optimization of the Solid-Rocket Assisted Space Shuttle Ascent Trajectory

An active‐constraint logic for non‐linear programming

On Converting Optimal Control Problems into Nonlinear Programming Problems

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