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On the global stability of Takagi-Sugeno general model.

Fernando Matía, Basil M. Al-Hadithi, Agustín Jiménez (1999)

Mathware and Soft Computing

Global stability of Takagi-Sugeno (T-S) fuzzy model is presented. First, stability conditions for T-S fuzzy model presented by Tanaka and Sugeno are reviewed. Second, new theorems for the stability of the general form of T-S model is derived in the sense of Lyapunov.The T-S model we studied includes a linear equation with a constant parameter in the consequent part of each rule while other authors have analyzed the model with no constant term, which does not represent a real system. This in turn...

On the observability of fuzzy second order control systems

Jong Yeoul Park, P. Balasubramaniam, Hyun Min Kim (2003)

Kybernetika

In this paper, the observability of fuzzy logic second order control system is studied from the aspect of fuzzy differential equations. The fuzzy observability in the weak sense is created using the concept of “likelihood” to indicate on which level and along which solution the state is most likely observable. One of the initial state range has been derived with the given input and output. The result generalizes the previous results.

On the stability of T-S fuzzy control for non-linear systems.

Zoe Doulgeri, John B. Theocharis (2000)

Mathware and Soft Computing

This work concerns the stability analysis of a non-linear system controlled by a fuzzy T-S control law. It is shown that the closed loop system is in general expressed by a T-S fuzzy system composed of rules with affine linear systems in their consequent parts. The stability of affine T-S systems is then investigated for a special case using as an example the regulation problem of single link robot arm. Stability conditions are derived using the indirect and direct Lyapunov method and simulation...

Refinement of a fuzzy control rule set.

Antonio González, Raúl Pérez (1998)

Mathware and Soft Computing

Fuzzy logic controller performance depends on the fuzzy control rule set. This set can be obtained either by an expert or from a learning algorithm through a set of examples. Recently, we have developed SLAVE an inductive learning algorithm capable of identifying fuzzy systems. The refinement of the rules proposed by SLAVE (or by an expert) can be very important in order to improve the accuracy of the model and in order to simplify the description of the system. The refinement algorithm is based...

Relaxed stability conditions for interval type-2 fuzzy-model-based control systems

Tao Zhao, Jian Xiao, Jialin Ding, Xuesong Deng, Song Wang (2014)

Kybernetika

This paper proposes new stability conditions for interval type-2 fuzzy-model-based (FMB) control systems. The type-1 T-S fuzzy model has been widely studied because it can represent a wide class of nonlinear systems. Many favorable results for type-1 T-S fuzzy model have been reported. However, most of conclusions for type-1 T-S fuzzy model can not be applied to nonlinear systems subject to parameter uncertainties. In fact, Most of the practical applications are subject to parameters uncertainties....

Residual generator fuzzy identification for automotive diesel engine fault diagnosis

Silvio Simani (2013)

International Journal of Applied Mathematics and Computer Science

Safety in dynamic processes is a concern of rising importance, especially if people would be endangered by serious system failure. Moreover, as the control devices which are now exploited to improve the overall performance of processes include both sophisticated control strategies and complex hardware (input-output sensors, actuators, components and processing units), there is an increased probability of faults. As a direct consequence of this, automatic supervision systems should be taken into...

Robust adaptive fuzzy filters output feedback control of strict-feedback nonlinear systems

Shaocheng Tong, Changliang Liu, Yongming Li (2010)

International Journal of Applied Mathematics and Computer Science

In this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of single input single output (SISO) strict-feedback nonlinear systems without measurements of states. The nonlinear systems addressed in this paper are assumed to possess unstructured uncertainties, unmodeled dynamics and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds is available. In recursive design, fuzzy logic systems...

Robust dynamic output feedback fault-tolerant control for Takagi-Sugeno fuzzy systems with interval time-varying delay via improved delay partitioning approach

Chao Sun, Fuli Wang, Xiqin He (2016)

Open Mathematics

This paper addresses the problem of robust fault-tolerant control design scheme for a class of Takagi-Sugeno fuzzy systems subject to interval time-varying delay and external disturbances. First, by using improved delay partitioning approach, a novel n-steps iterative learning fault estimation observer under H ∞ constraint is constructed to achieve estimation of actuator fault. Then, based on the online estimation information, a fuzzy dynamic output feedback fault-tolerant controller considered...

