Design of Takagi-Sugeno Fuzzy Region Controller Based on Rule Reduction, Robust Control, and Switching Concept

2006 ◽  
Vol 129 (2) ◽  
pp. 163-170 ◽  
Author(s):  
Chein-Chung Sun ◽  
Sheng-Ming Wu ◽  
Hung-Yuan Chung ◽  
Wen-Jer Chang
Keyword(s):  
Robust Control ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Robot System ◽  
Uncertain Model ◽  
Lyapunov Stability Criterion ◽  
Fuzzy Regions ◽  
The Stability ◽  
Takagi Sugeno ◽  
Fuzzy Region

This paper presents a new structure of Takagi-Sugeno (T-S) fuzzy controllers, which is called T-S fuzzy region controller or TSFRC for short. The fuzzy region concept is used to partition the plant rules into several fuzzy regions so that only one region is fired at the instant of each input vector being coming. Because each fuzzy region contains several plant rules, the fuzzy region can be regarded as a polytopic uncertain model. Therefore, robust control techniques would be essential for designing the feedback gains of each fuzzy region. To improve the speed of response, the decay rate constraint is imposed when deriving the stability conditions with Lyapunov stability criterion. To design TSFRC with the linear matrix inequality (LMI) solver, all stability conditions are represented in terms of LMIs. Finally, a two-link robot system is used to prove the feasibility and validity of the proposed method.

Further Results on Stability and Stabilization of T–S Fuzzy Neutral Systems with Time-Varying Delays Using Delay Dividing Approach

2014 ◽  
Vol 11 (04) ◽  
pp. 1442007
Author(s):  
Min Kook Song ◽  
Jin Bae Park ◽  
Young Hoon Joo
Keyword(s):  
Fuzzy Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Varying ◽  
Neutral Systems ◽  
Sufficient Stability ◽  
Stability And Stabilization ◽  
The Stability ◽  
Takagi Sugeno

This paper is concerned with the stability and the stabilization problem for Takagi–Sugeno (T–S) fuzzy systems with neutral time delays. The sufficient stability conditions are derived using novel Lyapunov–Krasovskii functionals (LKFs). The stability conditions are expressed as linear matrix inequalities (LMIs) and hence easily tractable numerically. These conditions are easily extended to the sufficient conditions for the existence of stabilizing state-feedback fuzzy gains for T–S fuzzy neutral systems with time-varying delays. An example is given to illustrate the effectiveness of the proposed methods.

scholarly journals Improved Approach to Robust Control for Type-2 T-S Fuzzy Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Bum Yong Park ◽  
JaeWook Shin
Keyword(s):  
Fuzzy Systems ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Parameter Uncertainties ◽  
Comprehensive Information ◽  
Stabilization Condition ◽  
Feasible Solutions ◽  
The Stability ◽  
Takagi Sugeno

This paper is concerned with the robust stability conditions to stabilize the type 2 Takagi-Sugeno (T-S) fuzzy systems. The conditions effectively handle parameter uncertainties using lower and upper membership functions. To improve the solvability of the stability conditions, we establish a multigain controller with comprehensive information of the lower and upper membership grades. In addition, a well-organized relaxation technique is proposed to fully exploit relationship among fuzzy weighting functions and their lower and upper membership grades, which enlarges a set of feasible solutions. Therefore, we derive a less conservative stabilization condition in terms of linear matrix inequalities (LMIs) than those in the literature. Two simulation examples illustrate the effectiveness and robustness of the derived stabilization conditions.

scholarly journals Takagi-Sugeno Fuzzy Modeling and PSO-Based Robust LQR Anti-Swing Control for Overhead Crane

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Xuejuan Shao ◽  
Jinggang Zhang ◽  
Xueliang Zhang
Keyword(s):  
Linear Quadratic Regulator ◽  
Pso Algorithm ◽  
Fuzzy Modeling ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Overhead Crane ◽  
Linear Quadratic ◽  
Highly Nonlinear ◽  
The Stability ◽  
Takagi Sugeno

The dynamic model of overhead crane is highly nonlinear and uncertain. In this paper, Takagi-Sugeno (T-S) fuzzy modeling and PSO-based robust linear quadratic regulator (LQR) are proposed for anti-swing and positioning control of the system. First, on the basis of sector nonlinear theory, the two T-S fuzzy models are established by using the virtual control variables and approximate method. Then, considering the uncertainty of the model, robust LQR controllers with parallel distributed compensation (PDC) structure are designed. The feedback gain matrices are obtained by transforming the stability and robustness of the system into linear matrix inequalities (LMIs) problem. In addition, particle swarm optimization (PSO) algorithm is used to overcome the blindness of LQR weight matrix selection in the design process. The proposed control methods are simple, feasible, and robust. Finally, the numeral simulations are carried out to prove the effectiveness of the methods.

