Adaptive backstepping sliding mode control with tuning functions for nonlinear uncertain systems

An adaptive backstepping tuning functions sliding mode controller is proposed for a class of strict-feedback nonlinear uncertain systems. In this control design, adaptive backstepping is used to deal with unknown or uncertain parameters and the matching condition restricting the Lyapunov based design. The main drawback of the Lyapunov based adaptive backstepping which is the overparametrisation is eliminated by the tuning functions. The adaptive backstepping tuning functions design is combined with the sliding mode control in order to overcome quickly varying parametric and unstructured uncertainties, and to obtain chattering free control. The proposed controller not only provides robustness property against uncertainty but also copes with the overparametrisation problem. Experimental results of the proposed controller are compared with those of the standard sliding mode controller. The proposed controller exhibits satisfactory transient performance, good estimates of the uncertain parameters, and less chattering.