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23955

Feedback Optimal Control in Low-Thrust Interplanetary Trajectory Design

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Last updated: 04 Jan 2025

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Abstract

The feedback optimal control problem in low-thrust interplanetary trajectory design is studied in this paper. The problem is tackled by solving the Hamilton-Jacobi-Bellman equation via a generating function technique devised for linear systems. Instead of solving the classical optimal control problem, this technique allows us to derive closed loop control laws in the preliminary design phase. The idea of the work consists in applying a globally diffeomorphic linearizing transformation that rearranges the original nonlinear two-body dynamics into a linear system of ordinary differential equations written in new variables. The generating function technique is then applied to this new dynamical system, the feedback optimal control is
solved, and the variables are back transformed in the original ones. We circumvent in this way the problem of expanding the vector field and truncating higher-order terms because no accuracy is lost in the undertaken approach. This technique can be applied to any planet-to-planet transfer; it has been successfully tested here for the classical Earth-Mars low-thrust transfer.

DOI

10.21608/asat.2007.23955

Keywords

Low-Thrust Transfers, Feedback Optimal Control, Generating Function, Hamilton-Jacobi-Bellman Equation

Authors

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A.

Last Name

Owis

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Affiliation

Dipartimento di Matematica, Universit`a di Milano Bicocca, and Astronomy Department, Cairo University.

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First Name

F.

Last Name

Topputo

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Affiliation

Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano.

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First Name

F.

Last Name

Bernelli-Zazzera

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Affiliation

Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano.

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Volume

12

Article Issue

ASAT Conference, 29-31 May 2007

Related Issue

4431

Issue Date

2007-05-01

Receive Date

2019-01-09

Publish Date

2007-05-01

Page Start

1

Page End

12

Print ISSN

2090-0678

Online ISSN

2636-364X

Link

https://asat.journals.ekb.eg/article_23955.html

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https://asat.journals.ekb.eg/service?article_code=23955

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40

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Original Article

Type Code

737

Publication Type

Journal

Publication Title

International Conference on Aerospace Sciences and Aviation Technology

Publication Link

https://asat.journals.ekb.eg/

MainTitle

Feedback Optimal Control in Low-Thrust Interplanetary Trajectory Design

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Article

Created At

22 Jan 2023