Adaptive Barrier Function based on Sliding Mode Control for High-Order Nonlinear Systems

In this paper, a new adaptive controller based on barrier function is designed for high-order nonlinear systems with a sum of the uncertainty. Accordingly, in this paper, a sliding mode controller is used, which can create asymptotic convergence and at the same time can deal with disturbances. The main drawbacks of sliding mode control can be considered as asymptotic convergence, chattering phenomenon, stimulus saturation, adaptive gain estimation and failure to deal with oscillating uncertainties. In this paper, the sliding mode control is used to deal with the phenomenon of asymptotic convergence and chattering and the barrier function is used to overcome the uncertainties of interest and fluctuation. The advantages of the proposed method include elimination of the chatting phenomenon, convergence in finite-time, compatibility with time-varying uncertainties, no use of estimation and no need for high information of disturbances. Stability analysis showed that under the proposed controller the tracking errors approach the convergence region close to zero and provide faster convergence. Finally, to prove the efficiency of the controller, based on hyperchaotic synchronization, we apply the proposed controller to the new 5D hyperchaotic system. The results showed that the proposed controller, despite the disturbances applied to the system, provides fast convergence and eliminates the chatting phenomenon.