Optimal control of the atmospheric reentry of a space shuttle by an homotopy method

Hermant, Audrey

doi:10.1002/oca.961

Cited by 19 publications

(21 citation statements)

References 23 publications

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“…This phenomenon is possible when the constraint is of order three at least. By using a properly modified continuation procedure, the reentry problem was solved in [55] and the results of [18] were retrieved. Now we have shown by examples in trajectory problems that the geometric optimal control theory can be used to analyze the problem and the numerical continuation can be used to design efficient numerical resolution methods.…”

Section: Atmospheric Reentry Problemmentioning

confidence: 99%

Geometric optimal control and applications to aerospace

2017

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This article deals with applications of optimal control to aerospace problems with a focus on modern geometric optimal control tools and numerical continuation techniques. Geometric optimal control is a theory combining optimal control with various concepts of differential geometry. The ultimate objective is to derive optimal synthesis results for general classes of control systems. Continuation or homotopy methods consist in solving a series of parameterized problems, starting from a simple one to end up by continuous deformation with the initial problem. They help overcoming the difficult initialization issues of the shooting method. The combination of geometric control and homotopy methods improves the traditional techniques of optimal control theory. A nonacademic example of optimal attitude-trajectory control of (classical and airborne) launch vehicles, treated in details, illustrates how geometric optimal control can be used to analyze finely the structure of the extremals. This theoretical analysis helps building an efficient numerical solution procedure combining shooting methods and numerical continuation. Chattering is also analyzed and it is shown how to deal with this issue in practice.

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Section: Atmospheric Reentry Problemmentioning

confidence: 99%

Geometric optimal control and applications to aerospace

2017

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“…Another approach to solve the atmospheric re-entry problem of Section 3.1 by a shooting method, implemented in [198], consists of carrying out a continuation on the maximal value of the state constraint on the thermal flux in order to introduce this constraint step by step. The procedure automatically determines the structure of the optimal trajectory, and permits to start from the easier problem without state constraint and to introduce the constraints progressively (see also [199]).…”

Section: Solving the Atmospheric Re-entry Problem By Continuationmentioning

confidence: 99%

“…To take into account this change of structure along the continuation, the usual continuation procedure must be modified accordingly. For the atmospheric re-entry problem with a constraint on the thermal flux, this procedure is described in details in [198], and permits to recover in a nice way the results of [97].…”

Section: Solving the Atmospheric Re-entry Problem By Continuationmentioning

confidence: 99%

Optimal Control and Applications to Aerospace: Some Results and Challenges

Trélat

2012

J Optim Theory Appl

189

179

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This article surveys the classical techniques of nonlinear optimal control such as the Pontryagin Maximum Principle and the conjugate point theory, and how they can be implemented numerically, with a special focus on applications to aerospace problems. In practice the knowledge resulting from the maximum principle is often insufficient for solving the problem in particular because of the well-known problem of initializing adequately the shooting method. In this survey article it is explained how the classical tools of optimal control can be combined with other mathematical techniques to improve significantly their performances and widen their domain of application. The focus is put onto three important issues. The first is geometric optimal control, which is a theory that has emerged in the 80's and is combining optimal control with various concepts of differential geometry, the ultimate objective being to derive optimal synthesis results for general classes of control systems. Its applicability and relevance is demonstrated on the problem of atmospheric re-entry of a space shuttle. The second is the powerful continuation or homotopy method, consisting of deforming continuously a problem towards a simpler one, and then of solving a series of parametrized problems to end up with the solution of the initial problem. After having recalled its mathematical foundations, it is shown how to combine successfully this method with the shooting method on several aerospace problems such as the orbit transfer problem. The third one consists of concepts of dynamical system theory, providing evidence of nice properties of the celestial dynamics that are of great interest for future mission design such as low cost interplanetary space missions. The article ends with open problems and perspectives.

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“…An application to the atmospheric reentry problem is provided in Hermant [2011]. So clearly the question of analyzing the transitions between structures of active set constraints is essentially open and challenging.…”

Section: Extensions and Referencesmentioning

confidence: 99%

The shooting approach to optimal control problems

Bonnans

2013

IFAC Proceedings Volumes

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Abstract:We give an overview of the shooting technique for solving deterministic optimal control problems. This approach allows to reduce locally these problems to a finite dimensional equation. We first recall the basic idea, in the case of unconstrained or control constrained problems, and show the link with second-order optimality conditions and the analysis or discretization errors. Then we focus on two cases that are now better undestood: state constrained problems, and affine control systems. We end by discussing extensions to the optimal control of a parabolic equation.

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Optimal control of the atmospheric reentry of a space shuttle by an homotopy method

Cited by 19 publications

References 23 publications

Geometric optimal control and applications to aerospace

Geometric optimal control and applications to aerospace

Optimal Control and Applications to Aerospace: Some Results and Challenges

The shooting approach to optimal control problems

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