Adaptive backstepping 2-SMC of multi-input cascade nonlinear uncertain systems

In this paper, a combined adaptive/second order sliding mode control approach for multi-input cascade uncertain nonlinear system is given; the control design is based on parameter estimation backstepping recursive design method. Due to the orders of the parameter update law are less than the number of the parameters, this design is not over-parameteried; the approach presented in this paper also introduces a suitable commutation logic that prevents an uncontrollable growth of the uncertainties. 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.