Nonlinear observer design to synchronize fractional-order chaotic systems via a scalar transmitted signal

2006 ◽  
Vol 359 ◽  
pp. 107-118 ◽  
Author(s):  
Jun Guo Lu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Transmitted Signal

A nonlinear fractional-order H∞ observer for SOC estimation of battery pack of electric vehicles

2021 ◽  
pp. 095440702199434
Author(s):  
Wei Yue ◽  
Cong-zhi Liu ◽  
Liang Li ◽  
Xiang Chen ◽  
Fahad Muhammad
Keyword(s):  
Fractional Order ◽  
Estimation Method ◽  
Equivalent Circuit Model ◽  
Lithium Ion ◽  
Open Circuit ◽  
Design Criterion ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Battery Pack ◽  
Soc Estimation

This work is focused on designing a fractional-order [Formula: see text] observer and applying it into the state of charge (SOC) estimation for lithium-ion battery pack system. Firstly, a fractional order equivalent circuit model based on the fractional capacitor is established and identified. Secondly, the SOC estimation method based on the fractional-order [Formula: see text] observer is proposed. The nonlinear intrinsic relationship between the open-circuit voltage and SOC is described as a polynomial function, and its Lipschitz proposition has been discussed. Then, the nonlinear observer design criterion is established based on the Lyapunov method. Finally, the effectiveness of the proposed method is verified with high accuracy and robustness by the experiment results.

OBSERVER-BASED SYNCHRONIZATION FOR A CLASS OF FRACTIONAL CHAOTIC SYSTEMS VIA A SCALAR SIGNAL: RESULTS INVOLVING THE EXACT SOLUTION OF THE ERROR DYNAMICS

2011 ◽  
Vol 21 (03) ◽  
pp. 955-962 ◽  
Author(s):  
DONATO CAFAGNA ◽  
GIUSEPPE GRASSI
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Exact Analytical Solution ◽  
Fractional Order Systems ◽  
Fractional Error ◽  
Transmitted Signal ◽  
Error Dynamics

This paper deals with chaos synchronization for a class of fractional-order systems characterized by one nonlinearity. In particular, an observer-based approach is illustrated, which presents two remarkable features: (i) it provides an exact analytical solution of the fractional error dynamics, written in terms of Mittag-Leffler function; (ii) it enables synchronization to be achieved using a scalar transmitted signal. Finally, a synchronization example based on fractional Chua's system is illustrated, with the aim to show the capabilities of the developed approach.

scholarly journals Robust Synchronization Control of Uncertain Fractional-Order Chaotic Systems via Disturbance Observer

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Kaijuan Xue ◽  
Yongbing Huangfu
Keyword(s):  
Fractional Order ◽  
Disturbance Observer ◽  
Chaotic Systems ◽  
Control Method ◽  
Observer Design ◽  
Synchronization Error ◽  
Synchronization Control ◽  
Compact Set ◽  
Control Scheme ◽  
Unknown Disturbances

This paper studies the synchronization of two different fractional-order chaotic systems through the fractional-order control method, which can ensure that the synchronization error converges to a sufficiently small compact set. Afterwards, the disturbance observer of the synchronization control scheme based on adaptive parameters is designed to predict unknown disturbances. The Lyapunov function method is used to verify the appropriateness of the disturbance observer design and the convergence of the synchronization error, and then the feasibility of the control scheme is obtained. Finally, our simulation studies verify and clarify the proposed method.

scholarly journals A Fractional High-Gain Nonlinear Observer Design—Application for Rivers Environmental Monitoring Model

2020 ◽  
Vol 25 (3) ◽  
pp. 44
Author(s):  
Abraham Efraim Rodriguez-Mata ◽  
Yaneth Bustos-Terrones ◽  
Victor Gonzalez-Huitrón ◽  
Pablo Antonio Lopéz-Peréz ◽  
Omar Hernández-González ◽  
...  
Keyword(s):  
Fractional Order ◽  
Oxygen Demand ◽  
Environmental Water ◽  
High Gain ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Distribution Models ◽  
Luenberger Observer ◽  
Monitoring Model ◽  
Numerical Studies

The deterioration of current environmental water sources has led to the need to find ways to monitor water quality conditions. In this paper, we propose the use of Streeter–Phelps contaminant distribution models and state estimation techniques (observer) to be able to estimate variables that are very difficult to measure in rivers with online sensors, such as Biochemical Oxygen Demand (BOD). We propose the design of a novel Fractional Order High Gain Observer (FOHO) and consider the use of Lyapunov convergence functions to demonstrate stability, as it is compared to classical extended Luenberger Observer published in the literature, to study the convergence in BOD estimation in rivers. The proposed methodology was used to estimated Dissolved oxygen (DO) and BOD monitoring of River Culiacan, Sinaloa, Mexico. The use of fractional order in high-gain observers has a very effective effect on BOD estimation performance, as shown by our numerical studies. The theoretical results have shown that robust observer design can help solve problems in estimating complex variables.

scholarly journals Chaotic Systems Synchronization Via High Order Observer Design

2011 ◽  
Vol 9 (01) ◽  
Author(s):  
J. L. Mata-Machuca ◽  
R. Martínez-Guerra ◽  
R. Aguilar-López
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Nonlinear Oscillators ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Sufficient Condition ◽  
Exponential Polynomial ◽  
Synchronization Problem

In this paper, we consider the synchronization problem via a nonlinear observer design. A new exponential polynomial observer for a class of nonlinear oscillators is proposed, which is robust against output noises. A sufficient condition for synchronization is derived analytically with the help of the Lyapunov stability theory. The proposed technique has been applied to synchronize chaotic systems (Rikitake and Rössler systems) by numerical simulation.

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