Title :
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
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;
Conference_Titel :
Southeastcon '92, Proceedings., IEEE
Conference_Location :
Birmingham, AL
Print_ISBN :
0-7803-0494-2
DOI :
10.1109/SECON.1992.202383
