Fuzzy neural networks for direct adaptive control

It is well known that sliding-mode control is simple and insensitive to uncertainties and disturbances. However, control input chattering is the main problem of the classical sliding-mode controller (SMC). In this paper, a fuzzy neural network SMC (FNNSMC) is presented for a class of nonlinear systems. The FNNSMC can eliminate the chattering, unlike the SMC, but there is larger rising time in the FNNSMC than in the SMC. In some cases, small rise time is important. To decrease the rising time of the FNNSMC, an adaptive controller is proposed where the SMC and the FNNSMC are incorporated by a smooth transformation. This adaptive control scheme can improve the dynamical performance and eliminate the high-frequency chattering in the control signal. The system stability is proved by using the Lyapunov function. The simulation results demonstrate the advantages of the proposed adaptive controller.