2002 Fiscal Year Final Research Report Summary
A study on the HamiltonJacobi equation arising from nonlinear control theory
Project/Area Number 
13650482

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Control engineering

Research Institution  Nagoya University 
Principal Investigator 
SAKAMOTO Noboru Nagoya University, Graduate School of Engineering, Associate Prof., 工学研究科, 助教授 (00283416)

CoInvestigator(Kenkyūbuntansha) 
SATO Mitsumasa Kawasaki Heavy Industory, Researcher, 研究員
HODAKA Ichijyo Nagoya University, Graduate School of Engineering, Assistant Prof., 工学研究科, 助教授 (00293663)
SUZUKI Masayuki Nagoya University, Graduate School of Engineering, Professor, 工学研究科, 教授 (20023286)

Project Period (FY) 
2001 – 2002

Keywords  HamiltonJacobi equation / Nonlinear Cotrol / Symplectic Geometry / Riccati equation 
Research Abstract 
Firstly, the theory of partialdifferential equations of the 1st order is outlined in the context of the Hamilt onJacobi equation. According to the theory, to solve the HamiltonJacobi equation, all one has to do is solve a system of ordinary differential equations and/orintegrate a completely integrable Pfaffian system. Secondly, attention is paid to a special kind of solution, a stabilizing solution, which plays an important role in control theory. The wellknown theory by Arimoto and Potter, that is, a necessary and sufficient condition of the existence of a stabilizing solution, is reviewed as a part of the theory of the HamiltonJacobi equation. In control theory, we are interested in obtaining as many solutions as possible. To do this, more information on the structure of the HamiltonJacobi equation will be necessary, which is indicated by an example. Finally, the theory of the generating function for symplectic transforms is introduced ; this will play a central role in a later subsection. Given a solution to the HamiltonJacobi equation, an auxiliary equation is derived that determines the other solutions using the generating function of symplectic transforms. It will also be seen that the auxiliary equation even characterizes the whole structure of the HamiltonJacobi equation. The linear control theoretic explanation of this structure will also be provided.

Research Products
(2 results)