IMMERSION AND INVARIANCE ADAPTIVE ROBUST CONTROL FOR A CLASS OF NONLINEAR SYSTEMS WITH UNCERTAINTIES AND DISTURBANCES

This paper presents an immersion and invariance adaptive robust control framework for a class of nonlinear systems with uncertainties and external disturbances. Sliding mode control law with continuous reaching law is used to avoid chattering. A novel immersion and invariance (I&I) adaptive law is developed to estimate the time varying lumped uncertainty. In the proposed adaptive approach, there is an additional term that can shape the dynamics of the estimation errors. By ingeniously designing this additional item, the two proposed adaptive robust control approaches enable the tracking error to converge to zero in finite time. The salient feature of the proposed control is to suppress time-varying uncertainty in the controlled system without using a large learning rate in the adaptive laws. Simulation results of robot manipulator show the effectiveness of the proposed method.