An algebraic approach to Hamilton´s canonical equations

Author

Kawano, Yu ; Ohtsuka, Toshiyuki

Author_Institution

Grad. Sch. of Eng. Sci., Osaka Univ., Toyonaka, Japan

fYear

2011

fDate

13-18 Sept. 2011

Firstpage

370

Lastpage

375

Abstract

Hamilton´s canonical equations play important roles in the analysis and control of nonlinear systems. How ever, it is difficult to obtain their analytic solutions because they are nonlinear ordinary differential equations. In this paper, we introduce a new algebraic solution method for the equations in the case that the Hamiltonian is a polynomial of the costate with coefficients consisting of the rational functions of the state and the meromorphic functions of time, and the costate is a function of the state and time. By our method, for some classes of problems, analytic solutions of the equation can be obtained by solving only algebraic equations.

Keywords

nonlinear control systems; nonlinear differential equations; polynomials; rational functions; Hamilton canonical equation; algebraic equation; algebraic solution method; costate function; meromorphic function; nonlinear control system; nonlinear ordinary differential equation; rational function; Differential equations; Nonlinear systems; Optimal control; Polynomials; Regulators; Trajectory; Hamilton´s canonical equation; commutative algebra; nonlinear systems;

fLanguage

English

Publisher

ieee

Conference_Titel

SICE Annual Conference (SICE), 2011 Proceedings of

Conference_Location

Tokyo

ISSN

pending

Print_ISBN

978-1-4577-0714-8

Type

conf

Filename

6060682