DocumentCode
3262441
Title
Analysis of the Hamilton-Jacobi equation in nonlinear control theory by symplectic geometry
Author
Sakamoto, Noboru
Author_Institution
Dept. of Aerosp. Eng., Nagoya Univ., Japan
Volume
2
fYear
2002
fDate
10-13 Dec. 2002
Firstpage
1540
Abstract
The geometric property and structure of the Hamilton-Jacobi equation arising from nonlinear control theory are investigated using symplectic geometry. The generating function of symplectic transforms plays an important role to reveal the structure of the Hamilton-Jacobi equation. It is seen that many of fundamental properties of the Riccati equation can be generalized in the Hamilton-Jacobi equation, and therefore, the theory of the Hamilton-Jacobi equation naturally contains that of the Riccati equation.
Keywords
Riccati equations; geometry; nonlinear control systems; partial differential equations; Hamilton-Jacobi equation; Riccati equation; nonlinear control theory; partial differential equations; symplectic geometry; symplectic transforms; Control systems; Control theory; Ear; Geometry; Jacobian matrices; Lagrangian functions; Nonlinear equations; Optimal control; Partial differential equations; Riccati equations;
fLanguage
English
Publisher
ieee
Conference_Titel
Decision and Control, 2002, Proceedings of the 41st IEEE Conference on
ISSN
0191-2216
Print_ISBN
0-7803-7516-5
Type
conf
DOI
10.1109/CDC.2002.1184738
Filename
1184738
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