The snippet could not be located in the article text. This may be because the snippet appears in a figure legend, contains special characters or spans different sections of the article. PLoS One. Published online May 3. PMID: China, Find articles by Jian Liu. China, Find articles by Kexin Liu. China, Find articles by Shutang Liu. Jun Ma, Editor.
Adaptive control of nonlinear fractional-order systems using T–S fuzzy method
Competing Interests: The authors have declared that no competing interests exist. Conceptualization: JL. Received Aug 5; Accepted Mar This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article has been cited by other articles in PMC. Abstract In this paper, adaptive control is extended from real space to complex space, resulting in a new control scheme for a class of n -dimensional time-dependent strict-feedback complex-variable chaotic hyperchaotic systems CVCSs in the presence of uncertain complex parameters and perturbations, which has not been previously reported in the literature.
Introduction Chaos is a ubiquitous phenomenon in nonlinear system. Open in a separate window. Fig 1. Preliminaries Notation The notations used throughout the paper are standard. Wirtinger calculus In this subsection, we first recall briefly the definition of Wirtinger calculus and some basic facts. Relevant lemmas Lemma 1. Adaptive complex scalar controller design based on back-stepping In this subsection, we employ the adaptive back-stepping control technique to design our complex scalar controller and complex update laws for n -dimensional CVCSs.
Step 1. Stability analysis Theorem 1. Numerical example In this section, we take the Duffing CVCSs as an example to verify and demonstrate the effectiveness of the proposed control scheme. Fig 2. Fig 3. Time response for controlled Duffing CVCSs Eq 38 with the adaptive complex scalar controller Eq 39 and complex update law Eqs 40 and 41 , and at the same parameter values and initial conditions as in Fig 1.
Discussion and conclusions In this paper, we have developed a new unified framework for the stabilization of a class of n -dimensional time-dependent strict-feedback CVCSs with uncertain complex parameters and perturbations. Data Availability All relevant data are within the paper. References 1. Lorenz E.
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