Adaptive Finite-Time Stabilization of Chaotic Flow with a Single Unstable Node Using a Nonlinear Function-Based Global Sliding Mode
This article presents a novel adaptive finite-time stabilization technique based on global sliding mode for disturbed chaotic flow with a single unstable node. The considered chaotic flow has unusual characteristics containing attractor merging, symmetry breaking, attracting tori and different forms of multi-stability. A nonlinear function is employed in the global sliding surface to modify damping ratio and improve the transient performance. The damping ratio of the closed-loop system is improved when the states converge to the origin. Using the new chattering-free controller, the reaching mode is removed and the sliding behavior is presented right from the first instant. The adaptive finite-time tuning law eliminates the requirement of the information about the disturbances’ bounds. Illustrative simulations are provided to display the efficiency of the proposed scheme.
KeywordsGlobal sliding mode Adaptive gain tuning Finite-time control Chaotic flow Unstable node
This work was partially supported by the Spanish Ministry of Economy, Industry and Competitiveness, under Grants DPI2016-77407-P (AEI/FEDER, UE) and DPI2015-64170-R (MINECO/FEDER).
- Li S-B, Li K-Q, Wang J-Q, Yang B (2010) Nonsingular fast terminal-sliding-mode control method and its application on vehicular following system. Control Theory Appl 5:004Google Scholar
- Li X-B, Ma L, Ding S-H (2015) A new second-order sliding mode control and its application to inverted pendulum. Acta Automatica Sinica 1:022Google Scholar
- Xu Y, Ke Z, Xie C, Zhou W (2018b) Dynamic evolution analysis of stock price fluctuation and its control. Complexity 2018:9 pages, Article ID 5728090Google Scholar
- Zhong T, Yuanwei J, Chengyin Y, Nan J (2014) Global sliding mode control based on observer for TCP network. In: The 26th chinese control and decision conference (2014 CCDC) 2014, p 4946–4950Google Scholar