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Abstract This paper presents a novel control technique for a class of uncertain and time varying n th-order non-affine non-linear systems with an integral terminal sliding mode augmented with uncertainty and disturbance estimator (UDE). These non-linear systems are difficult to control due to non-affine nature of their inputs, failure of feedback linearization approach and control singularity problems. Therefore, an integral terminal sliding surface is chosen to ensure the faster and finite time convergence of the system dynamics to the desired dynamics. UDE provides a chatter-free auxiliary controller for eliminating the impacts of complex system non-affine uncertainties. Moreover, the system uncertainties and external disturbances are tackled without requiring information about their upper bounds. Furthermore, the superior tracking performances and stability are guaranteed through Lyapunov's direct method. Also, three simulation examples are presented to illustrate the efficacy of the proposed methodology by comparing with the previous methods in literature. Highlights • A novel sliding mode control with UDE is derived for the non-affine non-linear systems. • A chatter-free controller is designed without considering the upper bounds on the system uncertainties. • Ensures the tracking of reference model while tackling system affine and non-affine uncertainties. • Three examples are taken to validate the derived results. • Comparison of the proposed method with the previous DOBC-ISMC and ISMC based control schemes. [ABSTRACT FROM AUTHOR]

Highlights • Finite time synchronization of fractional order chaotic/hyperchaotic systems. • A novel chatter free fractional order sliding mode control technique is proposed. • System uncertainties are considered in every chaotic state. • Bounds of uncertainties are not even required in control design. • Uncertainty and disturbance estimator is added to tackle unknown uncertainties. Abstract This paper deals with a finite time robust synchronization problem of a class of uncertain fractional chaotic/hyper-chaotic systems with a novel fractional sliding mode control technique. Firstly, a fractional order sliding surface is proposed to mimic the behavior of master chaotic system. Then, a fractional order sliding mode control (FOSMC) methodology is derived analytically for convergence of all the synchronizing errors to zero in finite time. Finally, the derived control strategy is augmented with an auxiliary control based on uncertainty and disturbance estimator (UDE) for ensuring the robustness of the closed loop system dynamics in the presence of system uncertainties. Further, the uncertainties with unknown bounds are tackled for depicting the practical scenario and these results are also applicable to the N-dimensional uncertain chaotic as well as hyper-chaotic systems. Moreover, Mittag-Leffler and fractional order Lyapunov results are utilized to prove the stability and finite time convergence. Also, the proposed method delivers chatter-free control signal which is a major issue in sliding mode. MATLAB simulations are carried out to verify the efficacy and robustness of the derived results by considering two examples from literature. [ABSTRACT FROM AUTHOR]