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首页> 外文期刊>Journal of physics, A. Mathematical and theoretical >Delayed feedback control of fractional-order chaotic systems
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Delayed feedback control of fractional-order chaotic systems

机译：分数阶混沌系统的延迟反馈控制

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摘要

We study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional-order dynamical systems by the time-delayed feedback method. By performing a linear stability analysis, we establish the parameter ranges for successful stabilization of unstable equilibria in the plane parameterized by the feedback gain and the time delay. An insight into the control mechanism is gained by analyzing the characteristic equation of the controlled system, showing that the control scheme fails to control unstable equilibria having an odd number of positive real eigenvalues. We demonstrate that the method can also stabilize unstable periodic orbits for a suitable choice of the feedback gain, providing that the time delay is chosen to coincide with the period of the target orbit. In addition, it is shown numerically that delayed feedback control with a sinusoidally modulated time delay significantly enlarges the stability region of steady states in comparison to the classical timedelayed feedback scheme with a constant delay.
机译：我们通过时滞反馈方法研究了在混沌分数阶动力系统中稳定不稳定稳态和不稳定周期轨道的可能性。通过执行线性稳定性分析，我们建立了通过反馈增益和时延参数化的平面中不稳定平衡的成功稳定参数范围。通过分析受控系统的特征方程，可以深入了解控制机制，表明该控制方案无法控制具有奇数个正实特征值的不稳定平衡。我们证明，该方法还可以稳定不稳定的周期性轨道，以适当选择反馈增益，条件是所选择的时间延迟与目标轨道的周期一致。另外，从数值上显示，与具有恒定延迟的经典时滞反馈方案相比，具有正弦调制时滞的延迟反馈控制显着扩大了稳态的稳定范围。

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