A constrained LQ approach to numerical solutions for constrained nonlinear optimal control problems

Joe Imae; Tomonari Ando; Tomoaki Kobayashi; Guisheng Zhai

doi:10.1109/ICNSC.2009.4919267

A constrained LQ approach to numerical solutions for constrained nonlinear optimal control problems

Joe Imae, Tomonari Ando, Tomoaki Kobayashi, Guisheng Zhai

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

1 Citation (Scopus)

Abstract

We propose a new algorithm for numerical solutions of constrained nonlinear optimal control problems, based on constrained LQ problems. The proposed algorithm is described as follows. First, we approximate the constrained nonlinear optimal control problems by the Taylor expansion technique, resulting in the standard LQ problems, but with linearized constraints. Then, by making use of penalty function methods, we construct the augmented LQ problem, which is one of unconstrained optimal control problems, and therefore we can easily obtain the optimal solution of the augmented LQ problem by Riccati transformation. Finally, repeating the above procedure with a certain type of filter, we ventually obtain the numerical solutions for constrained nonlinear optimal control problems. The effectiveness is demonstrated through simulation.

Original language	English
Title of host publication	Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009
Pages	176-180
Number of pages	5
DOIs	https://doi.org/10.1109/ICNSC.2009.4919267
Publication status	Published - 2009
Externally published	Yes
Event	2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009 - Okayama, Japan Duration: 2009 Mar 26 → 2009 Mar 29

Publication series

Name	Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009

Conference

Conference	2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009
Country/Territory	Japan
City	Okayama
Period	09/3/26 → 09/3/29

Keywords

Computational method
Constrained nonlinear optimal control problem
LQ problem
Penalty function

ASJC Scopus subject areas

Computer Networks and Communications
Electrical and Electronic Engineering

Access to Document

10.1109/ICNSC.2009.4919267

Cite this

Imae, J., Ando, T., Kobayashi, T., & Zhai, G. (2009). A constrained LQ approach to numerical solutions for constrained nonlinear optimal control problems. In Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009 (pp. 176-180). [4919267] (Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009). https://doi.org/10.1109/ICNSC.2009.4919267

A constrained LQ approach to numerical solutions for constrained nonlinear optimal control problems. / Imae, Joe; Ando, Tomonari; Kobayashi, Tomoaki et al.

Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009. 2009. p. 176-180 4919267 (Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009).

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

Imae, J, Ando, T, Kobayashi, T & Zhai, G 2009, A constrained LQ approach to numerical solutions for constrained nonlinear optimal control problems. in Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009., 4919267, Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009, pp. 176-180, 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009, Okayama, Japan, 09/3/26. https://doi.org/10.1109/ICNSC.2009.4919267

Imae J, Ando T, Kobayashi T, Zhai G. A constrained LQ approach to numerical solutions for constrained nonlinear optimal control problems. In Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009. 2009. p. 176-180. 4919267. (Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009). doi: 10.1109/ICNSC.2009.4919267

Imae, Joe ; Ando, Tomonari ; Kobayashi, Tomoaki et al. / A constrained LQ approach to numerical solutions for constrained nonlinear optimal control problems. Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009. 2009. pp. 176-180 (Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009).

@inproceedings{c0a3bb38f6164ab9991d7b19bb921a14,

title = "A constrained LQ approach to numerical solutions for constrained nonlinear optimal control problems",

abstract = "We propose a new algorithm for numerical solutions of constrained nonlinear optimal control problems, based on constrained LQ problems. The proposed algorithm is described as follows. First, we approximate the constrained nonlinear optimal control problems by the Taylor expansion technique, resulting in the standard LQ problems, but with linearized constraints. Then, by making use of penalty function methods, we construct the augmented LQ problem, which is one of unconstrained optimal control problems, and therefore we can easily obtain the optimal solution of the augmented LQ problem by Riccati transformation. Finally, repeating the above procedure with a certain type of filter, we ventually obtain the numerical solutions for constrained nonlinear optimal control problems. The effectiveness is demonstrated through simulation.",

keywords = "Computational method, Constrained nonlinear optimal control problem, LQ problem, Penalty function",

author = "Joe Imae and Tomonari Ando and Tomoaki Kobayashi and Guisheng Zhai",

year = "2009",

doi = "10.1109/ICNSC.2009.4919267",

language = "English",

isbn = "9781424434923",

series = "Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009",

pages = "176--180",

booktitle = "Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009",

note = "2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009 ; Conference date: 26-03-2009 Through 29-03-2009",

}

TY - GEN

T1 - A constrained LQ approach to numerical solutions for constrained nonlinear optimal control problems

AU - Imae, Joe

AU - Ando, Tomonari

AU - Kobayashi, Tomoaki

AU - Zhai, Guisheng

PY - 2009

Y1 - 2009

N2 - We propose a new algorithm for numerical solutions of constrained nonlinear optimal control problems, based on constrained LQ problems. The proposed algorithm is described as follows. First, we approximate the constrained nonlinear optimal control problems by the Taylor expansion technique, resulting in the standard LQ problems, but with linearized constraints. Then, by making use of penalty function methods, we construct the augmented LQ problem, which is one of unconstrained optimal control problems, and therefore we can easily obtain the optimal solution of the augmented LQ problem by Riccati transformation. Finally, repeating the above procedure with a certain type of filter, we ventually obtain the numerical solutions for constrained nonlinear optimal control problems. The effectiveness is demonstrated through simulation.

AB - We propose a new algorithm for numerical solutions of constrained nonlinear optimal control problems, based on constrained LQ problems. The proposed algorithm is described as follows. First, we approximate the constrained nonlinear optimal control problems by the Taylor expansion technique, resulting in the standard LQ problems, but with linearized constraints. Then, by making use of penalty function methods, we construct the augmented LQ problem, which is one of unconstrained optimal control problems, and therefore we can easily obtain the optimal solution of the augmented LQ problem by Riccati transformation. Finally, repeating the above procedure with a certain type of filter, we ventually obtain the numerical solutions for constrained nonlinear optimal control problems. The effectiveness is demonstrated through simulation.

KW - Computational method

KW - Constrained nonlinear optimal control problem

KW - LQ problem

KW - Penalty function

UR - http://www.scopus.com/inward/record.url?scp=70349095544&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349095544&partnerID=8YFLogxK

U2 - 10.1109/ICNSC.2009.4919267

DO - 10.1109/ICNSC.2009.4919267

M3 - Conference contribution

AN - SCOPUS:70349095544

SN - 9781424434923

T3 - Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009

SP - 176

EP - 180

BT - Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009

T2 - 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009

Y2 - 26 March 2009 through 29 March 2009

ER -

A constrained LQ approach to numerical solutions for constrained nonlinear optimal control problems

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this