Robust observer design for Sugeno systems with incremental quadratic nonlinearity in the consequent

Hoda Moodi, Mohammad Farrokhi (2013)

International Journal of Applied Mathematics and Computer Science

This paper is concerned with observer design for nonlinear systems that are modeled by T-S fuzzy systems containing parametric and nonparametric uncertainties. Unlike most Sugeno models, the proposed method contains nonlinear functions in the consequent part of the fuzzy IF-THEN rules. This will allow modeling a wider class of systems with smaller modeling errors. The consequent part of each rule contains a linear part plus a nonlinear term, which has an incremental quadratic constraint. This constraint...

Rule weights in a neuro-fuzzy system with a hierarchical domain partition

Krzysztof Simiński (2010)

International Journal of Applied Mathematics and Computer Science

The paper discusses the problem of rule weight tuning in neuro-fuzzy systems with parameterized consequences in which rule weights and the activation of the rules are not interchangeable. Some heuristic methods of rule weight computation in neuro-fuzzy systems with a hierarchical input domain partition and parameterized consequences are proposed. Several heuristics with experimental results showing the advantage of their usage are presented.

Safety regulations and fuzzy-logic control to nuclear reactors.

Da Ruan (2000)

Mathware and Soft Computing

We present an R&D project on fuzzy-logic control applicatios tor the Belgian Nuclear Reactor 1 (BR1) at the Belgian Nuclear Research Centre (SCK·CEN). The project started in 1995 and aimed at investigating the added value of fuzzy logic control for nuclear reactors. We first review some relevant literature on fuzzy logic control in nuclear reactors, then present the state-of-the-art of the BR1 project, with an understanding of the safety requirements for this real fuzzy-logic control application...

Similarity in fuzzy reasoning.

Frank Klawonn, Juan Luis Castro (1995)

Mathware and Soft Computing

Fuzzy set theory is based on a `fuzzification' of the predicate in (element of), the concept of membership degrees is considered as fundamental. In this paper we elucidate the connection between indistinguishability modelled by fuzzy equivalence relations and fuzzy sets. We show that the indistinguishability inherent to fuzzy sets can be computed and that this indistinguishability cannot be overcome in approximate reasoning. For our investigations we generalize from the unit interval as the basis...

Soft computing in modelbased predictive control footnotemark

Piotr Tatjewski, Maciej Ławrynczuk (2006)

International Journal of Applied Mathematics and Computer Science

The application of fuzzy reasoning techniques and neural network structures to model-based predictive control (MPC) is studied. First, basic structures of MPC algorithms are reviewed. Then, applications of fuzzy systems of the Takagi-Sugeno type in explicit and numerical nonlinear MPC algorithms are presented. Next, many techniques using neural network modeling to improve structural or computational properties of MPC algorithms are presented and discussed, from a neural network model of a process...

Some properties of B -operations

Bohdan Butkiewicz (2007)

Kybernetika

In the paper the problem of mathematical properties of B -operations and weak W B -operations introduced by the author for interpretation of connectives “and”, “or”, and “also” in fuzzy rules is considered. In previous author’s papers some interesting properties of fuzzy systems with these operations were shown. These operations are weaker than triangular norms used commonly for a fuzzy system described by set of rules of the type if – then. Monotonicity condition, required for triangular norms, is...

Stability analysis and H ∞ control of discrete T-S fuzzy hyperbolic systems

Ruirui Duan, Junmin Li, Yanni Zhang, Ying Yang, Guopei Chen (2016)

International Journal of Applied Mathematics and Computer Science

This paper focuses on the problem of constraint control for a class of discrete-time nonlinear systems. Firstly, a new discrete T-S fuzzy hyperbolic model is proposed to represent a class of discrete-time nonlinear systems. By means of the parallel distributed compensation (PDC) method, a novel asymptotic stabilizing control law with the “soft” constraint property is designed. The main advantage is that the proposed control method may achieve a small control amplitude. Secondly, for an uncertain...

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