Adaptive Sliding Mode Control for Uncertain General Fractional Chaotic Systems

This chapter focuses on the Lyapunov stability analysis of general fractional differential systems (GFDSs), as well as adaptive sliding mode control (ASMC) of uncertain general fractional chaotic systems (UGFCSs) with uncertainty and external disturbances. Initially, the existence and uniqueness of solutions and the Lyapunov stability criterion for GFDSs are presented and verified. Furthermore, general fractional integral type sliding surfaces and reaching law are established. Based on the proposed stability criterion, it is shown that the states of UGFCSs can reach the sliding surface and asymptotically converge to zero along the sliding surface. Lastly, the efficacy and efficiency of the proposed fractional controllers are demonstrated by numerical simulations.