scholarly journals Robust Stabilization of Nonlinear Fractional Order Interconnected Systems Based on T-S Fuzzy Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Yuting Li
Keyword(s):  
Fractional Order ◽  
Direct Method ◽  
Robust Stabilization ◽  
Fuzzy Model ◽  
Interconnected Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lyapunov Direct Method ◽  
Takagi Sugeno ◽  
Order Extension

This paper concerns robust stabilization of nonlinear fractional order interconnected systems. Based on uncertain fractional order Takagi–Sugeno fuzzy model and the fractional order extension of lyapunov direct method, a parallel distributed compensate controller is designed to asymptotically stabilize the fractional order interconnected systems. Then, a sufficient condition is given in the format of linear matrix inequalities. Simulation example is given to validate the effectiveness of the approach.

Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay

2021 ◽  
pp. 107754632110069
Author(s):  
Parvin Mahmoudabadi ◽  
Mahsan Tavakoli-Kakhki
Keyword(s):  
Fractional Order ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed Systems ◽  
Fuzzy Observer ◽  
Time Varying Delay ◽  
Takagi Sugeno

In this article, a Takagi–Sugeno fuzzy model is applied to deal with the problem of observer-based control design for nonlinear time-delayed systems with fractional-order [Formula: see text]. By applying the Lyapunov–Krasovskii method, a fuzzy observer–based controller is established to stabilize the time-delayed fractional-order Takagi–Sugeno fuzzy model. Also, the problem of disturbance rejection for the addressed systems is studied via the state-feedback method in the form of a parallel distributed compensation approach. Furthermore, sufficient conditions for the existence of state-feedback gains and observer gains are achieved in the terms of linear matrix inequalities. Finally, two numerical examples are simulated for the validation of the presented methods.

scholarly journals Non-Fragile Robust H∞ Filtering of Takagi-Sugeno Fuzzy Networked Control Systems with Sensor Failures

Sensors ◽  
2019 ◽  
Vol 20 (1) ◽  
pp. 27 ◽  
Author(s):  
Hao Wang ◽  
Shousheng Xie ◽  
Bin Zhou ◽  
Weixuan Wang
Keyword(s):  
Control Systems ◽  
Networked Control Systems ◽  
Fault Tolerant ◽  
Fuzzy Model ◽  
Networked Control ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Sensor Failures ◽  
Takagi Sugeno ◽  
Filtering Problem

The fault-tolerant robust non-fragile H∞ filtering problem for networked control systems with sensor failures is studied in this paper. The Takagi-Sugeno fuzzy model which can appropriate any nonlinear systems is employed. Based on the model, a filter which can maintain stability and H∞ performance level under the influence of gain perturbation of the filter and sensor failures is designed. Moreover, the gain matrix of sensor failures is converted into a dynamic interval to expand the range of allowed failures. And the sufficient condition for the existence of the desired filter is derived in terms of linear matrix inequalities (LMIs) solutions. Finally a simulation example is given to illustrate the effectiveness of the proposed method.

Adaptive impulsive synchronization for a class of fractional order complex chaotic systems

2019 ◽  
Vol 25 (10) ◽  
pp. 1614-1628 ◽  
Author(s):  
Xingpeng Zhang ◽  
Dong Li ◽  
Xiaohong Zhang
Keyword(s):  
Number Field ◽  
Fractional Order ◽  
Complex Number ◽  
Chaotic Systems ◽  
Direct Method ◽  
Order Complex ◽  
Lyapunov Direct Method ◽  
Impulsive Synchronization ◽  
Complex Chaotic Systems ◽  
Order Extension

In this paper, a new lemma is proposed to study the stability of a fractional order complex chaotic system without dividing the complex number into real and imaginary parts. The proving process of the new lemma combines the fundamental properties of the complex field and the fractional order extension of the Lyapunov direct method. It extends the fractional order extension of the Lyapunov direct method from the real number field to the complex number field. Based on the new lemma, we propose a new impulsive synchronization scheme for fractional order complex chaotic systems. The numerical simulation results also show the validity of our conclusion.

