Adaptive <i>H</i>₂/<i>H</i>_∞ tracking control for a class of uncertain robotic systems

Abstract

This paper addresses the problem of designing mixed H2/H∞ tracking control for a large class of uncertain robotic systems. Nonlinear H∞ control theory, H2 control theory and intelligent adaptive control algorithm are combined to construct a hybrid adaptive/robust H2/H∞ tracking control scheme. One adaptive neural network system is constructed to approximate the behaviour of uncertain robot dynamics, and the other adaptive control algorithm is designed to estimate the behaviour of the modelled disturbance. Moreover, a robust H∞ control algorithm is designed to attenuate the effects of the unmodelled disturbance. Only a set of algebraic matrix Riccati-like equations is required to implement the proposed mixed H2/H∞ tracking controller, and so an explicit and closed-form solution is obtained. Consequently, the mixed H2/H∞ adaptive/robust tracking controller developed here can be analytically computed and easily implemented. Finally, simulations are presented to illustrate the effectiveness of the proposed control algorithm.