Adaptive Fixed Time Control for Generalized Synchronization of Mismatched Dynamical Systems With Parametric Estimations

This paper is concerned with the adaptive fixed time control problem for generalized synchronization of mismatched dynamical systems with parametric estimations. We first introduce a new lemma of the fixed-time stability and give a high accuracy estimation of the convergence time. Then, according to the new lemma, the adaptive control scheme for fixed-time synchronization between integer-order dynamical systems is mathematically derived by taking uncertain parameters into account. Meanwhile, the corresponding adaptation laws are designed to estimate the parameter uncertainties. Further, Adaptive fixed time sliding mode control strategy for generalized synchronization of fractional-order dynamical systems is proposed. A novel fractional-order integral sliding mode surface is presented and its fixed time stability to origin is analytically proved using the Lyapunov stability theory. In addition, by considering the parametric estimations in the controller, an appropriate adaptive law is constructed to obtain the expected results. Finally, compared with the existing finite-time stability method, some numerical simulations are conducted to demonstrate the validity and superiority of the proposed approach.