论文标题
通过自适应延迟反馈控制，稳定未知分数系统的不稳定周期轨道
Stabilizing unstable periodic orbit of unknown fractional-order systems via adaptive delayed feedback control
论文作者
论文摘要
本文提出了一种自适应非线性延迟反馈控制方案，用于稳定未知分数混沌系统的不稳定周期轨道。所提出的控制框架使用Lyapunov方法和滑动模式控制技术来确保闭环系统在足够接近系统不稳定的周期性轨道的周期性轨迹上渐近稳定。提出的方法具有两个重要的优势。首先，它采用了直接的自适应控制方法，使得可以轻松地在具有未知参数的系统上实现此方法。其次，该框架仅需要不稳定的周期轨道的期限。闭环系统对系统不确定性的鲁棒性和范围未知的外部干扰。对分数duff和陀螺仪系统的模拟用于说明理论结果的有效性。仿真结果表明，我们的方法优于先前开发的线性反馈控制方法，用于稳定分数阶的混沌系统中不稳定的周期性轨道，尤其是在减少稳态误差和实现跟踪误差的更快收敛方面。
This article presents an adaptive nonlinear delayed feedback control scheme for stabilizing the unstable periodic orbit of unknown fractional-order chaotic systems. The proposed control framework uses the Lyapunov approach and sliding mode control technique to guarantee that the closed-loop system is asymptotically stable on a periodic trajectory sufficiently close to the unstable periodic orbit of the system. The proposed method has two significant advantages. First, it employs a direct adaptive control method, making it easy to implement this method on systems with unknown parameters. Second, the framework requires only the period of the unstable periodic orbit. The robustness of the closed-loop system against system uncertainties and external disturbances with unknown bounds is guaranteed. Simulations on fractional-order duffing and gyro systems are used to illustrate the effectiveness of the theoretical results. The simulation results demonstrate that our approach outperforms the previously developed linear feedback control method for stabilizing unstable periodic orbits in fractional-order chaotic systems, particularly in reducing steady-state error and achieving faster convergence of tracking error.
