scholarly journals A Simplified Output Regulator for a Class of Takagi-Sugeno Fuzzy Models

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Tonatiuh Hernández-Cortés ◽  
Jesús A. Meda Campaña ◽  
Luis A. Páramo Carranza ◽  
Julio C. Gómez Mancilla
Keyword(s):  
Fuzzy Systems ◽  
Membership Functions ◽  
Numerical Examples ◽  
Fuzzy Models ◽  
Mathematical Expressions ◽  
Takagi Sugeno

This paper is devoted to solve the regulation problem on the basis of local regulators, which are combined using “new” membership functions. As a result, the exact tracking of references is achieved. The design of linear local regulators is suggested in this paper, but now adequate membership functions are computed in order to ensure the proper combination of the local regulators in the interpolation regions. These membership functions, which are given as mathematical expressions, solve the fuzzy regulation problem in a relative simple way. The form of the new membership functions is systematically derived for a class of Takagi-Sugeno (T-S) fuzzy systems. Some numerical examples are used to illustrate the viability of the proposed approach.

scholarly journals A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy Models

2007 ◽  
Vol 17 (1) ◽  
pp. 39-51 ◽  
Author(s):  
Ibtissem Abdelmalek ◽  
Noureddine Goléa ◽  
Mohamed Hadjili
Keyword(s):  
Lyapunov Functions ◽  
Fuzzy Systems ◽  
Time Derivative ◽  
Stability Conditions ◽  
Membership Functions ◽  
Lyapunov Approach ◽  
Fuzzy Models ◽  
Quadratic Stabilization ◽  
Quadratic Lyapunov Functions ◽  
Takagi Sugeno

A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy ModelsIn this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization. The proposed approach is based on two assumptions. The first one relates to a proportional relation between multiple Lyapunov functions and the second one considers an upper bound to the time derivative of the premise membership functions. To illustrate the advantages of our proposal, four examples are given.

On switched control of discrete-time Takagi-Sugeno fuzzy systems with unknown membership functions

2018 ◽  
Author(s):  
Diogo R. de Oliveira ◽  
Gilberto R. dos Santos ◽  
Marcelo C. M. Teixeira ◽  
Edvaldo Assuncao ◽  
Rodrigo Cardim ◽  
...  
Keyword(s):  
Discrete Time ◽  
Fuzzy Systems ◽  
Membership Functions ◽  
Switched Control ◽  
Takagi Sugeno

A Gain-Scheduling Control Approach for Takagi–Sugeno Fuzzy Systems Based on Linear Parameter-Varying Control Theory

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Yang Liu ◽  
Xiaojun Ban ◽  
Fen Wu ◽  
H. K. Lam
Keyword(s):  
Fuzzy Control ◽  
Control Theory ◽  
Fuzzy Systems ◽  
Gain Scheduling ◽  
Control Problems ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Fuzzy Models ◽  
Gain Scheduling Control ◽  
Takagi Sugeno

Due to the universal approximation capability of Takagi–Sugeno (T–S) fuzzy models for nonlinear dynamics, many control issues have been investigated based on fuzzy control theory. In this paper, a transformation procedure is proposed to convert fuzzy models into linear fractional transformation (LFT) models. Then, T–S fuzzy systems can be regarded as a special case of linear parameter-varying (LPV) systems which proved useful for nonlinear control problems. The newly established connection between T–S fuzzy models and LPV models provides a new perspective of the control problems for T–S fuzzy systems and facilitates the fuzzy control designs. Specifically, an output feedback gain-scheduling control design approach for T–S fuzzy systems is presented to ensure globally asymptotical stability and optimize H∞ performance of the closed-loop systems. The control synthesis problem is cast as a convex optimization problem in terms of linear matrix inequalities (LMIs). Two examples have been used to illustrate the efficiency of the proposed method.

scholarly journals Stability analysis of Takagi-Sugeno fuzzy systems via LMI: methodologies based on a new fuzzy Lyapunov function

