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

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.<>