Bang-bang control design by combing pseudospectral method with a novel homotopy algorithm

Xiaoli Bai; James D. Turner; John L. Junkins

Bang-bang control design by combing pseudospectral method with a novel homotopy algorithm

Xiaoli Bai
, James D. Turner
, John L. Junkins

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The bang-bang type of control problem for spacecraft trajectory optimization is solved by using a hybrid approach. First, a pseudospectral method is utilized to generate approximate switching times, control structures, and initial co-states. Second, a homotopy method is used to solve the two-point boundary value problems derived from the Euler-Lagrangian equations. The unknown variables in the homotopy method include both switching times and the unknown initial states and co-states. The homotopy algorithm is made robust to the nonlinearity of the problems by enforcing the constraint satisfaction along the homotopy path. The optimization variables are treated as continuous variables and the final solutions have the same accuracy as the ordinary differential equation solvers. An orbit transfer problem is presented to show the advantages of this hybrid methodology.

Original language	American English
Title of host publication	AIAA Guidance, Navigation, and Control Conference and Exhibit
State	Published - 2009
Externally published	Yes
Event	AIAA Guidance, Navigation, and Control Conference and Exhibit - Chicago, IL, United States Duration: Aug 10 2009 → Aug 13 2009

Publication series

Name	AIAA Guidance, Navigation, and Control Conference and Exhibit

Other

Other	AIAA Guidance, Navigation, and Control Conference and Exhibit
Country/Territory	United States
City	Chicago, IL
Period	8/10/09 → 8/13/09

ASJC Scopus subject areas

Aerospace Engineering
Control and Systems Engineering
Electrical and Electronic Engineering

Cite this

@inproceedings{8aaac5b71e11457e9d7c78a0fe33cb86,

title = "Bang-bang control design by combing pseudospectral method with a novel homotopy algorithm",

abstract = "The bang-bang type of control problem for spacecraft trajectory optimization is solved by using a hybrid approach. First, a pseudospectral method is utilized to generate approximate switching times, control structures, and initial co-states. Second, a homotopy method is used to solve the two-point boundary value problems derived from the Euler-Lagrangian equations. The unknown variables in the homotopy method include both switching times and the unknown initial states and co-states. The homotopy algorithm is made robust to the nonlinearity of the problems by enforcing the constraint satisfaction along the homotopy path. The optimization variables are treated as continuous variables and the final solutions have the same accuracy as the ordinary differential equation solvers. An orbit transfer problem is presented to show the advantages of this hybrid methodology.",

author = "Xiaoli Bai and Turner, \{James D.\} and Junkins, \{John L.\}",

year = "2009",

language = "American English",

isbn = "9781563479786",

series = "AIAA Guidance, Navigation, and Control Conference and Exhibit",

booktitle = "AIAA Guidance, Navigation, and Control Conference and Exhibit",

note = "AIAA Guidance, Navigation, and Control Conference and Exhibit ; Conference date: 10-08-2009 Through 13-08-2009",

}

Bai, X, Turner, JD & Junkins, JL 2009, Bang-bang control design by combing pseudospectral method with a novel homotopy algorithm. in AIAA Guidance, Navigation, and Control Conference and Exhibit., 2009-5955, AIAA Guidance, Navigation, and Control Conference and Exhibit, AIAA Guidance, Navigation, and Control Conference and Exhibit, Chicago, IL, United States, 8/10/09.

Bang-bang control design by combing pseudospectral method with a novel homotopy algorithm. / Bai, Xiaoli; Turner, James D.; Junkins, John L.
AIAA Guidance, Navigation, and Control Conference and Exhibit. 2009. 2009-5955 (AIAA Guidance, Navigation, and Control Conference and Exhibit).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Bang-bang control design by combing pseudospectral method with a novel homotopy algorithm

AU - Bai, Xiaoli

AU - Turner, James D.

AU - Junkins, John L.

PY - 2009

Y1 - 2009

N2 - The bang-bang type of control problem for spacecraft trajectory optimization is solved by using a hybrid approach. First, a pseudospectral method is utilized to generate approximate switching times, control structures, and initial co-states. Second, a homotopy method is used to solve the two-point boundary value problems derived from the Euler-Lagrangian equations. The unknown variables in the homotopy method include both switching times and the unknown initial states and co-states. The homotopy algorithm is made robust to the nonlinearity of the problems by enforcing the constraint satisfaction along the homotopy path. The optimization variables are treated as continuous variables and the final solutions have the same accuracy as the ordinary differential equation solvers. An orbit transfer problem is presented to show the advantages of this hybrid methodology.

AB - The bang-bang type of control problem for spacecraft trajectory optimization is solved by using a hybrid approach. First, a pseudospectral method is utilized to generate approximate switching times, control structures, and initial co-states. Second, a homotopy method is used to solve the two-point boundary value problems derived from the Euler-Lagrangian equations. The unknown variables in the homotopy method include both switching times and the unknown initial states and co-states. The homotopy algorithm is made robust to the nonlinearity of the problems by enforcing the constraint satisfaction along the homotopy path. The optimization variables are treated as continuous variables and the final solutions have the same accuracy as the ordinary differential equation solvers. An orbit transfer problem is presented to show the advantages of this hybrid methodology.

UR - https://www.scopus.com/pages/publications/78049270934

UR - https://www.scopus.com/pages/publications/78049270934#tab=citedBy

M3 - Conference contribution

SN - 9781563479786

T3 - AIAA Guidance, Navigation, and Control Conference and Exhibit

BT - AIAA Guidance, Navigation, and Control Conference and Exhibit

T2 - AIAA Guidance, Navigation, and Control Conference and Exhibit

Y2 - 10 August 2009 through 13 August 2009

ER -

Bang-bang control design by combing pseudospectral method with a novel homotopy algorithm

Abstract

Publication series

Other

ASJC Scopus subject areas

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