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
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;
Conference_Titel :
Decision and Control, 2002, Proceedings of the 41st IEEE Conference on
Print_ISBN :
0-7803-7516-5
DOI :
10.1109/CDC.2002.1184738
