Solving the Goddard problem with thrust and dynamic pressure constraints using saturation functions
08 08 Category : Optimal control | All
Authors: K. Graichen and N. Petit Proc. of the 2008 IFAC World Congress, pp. 14301-14306
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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BibTeX:
@Proceedings{,
author = {Knut Graichen, Nicolas Petit},
editor = {},
title = {Solving the Goddard problem with thrust and dynamic pressure constraints using saturation functions},
booktitle = {17th World Congress of The International Federation of Automatic Control},
volume = {Proc. of the 2008 IFAC World Congress},
publisher = {IFAC},
address = {Seoul},
pages = {14301-14306},
year = {2008},
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.},
keywords = {Optimal control, State and input constraints, Two–point boundary value problem, Aerospace applications}}
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.
Download PDF
BibTeX:
@Proceedings{,
author = {Knut Graichen, Nicolas Petit},
editor = {},
title = {Solving the Goddard problem with thrust and dynamic pressure constraints using saturation functions},
booktitle = {17th World Congress of The International Federation of Automatic Control},
volume = {Proc. of the 2008 IFAC World Congress},
publisher = {IFAC},
address = {Seoul},
pages = {14301-14306},
year = {2008},
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.},
keywords = {Optimal control, State and input constraints, Two–point boundary value problem, Aerospace applications}}