Super-Twisting Algorithm-Based Sliding-Mode Observer for Synchronization of Nonlinear Incommensurate Fractional-Order Chaotic Systems Subject to Unknown Inputs

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

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Estimation and Fault Diagnosis of Lithium-Ion Batteries: A Fractional-Order System Approach

Mathematical Problems in Engineering ◽

10.1155/2018/8705363 ◽

2018 ◽

Vol 2018 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Shulan Kong ◽

Mehrdad Saif ◽

Guozeng Cui

Keyword(s):

Fault Diagnosis ◽

Fault Detection ◽

Fractional Order ◽

Sliding Mode ◽

Estimation Error ◽

Lithium Ion ◽

Fault Isolation ◽

Sliding Mode Observer ◽

Fault Detection And Isolation ◽

Order System

This study investigates estimation and fault diagnosis of fractional-order Lithium-ion battery system. Two simple and common types of observers are designed to address the design of fault diagnosis and estimation for the fractional-order systems. Fractional-order Luenberger observers are employed to generate residuals which are then used to investigate the feasibility of model based fault detection and isolation. Once a fault is detected and isolated, a fractional-order sliding mode observer is constructed to provide an estimate of the isolated fault. The paper presents some theoretical results for designing stable observers and fault estimators. In particular, the notion of stability in the sense of Mittag-Leffler is first introduced to discuss the state estimation error dynamics. Overall, the design of the Luenberger observer as well as the sliding mode observer can accomplish fault detection, fault isolation, and estimation. The effectiveness of the proposed strategy on a three-cell battery string system is demonstrated.

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Secure communication on fractional-order chaotic systems via adaptive sliding mode control with teaching–learning–feedback-based optimization

Nonlinear Dynamics ◽

10.1007/s11071-018-4625-z ◽

2018 ◽

Vol 95 (2) ◽

pp. 1221-1243 ◽

Cited By ~ 11

Author(s):

Rui-Guo Li ◽

Huai-Ning Wu

Keyword(s):

Sliding Mode Control ◽

Fractional Order ◽

Secure Communication ◽

Chaotic Systems ◽

Sliding Mode ◽

Adaptive Sliding Mode Control ◽

Adaptive Sliding Mode ◽

Mode Control ◽

Teaching Learning

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Adaptive synchronization of uncertain fractional-order chaotic systems using sliding mode control techniques

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1177/0959651819849284 ◽

2019 ◽

Vol 234 (1) ◽

pp. 3-9 ◽

Cited By ~ 3

Author(s):

Bahram Yaghooti ◽

Ali Siahi Shadbad ◽

Kaveh Safavi ◽

Hassan Salarieh

Keyword(s):

Control System ◽

Sliding Mode Control ◽

Fractional Order ◽

Chaotic Systems ◽

Closed Loop ◽

Sliding Mode ◽

Closed Loop Control ◽

Loop Control ◽

Closed Loop Control System ◽

Loop Control System

In this article, an adaptive nonlinear controller is designed to synchronize two uncertain fractional-order chaotic systems using fractional-order sliding mode control. The controller structure and adaptation laws are chosen such that asymptotic stability of the closed-loop control system is guaranteed. The adaptation laws are being calculated from a proper sliding surface using the Lyapunov stability theory. This method guarantees the closed-loop control system robustness against the system uncertainties and external disturbances. Eventually, the presented method is used to synchronize two fractional-order gyro and Duffing systems, and the numerical simulation results demonstrate the effectiveness of this method.

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