Affine Takagi-Sugeno Fuzzy Models Research Articles

Affine TS Fuzzy Model-Based Estimation and Control of Hindmarsh–Rose Neuronal Model

In this paper, an affine Takagi–Sugeno (TS) fuzzy modeling-based observer and controller are proposed for the estimation and control of a chaotic Hindmarsh–Rose (HR) neuronal model. The main contributions are given as follows. 1) First, an affine TS fuzzy model of the HR chaotic neuronal model is constructed using sector nonlinearity-based approach. 2) Based on the constructed TS fuzzy model, a TS fuzzy observer is designed for simultaneous state and parameter estimation of HR neuronal model for unmeasurable state and parameters. 3) In the same way, a novel affine TS fuzzy model-based output feedback control law is designed with observed state and parameters where the exponential stability of the designs are guaranteed by Lyapunov approach. 4) Finally, numerical simulations are conducted to illustrate the observation and stimulation with regular and fast spiking trains and annihilation of the membrane potential.

AQM router design for TCP network via input constrained fuzzy control of time-delay affine Takagi–Sugeno fuzzy models

In this article, Takagi–Sugeno (T–S) fuzzy control theory is proposed as a key tool to design an effective active queue management (AQM) router for the transmission control protocol (TCP) networks. The probability control of packet marking in the TCP networks is characterised by an input constrained control problem in this article. By modelling the TCP network into a time-delay affine T–S fuzzy model, an input constrained fuzzy control methodology is developed in this article to serve the AQM router design. The proposed fuzzy control approach, which is developed based on the parallel distributed compensation technique, can provide smaller probability of dropping packets than previous AQM design schemes. Lastly, a numerical simulation is provided to illustrate the usefulness and effectiveness of the proposed design approach.

Robust fuzzy control for continuous perturbed time‐delay affine takagi–sugeno fuzzy models

AbstractThe stability analysis and controller synthesis methodology for a continuous perturbed time‐delay affine (CPTDA) Takagi–Sugeno (T‐S) fuzzy model is proposed in this paper. The CPTDA T‐S fuzzy models include both linear nominal parts and uncertain parameters in each fuzzy rule. The proposed fuzzy control approach is developed based on an iterative linear matrix inequality (ILMI) algorithm to cope with the stability criteria and H∞ performance constraints for the CPTDA T‐S fuzzy models. Finally, a numerical simulation for the nonlinear inverted pendulum system is given to show the application and availability of the present design approach.Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Robust fuzzy control for discrete perturbed time-delay affine Takagi-Sugeno fuzzy models

The purpose of this paper is to study the stability analysis and controller synthesis principles of Discrete Perturbed Time-Delay Affine (DPTDA) Takagi-Sugeno (T-S) fuzzy models. In general, the T-S fuzzy model is a weighted sum of some linear subsystems via fuzzy membership functions. This paper considers fuzzy rules include both linear nominal parts and uncertain parameters in the time-delay affine T-S fuzzy model. For DPTDA T-S fuzzy models, the T-S fuzzy control scheme is used to confront the H∞ performance constraints. Some sufficient conditions are derived on robust H∞ disturbance attenuation in which both robust stability and a prescribed performance are required to be achieved. In order to find suitable fuzzy controllers, the Iterative Linear Matrix Inequality (ILMI) algorithm is employed to solve these sufficient conditions. At last, a numerical simulation for the nonlinear truck-trailer system is given to show the applications of the present design approach.

Observer-feedback fuzzy control with passivity property for discrete-time affine Takagi-Sugeno fuzzy models

By considering discrete-time affine Takagi-Sugeno fuzzy models, this paper presents an observer-feedback fuzzy control approach for achieving the passivity property of closed-loop systems. The passivity property of the system is used to deal with all external disturbances. The proposed observer-feedback fuzzy controller is developed based on the parallel distribution compensation technique. Also, an iterative linear matrix inequality algorithm is used to obtain a feasible solution for the proposed observer-feedback fuzzy control problem. Finally, two numerical simulations of discrete-time nonl-inear systems are presented that highlight the application of the proposed observer-feedback fuzzy controller design approach.

Affine Takagi-Sugeno fuzzy modelling algorithm by fuzzy c-regression models clustering with a novel cluster validity criterion

An effective approach is developed to establish affine Takagi-Sugeno (T-S) fuzzy model for a given nonlinear system from its input–output data. Firstly, the fuzzy c-regression model (FCRM) clustering technique is applied to partition the product space of the given input–output data into hyper-plan-shaped clusters. Each cluster is essentially a basis of the fuzzy rule that describes the system behaviour, and the number of clusters is just the number of fuzzy rules. Particularly, a novel cluster validity criterion for FCRM is set up to choose the appropriate number of clusters (rules). Once the number of clusters is determined, the consequent parameters of each IF-THEN rule are directly obtained from the functional cluster representatives (affine linear functions). The antecedent fuzzy sets of each IF-THEN fuzzy rule are acquired by projecting the fuzzy partitions matrix U onto the axes of individual antecedent variable to obtain point-wise defined fuzzy sets and to approximate these point-wise defined fuzzy sets by normal bell-shaped membership functions. Additionally, a check and repartition algorithm is suggested to prevent the inappropriate premise structure where separate regions of data shared the same regression model. Finally, the gradient descent algorithm is included to adjust the fuzzy model precisely. An affine T-S fuzzy model with compact IF-THEN rules could thus be generated systematically. Several simulation examples are provided to demonstrate the accuracy and effectiveness of the affine T-S fuzzy modelling algorithm.

Discrete fuzzy control of time-delay affine Takagi–Sugeno fuzzy models with H∞ constraint

Takagi–Sugeno (T–S) fuzzy models play an important role in nonlinear control because they can be used to approximate nonlinear systems. Also, for the affine T–S fuzzy models, the local linear sub-system properties can be easily related to the physics of the controlled nonlinear system. This is one advantage of the affine T–S fuzzy models relative to the homogeneous T–S fuzzy models. In the literature, however, most authors have focused on the homogeneous T–S fuzzy models and only a few have considered the affine T–S fuzzy models. Moreover, it is known that time delays exist in physical systems. To date, there has been no study to consider the time-delay effects in the analysis of affine T–S fuzzy models. Therefore the parallel distributed compensation-based H∞ fuzzy control problem for the discrete time-delay affine T–S fuzzy model is now presented. An iterative linear matrix inequality algorithm is used to solve the bilinear matrix inequality problems. Finally, numerical simulation for a time-delayed nonlinear truck–trailer system is given to show an application of the present approach.

Model-based fuzzy controller design for time-delay affine Takagi-Sugeno fuzzy models via ILMI algorithm

Recently, the Takagi-Sugeno T-S fuzzy model has become one of the most useful control approaches for complex systems. It provides an effective representation of complex nonlinear systems in terms o...

Synthesis of nonlinear discrete control systems via time-delay affine Takagi-Sugeno fuzzy models

The affine Takagi-Sugeno (TS) fuzzy model played a more important role in nonlinear control because it can be used to approximate the nonlinear systems more than the homogeneous TS fuzzy models. Besides, it is known that the time delays exist in physical systems and the previous works did not consider the time delay effects in the analysis of affine TS fuzzy models. Hence a parallel distributed compensation based fuzzy controller design issue for discrete time-delay affine TS fuzzy models is considered in this paper. The time-delay effect is considered in the discrete affine TS fuzzy models and the stabilization issue is developed for the nonlinear time-delay systems. Finally, a numerical simulation for a time-delayed nonlinear truck-trailer system is given to show the applications of the present approach.