Chaos Suppression in Uncertain Generalized Lorenz–Stenflo Systems via a Single Rippling Controller with Input Nonlinearity

Chih-Hsueh Lin, Guo-Hsin Hu and Jun-Juh Yan
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Chih-Hsueh Lin: Department of Electronic Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan
Guo-Hsin Hu: Department of Electronic Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan
Jun-Juh Yan: Department of Electronic Engineering, National Chin-Yi University of Technology, Taichung 41107, Taiwan

Mathematics, 2020, vol. 8, issue 3, 1-12

Abstract: In this paper, a robust control design of chaos suppression is considered for generalized four-dimensional (4D) Lorenz–Stenflo systems subjected to matched/mismatched uncertainties and input nonlinearity. It is implemented by using rippling sliding mode control (SMC). A proportional-integral (PI) type scalar switching surface is designed such that the controlled dynamics in the sliding manifold becomes easy to analyze. Furthermore, only by using single rippling SMC even with input nonlinearity can we ensure the existence of the sliding mode for the controlled dynamics and suppress the chaotic behavior in a manner of rippling. Under the proposed control scheme, the chaos behavior in uncertain generalized 4D Lorenz–Stenflo systems subjected to mismatched uncertainties can be robustly suppressed to predictable bounds, which is not addressed in the literature. The numerical simulation results including matched/mismatched uncertainties and nonlinear inputs are presented to verify the robustness and validity of the rippling sliding mode controller.

Keywords: mismatched uncertainty; input nonlinearity; sliding mode control; 4D Lorenz–Stenflo system; rippling control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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