scholarly journals Identification of time series models using sparse Takagi–Sugeno fuzzy systems with reduced structure

2022 ◽  
Author(s):  
Krzysztof Wiktorowicz ◽  
Tomasz Krzeszowski
Keyword(s):  
Time Series ◽  
Fuzzy Systems ◽  
Hybrid Methods ◽  
Time Series Prediction ◽  
Fuzzy Model ◽  
Quality Criterion ◽  
Pattern Search ◽  
Sparse Regression ◽  
Simulated Annealing Genetic Algorithm ◽  
Takagi Sugeno

AbstractSimplifying fuzzy models, including those for predicting time series, is an important issue in terms of their interpretation and implementation. This simplification can involve both the number of inference rules (i.e., structure) and the number of parameters. This paper proposes novel hybrid methods for time series prediction that utilize Takagi–Sugeno fuzzy systems with reduced structure. The fuzzy sets are obtained using a global optimization algorithm (particle swarm optimization, simulated annealing, genetic algorithm, or pattern search). The polynomials are determined by elastic net regression, which is a sparse regression. The simplification is based on reducing the number of polynomial parameters in the then-part by using sparse regression and removing unnecessary rules by using labels. A new quality criterion is proposed to express a compromise between the model accuracy and its simplification. The experimental results show that the proposed methods can improve a fuzzy model while simplifying its structure.

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.

Stable fuzzy controllers via LMI approach for non-linear systems described by type-2 T–S fuzzy model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Himanshukumar R. Patel ◽  
Vipul A. Shah
Keyword(s):  
Fuzzy Systems ◽  
Fuzzy Model ◽  
System Stability ◽  
Stability Conditions ◽  
Lmi Approach ◽  
Fuzzy Controllers ◽  
Content Type ◽  
Control Approach ◽  
Takagi Sugeno

PurposeThe purpose of this paper is to stabilize the type-2 Takagi–Sugeno (T–S) fuzzy systems with the sufficient and guaranteed stability conditions. The given conditions efficaciously handle parameter uncertainties by the upper and lower membership functions of the type-2 fuzzy sets (FSs).Design/methodology/approachThis paper reports on a relevant study of stable fuzzy controllers and type-2 T–S fuzzy systems and reported that the synthesis of controller for nonlinear systems described by the type-2 T–S fuzzy model is a key problem and it can be resolve to convex problems via linear matrix inequalities (LMIs).FindingsThe multigain fuzzy controllers are established to improve the solvability of the stability conditions, and the authors design multigain fuzzy controllers which have extensive information of upper and lower membership grades. Consequently, the authors derive the traditional stability condition in terms of LMIs. One simulation examples illustrate the effectiveness and robustness of the derived stabilization conditions.Originality/valueThe uncertain MIMO nonlinear system described by Type-2 Takagi-Sugeno (T-S) fuzzy model, and successively LMI approach used to determine the system stability conditions. The proposed control approach will give superior fault-tolerant control permanence under the actuator fault [partial loss of effectiveness (LOE)]. Also the controller robust against the unmeasurable process disturbances. Additionally, the statistical z-test are carried out to validate the proposed control approach against the control approach proposed by Himanshukumar and Vipul (2019a).

Robust Control for Uncertain Takagi–Sugeno Fuzzy Systems with Time-Varying Input Delay

2004 ◽  
Vol 127 (2) ◽  
pp. 302-306 ◽  
Author(s):  
Ho Jae Lee ◽  
Jin Bae Park ◽  
Young Hoon Joo
Keyword(s):  
Fuzzy Systems ◽  
Fuzzy Model ◽  
Input Delay ◽  
Time Varying ◽  
Convex Optimization Problem ◽  
Variation Rate ◽  
Mass Spring ◽  
Takagi Sugeno ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

A control problem of Takagi–Sugeno fuzzy systems with a time-varying input delay and norm-bounded uncertainties is addressed. The input delay is well-known in making the closed-loop stabilization difficult. A sufficient condition for the robust fuzzy-model-based stabilization is derived based on the Lyapunov–Razumikhin stability theorem, without the assumption of the variation rate on the delay. A constructive design scheme is presented in the form of the iterative convex optimization problem. The effectiveness of the proposed method is demonstrated by a numerical simulation of a nonlinear mass-spring-damper system.

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