A stability theorem for a class of second order nonlinear systems with an application to robotics

Author

Grabbe, N.T. ; Dawson, D.N.

Author_Institution

Clemson Univ., SC, USA

fYear

1992

fDate

12-15 Apr 1992

Firstpage

422

Abstract

Optimal control theory is used to generate a feedback control which stabilizes a class of second-order nonlinear systems. Specifically, the Hamilton-Jacobi-Bellman (HJB) equation of dynamic programming is used to show that the control is the solution to a quadratic optimal control problem in which the second-order system serves as a dynamic constraint. The stability result follows from the fact that the solution to the HJB equation serves as a Lyapunov function for the given system. An application of this result to the trajectory tracking of a robot manipulator is given

Keywords

dynamic programming; feedback; nonlinear control systems; optimal control; position control; robots; stability; Hamilton-Jacobi-Bellman equation; Lyapunov function; dynamic constraint; dynamic programming; feedback control; position control; quadratic optimal control; robot manipulator; second order nonlinear systems; second-order system; stability; trajectory tracking; Control systems; Dynamic programming; Feedback control; Lyapunov method; Nonlinear dynamical systems; Nonlinear equations; Nonlinear systems; Optimal control; Stability; Trajectory;

fLanguage

English

Publisher

ieee

Conference_Titel

Southeastcon '92, Proceedings., IEEE

Conference_Location

Birmingham, AL

Print_ISBN

0-7803-0494-2

Type

conf

DOI

10.1109/SECON.1992.202383

Filename

202383