STABILITY ANALYSIS OF NONLINEAR INTERCONNECTED SYSTEMS VIA T–S FUZZY MODELS

2004 ◽  
Vol 04 (01) ◽  
pp. 41-55 ◽  
Author(s):  
WEI-LING CHIANG ◽  
CHENG-WU CHEN ◽  
FENG-HSIAG HSIAO
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Direct Method ◽  
Interconnected Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Fuzzy Models ◽  
Fuzzy Techniques ◽  
The Stability ◽  
Takagi Sugeno

This paper is concerned with the stability problem of nonlinear interconnected systems. Each of them consists of a few interconnected subsystems which are approximated by Takagi–Sugeno (T–S) type fuzzy models. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the asymptotic stability of interconnected systems. It is shown that the stability analysis problems of nonlinear interconnected systems can be reduced to linear matrix inequality (LMI) problems via suitable Lyapunov functions and T–S fuzzy techniques. Finally, numerical examples with simulations are given to demonstrate the validity of the proposed approach.

scholarly journals Model reduction design for continuous systems with finite frequency specifications

2021 ◽  
Vol 11 (5) ◽  
pp. 3956
Author(s):  
Miloud Koumir ◽  
Abderrahim El-Amrani ◽  
Ismail Boumhidi
Keyword(s):  
Model Reduction ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Continuous Systems ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Error System ◽  
Takagi Sugeno

<p>This paper is concerned with the problem of model reduction design for continuous systems in Takagi-Sugeno fuzzy model. Through the defined FF H∞ gain performance, sufficient conditions are derived to design model reduction and to assure the fuzzy error system to be asymptotically stable with a FF H∞ gain performance index. The explicit conditions of fuzzy model reduction are developed by solving linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.</p>

Chaos Synchronization of Fractional-Order Lur’e Systems

2020 ◽  
Vol 30 (14) ◽  
pp. 2050206
Author(s):  
Mohammed Salah Bouridah ◽  
Toufik Bouden ◽  
Müştak Erhan Yalçin
Keyword(s):  
Fractional Order ◽  
Chaos Synchronization ◽  
Direct Method ◽  
Linear Matrix ◽  
Lyapunov Direct Method ◽  
Lur’E Systems ◽  
Controller Gain ◽  
Error System ◽  
Synchronization Scheme ◽  
Order Four

Based on some essential concepts of fractional calculus and the theorem related to the fractional extension of Lyapunov direct method, we present in this paper a synchronization scheme of fractional-order Lur’e systems. A quadratic Lyapunov function is chosen to derive the synchronization criterion. The derived criterion is a suffcient condition for the asymptotic stability of the error system, formulated in the form of linear matrix inequality (LMI). The controller gain can be achieved by solving the LMI. The proposed scheme is illustrated for fractional-order Chua’s circuits and fractional-order four-cell CNN. Numerical results, which agree well with the proposed theorem, are given to show the effectiveness of this scheme.

scholarly journals Stable Fault Tolerant Controller Design for Takagi–Sugeno Fuzzy Model-Based Control Systems via Linear Matrix Inequalities: Three Conical Tank Case Study

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2221 ◽  
Author(s):  
Himanshukumar R. Patel ◽  
Vipul A. Shah
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Control Systems ◽  
Linear Models ◽  
Fault Tolerant ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Fuzzy Models ◽  
Takagi Sugeno

This paper deals with a methodical design approach of fault-tolerant controller that gives assurance for the the stabilization and acceptable control performance of the nonlinear systems which can be described by Takagi–Sugeno (T–S) fuzzy models. Takagi–Sugeno fuzzy model gives a unique edge that allows us to apply the traditional linear system theory for the investigation and blend of nonlinear systems by linear models in a different state space region. The overall fuzzy model of the nonlinear system is obtained by fuzzy combination of the all linear models. After that, based on this linear model, we employ parallel distributed compensation for designing linear controllers for each linear model. Also this paper reports of the T–S fuzzy system with less conservative stabilization condition which gives decent performance. However, the controller synthesis for nonlinear systems described by the T–S fuzzy model is a complicated task, which can be reduced to convex problems linking with linear matrix inequalities (LMIs). Further sufficient conservative stabilization conditions are represented by a set of LMIs for the Takagi–Sugeno fuzzy control systems, which can be solved by using MATLAB software. Two-rule T–S fuzzy model is used to describe the nonlinear system and this system demonstrated with proposed fault-tolerant control scheme. The proposed fault-tolerant controller implemented and validated on three interconnected conical tank system with two constraints in terms of faults, one issed to build the actuator and sond is system component (leak) respectively. The MATLAB Simulink platform with linear fuzzy models and an LMI Toolbox was used to solve the LMIs and determine the controller gains subject to the proposed design approach.

