Stability and Robustness Analysis of a Class of Adaptive Controllers for Robotic Manipulators

Abstract

The stability and robustness properties of the adaptive control scheme proposed by Sadegh and Horowitz (1987) are stud ied. The properties include the global exponential stability and L p input/output stability of the nonadaptive (i.e., fixed- parameter) control system and the global asymptotic stability of the adaptive control scheme. Sufficient conditions for the convergence of the estimated parameters to their true values are also given. A computationally efficient adaptation scheme that is a modified version of the original scheme is proposed. The modified scheme utilizes the desired trajectory outputs, which can be calculated a priori, instead of the actual joint outputs in the parameter adaptation algorithm and the non linearity compensation controller. Sufficient conditions for guaranteeing all the stability properties of the original scheme in the modified scheme are also explicitly derived. A com puter simulation study of the performance of both schemes in the presence of noise disturbances is conducted.