Su Haipeng, Luo Runzi, Fu Jiaojiao, Huang Meichun
Department of Mathematics, Nanchang University, 330031, PR China.
ISA Trans. 2021 Dec;118:75-82. doi: 10.1016/j.isatra.2021.02.012. Epub 2021 Feb 14.
The main goal of this article is to consider the fixed time control problem of perturbed chaotic systems by virtue of sliding mode control. For this aim, this article presents a novel fixed time stability theorem at first by the Lyapunov tools. Then combining the obtained stability theorem and sliding mode technique, a new sliding mode surface is constructed and some novel controllers are designed appropriately to stabilize the discussed chaotic system. The proposed controllers have two main advantages: (1) The control criteria is robust against the effects of perturbations. (2) The convergence time, which is only dependent on the control parameters regardless of the initial conditions, is bounded by a fixed constant. Finally two typical systems are taken as the numerical examples to verify the validity of the control strategy.
本文的主要目标是借助滑模控制来研究受扰混沌系统的固定时间控制问题。为此，本文首先利用李雅普诺夫工具提出了一个新颖的固定时间稳定性定理。然后，结合所得到的稳定性定理和滑模技术，构造了一个新的滑模面，并适当地设计了一些新颖的控制器来稳定所讨论的混沌系统。所提出的控制器有两个主要优点：（1）控制准则对扰动的影响具有鲁棒性。（2）收敛时间仅取决于控制参数，而与初始条件无关，且由一个固定常数界定。最后，以两个典型系统作为数值例子来验证控制策略的有效性。