Discrete-time Inversion Model Control of a Double-damper System with Uncertain Parameters

2017 ◽  
Vol 6 (3) ◽  
pp. 168
Author(s):  
Marwa Hannachi ◽  
Ikbel Bencheikh Ahmed ◽  
Dhaou Soudani
Keyword(s):  
Discrete Time ◽  
Algebraic Approach ◽  
Building Blocks ◽  
Internal Model Control ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Inversion ◽  
Time Model ◽  
Model Control ◽  
The Stability

<span>This paper addresses the control at discrete time of physical complex systems multi-inputs multi-outputs with variables parameters. Classified among the robust control laws the Internal Model Control (IMC) is adopted in this work to ensure the desired performances adjacent to the complexities of the system. However, the application of this control strategy requires that these different building blocks be open loop stable, which invites us, on the one hand, to apply the algebraic approach of Kharitinov for delimiting the summits stability domain’s system. On the other case, the Linear Matrix Inequalities (LMI) approach is applied to determine the corrector’s stability conditions obtained by a specific inversion of the chosen model. It is in this sense that we contribute by this work to execute the command by inversion the discrete-time model in order to ensure the stability and to maintain the performances the stability conditions of required for the double damper system with variable parameters.</span>

Improved Delay-Dependent Stability of Nonlinear Quadratic TS Fuzzy Systems

2019 ◽  
Vol 29 (09) ◽  
pp. 2050134 ◽  
Author(s):  
Khadija Naamane ◽  
El Houssaine Tissir
Keyword(s):  
Fuzzy Systems ◽  
Model Transformation ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Small Gain ◽  
The Stability ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper focuses on the problem of delay-dependent stability for nonlinear quadratic Takagi–Sugeno (TS) fuzzy systems with time-varying delay using the input–output approach. The results are based on the model transformation by employing a three-terms approximation of delayed state vector. By applying the scaled small-gain theorem and Lyapunov–Krasovskii functional, the stability criteria is obtained in terms of linear matrix inequalities. Furthermore, the Wirtinger-based integral inequality approach has been employed to derive less conservative results. Finally, the numerical examples are provided to demonstrate the effectiveness of the obtained results and for comparison with previous work.

scholarly journals Improved Delay-Dependent Stability and Stabilization Conditions of T-S Fuzzy Time-Delay Systems via an Augmented Lyapunov-Krasovskii Functional Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Zifan Gao ◽  
Jiaxiu Yang ◽  
Shuqian Zhu
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Stability Conditions ◽  
State Variables ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Stability And Stabilization ◽  
The Stability ◽  
Delay Dependent

This paper develops some improved stability and stabilization conditions of T-S fuzzy system with constant time-delay and interval time-varying delay with its derivative bounds available, respectively. These conditions are presented by linear matrix inequalities (LMIs) and derived by applying an augmented Lyapunov-Krasovskii functional (LKF) approach combined with a canonical Bessel-Legendre (B-L) inequality. Different from the existing LKFs, the proposed LKF involves more state variables in an augmented way resorting to the form of the B-L inequality. The B-L inequality is also applied in ensuring the positiveness of the constructed LKF and the negativeness of derivative of the LKF. By numerical examples, it is verified that the obtained stability conditions can ensure a larger upper bound of time-delay, the larger number of Legendre polynomials in the stability conditions can lead to less conservative results, and the stabilization condition is effective, respectively.

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.

SYNCHRONIZATION OF TIME-DELAYED T–S FUZZY CHAOTIC SYSTEMS VIA SCALAR OUTPUT VARIABLE

2005 ◽  
Vol 15 (08) ◽  
pp. 2593-2601 ◽  
Author(s):  
JAE-HUN KIM ◽  
HYUNSEOK SHIN ◽  
EUNTAI KIM ◽  
MIGNON PARK
Keyword(s):  
Time Delay ◽  
Fuzzy Model ◽  
Order System ◽  
Linear Matrix ◽  
Output Variable ◽  
First Order ◽  
Scalar Output ◽  
The Stability ◽  
Takagi Sugeno ◽  
System With Time Delay

It has been known that very complex chaotic behaviors can be observed in a simple first-order system with time-delay. This paper presents a fuzzy model-based approach for synchronization of time-delayed chaotic system via a scalar output variable. Takagi–Sugeno (T–S) fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive and response system with time-delay. Since only a scalar output variable is available for synchronization, a fuzzy observer based on T–S fuzzy model is designed and applied to chaotic synchronization. We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov–Krasovskii theory and derive stability conditions by solving linear matrix inequalities (LMI's) problem. A numerical example is given to demonstrate the validity of the proposed synchronization approach.

scholarly journals Improved Stabilization Conditions for Nonlinear Systems with Input and State Delays via T-S Fuzzy Model

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Chang Che ◽  
Jiayao Peng ◽  
Tao Zhao ◽  
Jian Xiao ◽  
Jie Zhou
Keyword(s):  
Nonlinear Systems ◽  
Integral Inequality ◽  
Fuzzy Systems ◽  
Fuzzy Model ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Approach ◽  
State Delays ◽  
Lyapunov Stability Criterion ◽  
Takagi Sugeno

This paper focuses on the problem of nonlinear systems with input and state delays. The considered nonlinear systems are represented by Takagi-Sugeno (T-S) fuzzy model. A new state feedback control approach is introduced for T-S fuzzy systems with input delay and state delays. A new Lyapunov-Krasovskii functional is employed to derive less conservative stability conditions by incorporating a recently developed Wirtinger-based integral inequality. Based on the Lyapunov stability criterion, a series of linear matrix inequalities (LMIs) are obtained by using the slack variables and integral inequality, which guarantees the asymptotic stability of the closed-loop system. Several numerical examples are given to show the advantages of the proposed results.

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