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A fractional sliding mode for finite-time control scheme with application to stabilization of electrostatic and electromechanical transducers

机译：有限时间控制方案的分数滑模，应用于稳定静电和机电换能器

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摘要

Chaos suppression of non-autonomous uncertain chaotic systems is a very important and attractive topic in the field of physics and engineering. On the other hand, the use of fractional calculus in both research and practice has become as an increasing and interesting issue in recent years. In this paper, we introduce a novel fractional control method for chaos control of integer-order non-autonomous chaotic systems. It is assumed that the system is disturbed by some model uncertainties and external noises. A novel fractional nonsingular terminal sliding manifold which is appropriate for integer-order systems is proposed. Then, on the basis of fractional Lyapunov stability theorem, a suitable robust sliding mode control law is designed to force the state trajectories of the system into the sliding manifold. It is proved that both the sliding mode and reaching phase are realized in a given finite time. Finally, the proposed method is applied for stabilization of chaotic electrostatic and electromechanical transducers.
机译：非自治不确定混沌系统的混沌抑制是物理和工程领域非常重要和有吸引力的课题。另一方面，近年来，在研究和实践中使用分数微积分已经成为一个越来越重要的问题。本文介绍了一种新颖的分数阶控制方法，用于整数阶非自治混沌系统的混沌控制。假定系统受到模型不确定性和外部噪声的干扰。提出了一种适用于整数阶系统的分数阶非奇异终端滑动流形。然后，基于分数次Lyapunov稳定性定理，设计了一种合适的鲁棒滑模控制律，以迫使系统的状态轨迹进入滑动流形。证明在给定的有限时间内都实现了滑模和到达相位。最后，将所提出的方法应用于混沌静电和机电换能器的稳定化。

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