Successive collocation: an approximation to optimal nonlinear control

Author

Curtis, J. Willard ; Beard, Randal W.

Author_Institution

Dept. of Electr. & Comput. Eng., Brigham Young Univ., Provo, UT, USA

Volume

5

fYear

2001

fDate

2001

Firstpage

3481

Abstract

A novel approach to solving the optimal nonlinear control problem is presented. Instead of seeking a global approximation to the Hamilton-Jacobi-Bellman equation, a local approximation is obtained by successively solving the Generalized Hamilton-Jacobi-Bellman (GHJB) equation on a local region of the state space. The optimal control is generated by solving the GHJB equation algebraically at several points close to the current state and using this information to generate a value function that fits the optimal value function close to the current state. This method (the method of orthogonal collocation and successive approximation) is applied to a two-dimensional nonlinear oscillator system, and it is shown to be a practical control law that converges to the optimal control

Keywords

H^∞ control; nonlinear control systems; optimal control; state-space methods; control law; generalized Hamilton-Jacobi-Bellman equation; local approximation; nonlinear oscillator system; optimal nonlinear control; optimal nonlinear control problem; optimal value function; orthogonal collocation; state space; successive approximation; Control systems; Cost function; Differential equations; Ear; Jacobian matrices; Nonlinear control systems; Nonlinear equations; Optimal control; Oscillators; State-space methods;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2001. Proceedings of the 2001

Conference_Location

Arlington, VA

ISSN

0743-1619

Print_ISBN

0-7803-6495-3

Type

conf

DOI

10.1109/ACC.2001.946169

Filename

946169