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Abstract: A novel type of control strategy combining the fractional calculus with terminal sliding mode control called fractional terminal sliding mode control is introduced for a class of dynamical systems subject to uncertainties. A fractional-order switching manifold is proposed and the corresponding control law is formulated based on the Lyapunov stability theory to guarantee the sliding condition. The proposed fractional-order terminal sliding mode controller ensures the finite time stability of the closed-loop system. Finally, numerical simulation results are presented and compared to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: We address the problem of control and synchronization of a class of uncertain chaotic systems. Our approach follows techniques of sliding mode control and adaptive estimation law. The adaptive algorithm is constructed based on the sliding mode control to ensure perfect tracking and synchronization in presence of system uncertainty and external disturbance. Stability of the closed-loop system is proved using Lyapunov stability theory. Our theoretical findings are supported by simulation results. [ABSTRACT FROM AUTHOR]

Abstract: An adaptive sliding mode control (ASMC) technique is introduced in this paper for a chaotic dynamical system (Genesio–Tesi system). Using the sliding mode control technique, a sliding surface is determined and the control law is established. An adaptive sliding mode control law is derived to make the states of the Genesio–Tesi system asymptotically track and regulate the desired state. The designed control scheme can control the uncertain chaotic behaviors to a desired state without oscillating very fast and guarantee the property of asymptotical stability. An illustrative simulation result is given to demonstrate the effectiveness of the proposed adaptive sliding mode control design. [Copyright &y& Elsevier]

Abstract: This paper proposes a sliding mode control strategy for a new uncertain chaotic dynamical system (Liu system). Using the sliding mode control technique and based on Lyapunov stability theory, a sliding surface is determined and a robust control law is established which stabilizes the uncertain chaotic system. The chattering phenomenon, which is inherent in conventional switching-type sliding controllers, due to this control law is very small and is damped quickly. An illustrative simulation result is given to demonstrate the effectiveness of the proposed sliding mode control design. [Copyright &y& Elsevier]