Properties of a combined adaptive/second-order sliding mode control algorithm for some classes of uncertain nonlinear systems

In this paper, a combined adaptive/variable structure control approach is presented that exploits the good properties of the backstepping procedure and of a second-order sliding-mode control algorithm. This algorithm enables one to attain the conditions S=0, S˙=0 (second-order sliding mode) in a finite time, S=0 being a predefined sliding manifold. The combined approach retains the stability and convergence features of the original adaptive strategy. In addition, it allows one to deal with systems with uncertainties of more general types, ensuring robustness, as well as a reduction in the computational load