A Simple, Natural and Effective Framework of Nonlinear Systems Control and its Application to Aerial Robots

2014 ◽  
Vol 26 (2) ◽  
pp. 140-147 ◽  
Author(s):  
Motoyasu Tanaka ◽  
◽  
Hiroshi Ohtake ◽  
Kazuo Tanaka ◽  
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Design Problems ◽  
Model Based Control ◽  
Aerial Robots ◽  
Control Framework ◽  
Systems Control ◽  
Takagi Sugeno

This paper presents a simple, natural and effective framework of nonlinear systems control and its application to aerial robots. First, we present a framework of Takagi-Sugeno fuzzy model-based control and also discuss its feature. Next, a number of design problems for the control framework are formulated as numerically feasibility problems of representing in terms of linear matrix inequalities. Finally, we provide two applications of the control framework to aerial robots. The control results of aerial robots show the utility of the control framework.

Robust Stabilization And Control Of Takagi-Sugeno Fuzzy Systems With Parameter Uncertainties And Disturbances Via State Feedback And Output Feedback

2020 ◽  
Vol 9 (3) ◽  
pp. 63-99
Author(s):  
Iqbal Ahammed A.K. ◽  
Mohammed Fazle Azeem
Keyword(s):  
Output Feedback ◽  
Fuzzy Systems ◽  
State Feedback ◽  
Robust Stabilization ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Ts Fuzzy Model ◽  
Takagi Sugeno ◽  
And Control

Most of the systems in the industry contain extreme non-linearity and uncertainties, which are hard to design and control utilizing general nonlinear systems. To conquer this sort of troubles, different plans have been produced in the most recent two decades, among which a popular methodology is Takagi-Sugeno fuzzy control. In this article, we present robust stabilization and control of Takagi-Sugeno (T-S) fuzzy systems with parameter uncertainties and disturbances. Initially, Takagi and Sugeno (TS) fuzzy model is used to represent a nonlinear system. Based on this T-S fuzzy model, fuzzy controller design schemes for state feedback and output feedback is also developed. Then, necessary conditions are derived for robust stabilization in the intelligence of Lyapunov asymptotic stability and are expressed in the arrangement of linear matrix inequalities (LMIs). The proposed system is implemented in the working platform of MATLAB and the simulation results are provided to illustrate the effectiveness of the proposed methods.

Nonlinear control design using Takagi-Sugeno fuzzy applied to under-actuated visual servo system

2020 ◽  
Vol 42 (15) ◽  
pp. 2969-2983
Author(s):  
Vimala Kumari Jonnalagadda ◽  
Vinodh Kumar Elumalai ◽  
Harvir Singh ◽  
Amit Prasad
Keyword(s):  
Fuzzy Control ◽  
Moving Objects ◽  
Direct Method ◽  
Fuzzy Model ◽  
Control Design ◽  
Linear Matrix ◽  
Nonlinear Stabilization ◽  
Ts Fuzzy Model ◽  
Takagi Sugeno ◽  
Plate System

This paper presents the Takagi-Sugeno (TS) fuzzy control design for nonlinear stabilization and tracking control of a ball on plate system. To deal with the plant nonlinearity and the fuzzy convergence issue, we formulate the parallel distributed compensator (PDC) TS fuzzy model to characterize the global behaviour of the nonlinear system and synthesize a feasible control framework using a velocity compensation scheme. The nonlinear dynamics of the ball on plate system is obtained using the Euler-Lagrangian energy based approach. To identify the moving objects in the video stream, a background subtraction algorithm using thresholding technique is formulated. Moreover, the stability analysis of the TS fuzzy control is reduced to linear matrix inequality (LMI) problem and solved using the Lyapunov direct method. The potential benefits of the proposed control structure for real time test cases are experimentally assessed using hardware in loop (HIL) testing on a ball on plate system. Experimental results substantiate that the TS fuzzy scheme can significantly improve not only the tracking performance but also the robustness of the closed loop system.

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