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Solving the Goddard problem with thrust and dynamic pressure constraints using saturation functions

Abstract : This paper addresses the well-known Goddard problem in the formulation of Seywald and Cliff with the objective to maximize the altitude of a vertically ascending rocket sub ject to dynamic pressure and thrust constraints. The Goddard problem is used to propose a new method to systematically incorporate the constraints into the system dynamics by means of saturation functions. This procedure results in an unconstrained and penalized optimal control problem which strictly satisfies the constraints. The approach requires no knowledge of the switching structure of the optimal solution and avoids the explicit consideration of singular arcs. A collocation method is used to solve the BVPs derived from the optimality conditions and demonstrates the applicability of the method to constrained optimal control problems.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-00473201
Contributor : François Chaplais <>
Submitted on : Wednesday, April 14, 2010 - 4:20:30 PM
Last modification on : Thursday, September 24, 2020 - 5:04:18 PM

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  • HAL Id : hal-00473201, version 1

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Knut Graichen, Nicolas Petit. Solving the Goddard problem with thrust and dynamic pressure constraints using saturation functions. 17th World Congress of The International Federation of Automatic Control, Nov 2008, Seoul, South Korea. pp.14301-14306. ⟨hal-00473201⟩

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