This article presents a simple stabilizing control algorithm for a class of underactuated mechanical systems for two degrees of freedom (2DoF). In this respect, the adaptive sliding mode based strategy is proposed for the considered class. The controller, along with the adapted laws, is decided in such a way that the time derivative of a Lyapunov function grows negative. The proposed control technique has been applied to three classic benchmark 2DOF systems, the acrobot, pendoubt, and the cart-pole system. The effectiveness of the proposed strategy is proved in the light of simulation results for all said systems considered as an illustrative example.
In this article, complete synchronization and antisynchronization in the identical financial chaotic system are presented. The proposed control strategies depend on first-order sliding mode and adaptive integral sliding mode for complete synchronization and antisynchronization of the identical financial chaotic system. In the primary case, the system parameters should be known, and first-order sliding mode control is utilized for synchronization and antisynchronization while in the second case, the system parameters are considered unknown. An adaptive integral sliding mode control strategy is utilized for synchronization and antisynchronization of the system considering the parameters unknown. The error system is changed into a particular structure containing a nominal part and several unknown terms to utilize the adaptive integral sliding mode control. Then, this error system is stabilized using integral sliding mode control. The stabilizing controller is usually developed based on the nominal part plus the compensator control part. To suppress the high-frequency oscillation (chattering) phenomenon, smooth continuous compensator control can be used rather than conventional discontinuous control. The compensator controller along with the adapted law is derived such that the time derivative of the Lyapunov function becomes strictly negative. The effectiveness of the proposed method was tested through computer simulations. The proposed control strategies are verified for that Identical 4D hyperchaotic financial system to attain complete synchronization and antisynchronization along with the improved performance.
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