2011 ◽  
Vol 22 (6) ◽  
pp. 664-676 ◽  
Author(s):  
Leonardo Amaral Mozelli ◽  
Reinaldo Martinez Palhares
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Fuzzy Systems ◽  
Time Derivative ◽  
Time Varying ◽  
Membership Functions ◽  
Fuzzy Lyapunov Function ◽  
Numerical Tools ◽  
Takagi Sugeno ◽  
First Time

Stability analysis of TS fuzzy systems can be much improved by resorting to fuzzy Lyapunov functions, since they are parameterized by membership functions and can better characterize the time-varying feature of these systems by means of the information regarding the first time-derivative of the membership functions. In this paper an enhanced fuzzy Lyapunov function is used to develop stability conditions that evaluate also the second time-derivative of membership functions, improving the time-varying characterization of TS systems. By using diferent strategies to consider the information regarding such derivatives and employing some numerical tools that decouple system from Lyapunov function matrices new LMI tests are developed. Numerical examples illustrate the effectiveness of those methodologies.

scholarly journals Continuous Stability TS Fuzzy Systems Novel Frame Controlled by a Discrete Approach and Based on SOS Methodology

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3129
Author(s):  
Ameni Ellouze ◽  
Omar Kahouli ◽  
Mohamed Ksantini ◽  
Ali Rebhi ◽  
Nidhal Hnaien ◽  
...  
Keyword(s):  
Fuzzy Systems ◽  
Discrete Systems ◽  
Continuous Systems ◽  
Fuzzy Models ◽  
Discrete Approach ◽  
Quadratic Lyapunov Functions ◽  
The Stability ◽  
Takagi Sugeno ◽  
Stability Results ◽  
Discrete Controller

Generally, the continuous and discrete TS fuzzy systems’ control is studied independently. Unlike the discrete systems, stability results for the continuous systems suffer from conservatism because it is still quite difficult to apply non-quadratic Lyapunov functions, something which is much easier for the discrete systems. In this paper and in order to obtain new results for the continuous case, we proposed to connect the continuous with the discrete cases and then check the stability of the continuous TS fuzzy systems by means of the discrete design approach. To this end, a novel frame was proposed using the sum of square approach (SOS) to check the stability of the continuous Takagi Sugeno (TS) fuzzy models based on the discrete controller. Indeed, the control of the continuous TS fuzzy models is ensured by the discrete gains obtained from the Euler discrete form and based on the non-quadratic Lyapunov function. The simulation examples applied for various models, by modifying the order of the Euler discrete fuzzy system, are presented to show the effectiveness of the proposed methodology.

Fuzzy Modeling with Local and Global Objectives

1999 ◽  
Vol 3 (5) ◽  
pp. 373-385
Author(s):  
John Yen ◽  
◽  
Wayne Gillespie ◽  
Keyword(s):  
Fuzzy Model ◽  
Current Method ◽  
Training Data ◽  
Local Behavior ◽  
Membership Functions ◽  
Training Set ◽  
Fuzzy Models ◽  
Output Mapping ◽  
Takagi Sugeno ◽  
A Current

Most of the techniques for constructing fuzzy models from data focus only on minimizing the error between the model’s output and the training data; however, these approaches may result in a fuzzy model where individual rules are misleading. The goal of our research is to develop a scheme for identifying Takagi-Sugeno-Kang (TSK) models whose individual rules approximate the training data covered by a single rule, local fitness, while the entire model approximates the whole training set, global fitness. We propose an approach that is a modification of a current method for estimating the consequence portion of a TSK model with predefined membership functions. Then we propose a method for developing membership functions which partition the input space into regions that are more easily modeled in the TSK framework to provide consistent local behavior for all the rules of the model. This approach ensures that a TSK model constructed not only approximates the input-output mapping relationship in the data, but also captures insights about the local behavior of the model.

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