On the interpretation and identification of dynamic Takagi-Sugenofuzzy models

Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. It is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Robust passivity and passification of stochastic fuzzy time-delay systems

The official published version can be obtained from the link below.In this paper, the passivity and passification problems are investigated for a class of uncertain stochastic fuzzy systems with time-varying delays. The fuzzy system is based on the Takagi–Sugeno (T–S) model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. To reflect more realistic dynamical behaviors of the system, both the parameter uncertainties and the stochastic disturbances are considered, where the parameter uncertainties enter into all the system matrices and the stochastic disturbances are given in the form of a Brownian motion. We first propose the definition of robust passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the Itô differential rule and the matrix analysis techniques, we establish several sufficient criteria such that, for all admissible parameter uncertainties and stochastic disturbances, the closed-loop stochastic fuzzy time-delay system is robustly passive in the sense of expectation. The derived criteria, which are either delay-independent or delay-dependent, are expressed in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.This work was supported by the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China, the Specialized Research Fund for the Doctoral Program of Higher Education for New Teachers 200802861044, the National Natural Science Foundation of China under Grant 60804028 and the Royal Society of the United Kingdom

New Optimal Approach for the Identification of Takagi-Sugeno Fuzzy Model

A novel optimal method is developed to improve the identification and estimation of Takagi-Sugeno (TS) fuzzy model. The idea comes from the fact that the main drawback of T-S model is that it can not be applied when the membership functions are overlapped by pairs. This limits the application of the T-S model because this type of membership function has been widely used in the stability and controller design of fuzzy systems. It is also very popular in industrial control applications. The method presented here can be considered as a generalized version of T-S fuzzy model with optimized performance in approximating nonlinear functions. Various examples are chosen to show the high function approximation accuracy and fast convergence obtained by applying the proposed method in approximating nonlinear systems locally and globally in comparison with the original T-S model

Non-linear predictive control for manufacturing and robotic applications

The paper discusses predictive control algorithms in the context of applications to robotics and manufacturing systems. Special features of such systems, as compared to traditional process control applications, require that the algorithms are capable of dealing with faster dynamics, more significant unstabilities and more significant contribution of non-linearities to the system performance. The paper presents the general framework for state-space design of predictive algorithms. Linear algorithms are introduced first, then, the attention moves to non-linear systems. Methods of predictive control are presented which are based on the state-dependent state space system description. Those are illustrated on examples of rather difficult mechanical systems

An Optimal T-S Model for the Estimation and Identification of Nonlinear Functions

A novel optimal method is developed to improve the identification and estimation of Takagi-Sugeno (TS) fuzzy model. The idea comes from the fact that the main drawback of T-S model is that it can not be applied when the membership functions are overlapped by pairs. This limits the application of the T-S model because this type of membership function has been widely used in the stability and controller design of fuzzy systems. It is also very popular in industrial control applications. The method presented here can be considered as a generalized version of T-S fuzzy model with optimized performance in approximating nonlinear functions. Various examples are chosen to show the high function approximation accuracy and fast convergence obtained by applying the proposed method in approximating nonlinear systems locally and globally in comparison with the original T-S model

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use

Improvement of Takagi-Sugeno Fuzzy Model for the Estimation of Nonlinear Functions

Two new and efficient approaches are presented to improve the local and global estimation of the Takagi-Sugeno (T-S) fuzzy model. The main aim is to obtain high function approximation accuracy and fast convergence. The main problem is that the T-S identification method can not be applied when the membership functions are overlapped by pairs. The approaches developed here can be considered as generalized versions of T-S method with optimized performance. The first uses the minimum norm approach to search for an exact optimum solution at the expense of increasing complexity and computational cost. The second is a simple and less computational method, based on weighting of parameters. Illustrative examples are chosen to evaluate the potential, simplicity and remarkable performance of the proposed methods and the high accuracy obtained in comparison with the original T-S model