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Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 ISSN Print: 2576-0645 CODEN: JAMCEZ
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ArticleOpen Access http://dx.doi.org/10.26855/jamc.2023.12.001

Time-delayed Feedback Control of Chaotic Systems Based on Fractional Order Integration

Wubin Wang, Yanmao Chen*, Qixian Liu

Department of Theoretical and Applied Mechanics, Shenzhen Campus of Sun Yat-sen University, Shenzhen, Guangdong, China.

*Corresponding author: Yanmao Chen

Published: November 23,2023

Abstract

Research has been conducted to address challenges in controlling chaotic responses, particularly related to stabilizing unstable periodic orbits (UPOs) within chaotic systems. To address this issue, a delayed feedback controller was designed. Given the observation that integrations are insensitive to state errors and can be leveraged to reduce the degree of error, we implemented fractional integrations to the feedback states instead of commonly used derivatives. This was done with the aim of improving control precision. As part of the methodology, the short-term memory principle was employed to optimize computational efficiency. The memory interval was truncated to match the time delay, ensuring efficient handling of fractional integrations. Several chaotic systems were used as application examples in this experiment. Our results revealed that the proposed controller exhibits higher control precision than that achieved by the traditional delayed feedback control approach. A significant aspect of our work is the introduction of adjustable fractional order, which offers enhanced applicability in scenarios where the classical approach may be ineffective. In terms of conclusions, we selected the minimum steady-state error of the system as the optimization objective. We employed a swarm intelligence optimization algorithm to optimize the control parameters of the fractional delayed feedback controller. Notably, our optimized system showed a significant reduction in steady-state error, thereby confirming the effectiveness of our method.

Keywords

Chaos Control, Delayed Feedback, Fractional Integration, Unstable Periodic Orbit

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How to cite this paper

Time-delayed Feedback Control of Chaotic Systems Based on Fractional Order Integration

How to cite this paper: Wubin Wang, Yanmao Chen, Qixian Liu. (2023) Time-delayed Feedback Control of Chaotic Systems Based on Fractional Order Integration. Journal of Applied Mathematics and Computation7(4), 415-425.

DOI: http://dx.doi.org/10.26855/jamc.2023.12.001