An Adaptive Quasi-Sliding Mode Control without Chattering

The main problem hindering the engineering application of the conventional sliding mode control (CSMC) is the well-known chattering phenomenon. This work investigates how to design a chattering-free adaptive sliding mode controller for a class of nth-order nonlinear uncertain systems. To remove the undesired chattering of the CSMC method, a novel continuous sigmoid function has been introduced to generate the quasi-sliding mode process instead of using the discontinuous sign function. At the same time, an effective adaptive control gain is designed by using the same sigmoid function. Compared with the existing works on the adaptive sliding mode control design, the adaptive mechanism proposed in this paper can effectively relax the restrictions on the prior information of the system uncertainties. In particular, the designed parameters and the adaptive control gain can characterize the admissible boundary of the high-frequency gain uncertainty of the control input in real time. We refer this approach as an adaptive quasi-sliding mode control (AQSMC). The stability analysis of the AQSMC method has also been provided with the help of Lyapunov theory. Finally, some numerical simulation results are presented to demonstrate its effectiveness and superiority.