Synchronization of chaotic systems using adaptive T-S fuzzy terminal sliding-function control

This paper presents an adaptive Takgi-Sugeno (T-S) fuzzy terminal sliding-function controller (AFTSFC) approach to synchronize two chaotic systems with parameter mismatch. First, an appropriate terminal sliding function (TSF) is designed and then represented by the T-S fuzzy model. The T-S fuzzy terminal sliding-function (FTSF) is applied to the control law. Different from classical terminal sliding mode control, which uses a discontinuous switching control law, the FTSF control uses a continuous control law and thus avoids the chattering problem. The linear matrix inequality (LMI) problem is solved to obtain the initial feedback control gain, and the adaptive law of the control gain is adapted online to estimate parametric mismatch. Based on the Lyapunov stability theory, the AFTSFC guarantees that the error of synchronization is uniformly ultimately bounded (UUB); i.e., the drive and response chaotic systems can be synchronized with only a small bounded error. The simulation results demonstrate that the proposed method is able to provide a satisfactory synchronization performance.