No abstract

The gyro is an interesting and everlasting nonlinear nonautonomous dynamical system that exhibits very rich and complex behavior such as chaos. However, in recent years, modeling and control of fractional-order dynamical systems have become important and useful topics in both research and engineering applications. In this article, the dynamical behavior of a nonautonomous fractional-order gyro system is investigated. We apply the maximal Lyapunov exponent criterion to show that the fractional-order gyro system exhibits chaos. Strange attractors of the system are also plotted to validate the chaotic behavior of the system. Subsequently, in order to suppress the chaotic state of the fractional-order gyro system, a robust finite-time fractional controller is designed. The convergence time of the proposed control scheme is estimated. And the fractional Lyapunov theory is adopted to prove the finite-time stability and robustness of the proposed method. Besides, some computer simulations are given to illustrate the effectiveness and applicability of the proposed fractional controller.

This paper solves the problem of robust synchronization of nonlinear chaotic gyrostat systems in a given finite time. The parameters of both master and slave chaotic gyrostat systems are assumed to be unknown in advance. In addition, the gyrostat systems are disturbed by unknown model uncertainties and external disturbances. Suitable update laws are proposed to estimate the unknown parameters. Based on the finite-time control idea and update laws, appropriate control laws are designed to ensure the stabilization of the closed-loop system in finite time. The precise value of the convergence time is given. A numerical simulation demonstrates the applicability and efficiency of the proposed finite-time synchronization strategy.

No abstract

The centrifugal flywheel governor is a mechanical device that automatically controls the speed of an engine and avoids the damage caused by an abrupt change of load torque. Recent research has discovered that this system exhibits very rich and complex dynamics such as chaos. In this paper, the problem of finite-time stabilization of non-autonomous chaotic centrifugal flywheel governor systems in the presence of model uncertainties, external disturbances, fully unknown parameters and input nonlinearities is studied. Appropriate adaptation laws are designed to undertake the system’s unknown parameters. Using the adaptation laws and finite-time control theory, a robust adaptive controller is derived to stabilize the non-autonomous uncertain centrifugal flywheel governor system with nonlinear control inputs in a given finite time. The finite-time stability and convergence of the closed-loop system are analytically proved. A numerical simulation is given to show the robustness and effectiveness of the proposed finite-time controller and to verify the theoretical results of the paper.