TS Fuzzy Research Articles

A fuzzy Lyapunov function approach for stabilization and [formula omitted] control of switched TS fuzzy systems

In this work, sufficient conditions for the existence of switching laws for stabilizing switched TS fuzzy systems via a fuzzy Lyapunov function are proposed. The conditions are found by exploring properties of the membership functions and are formulated in terms of linear matrix inequalities (LMIs). Stabilizing switching conditions with bounds on the decay rate solution and H∞ performance are also obtained. Numerical examples illustrate the effectiveness of the proposed design methods.

Intelligent Information of TS Fuzzy PID Control System of BLDCM

This paper presented a new method based on the Fuzzy self - adaptive PID for BLDCM. This method overcomes some defects of the traditional PID control. Such as lower control precision and worse anti - jamming performance. It dynamic model of BLDCM was built, and then design method for TS fuzzy PID model is given, At last, it compared simulation results of PID control method with TS Fuzzy PID control method. The results show that the TS Fuzzy PID control method has more excellent dynamic antistatic performances, as well as anti-jamming performance. The experiment shows that TS fuzzy PID control has the stronger adaptability robustness and transplant.

Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions

In this article, the fuzzy Lyapunov function approach is considered for stabilising continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing slack LMI variables into the problem formulation. The relaxation conditions given can also be used with a class of fuzzy Lyapunov functions which also depends on the membership function first-order time-derivative. The stability results are thus extended to systems with large number of rules under membership function order relations and used to design parallel-distributed compensation (PDC) fuzzy controllers which are also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilising conditions presented.

Stability Analysis and Controller Design of Discrete Interval Type‐2 Fuzzy Systems

ABSTRACTThis paper is concerned with trajectory stabilization of a computer simulated model car with uncertain velocity via type‐2 fuzzy control systems. First, stability conditions of discrete interval type‐2 fuzzy control systems are given in accordance with the definition of stability in the sense of Lyapunov. Then, we approximate a computer simulated model car, whose dynamics are nonlinear and velocity is uncertain. A type‐2 Takagi–Sugeno TS fuzzy controller is designed to handle system uncertainty. The control rules, which guarantee stability of the system, are derived from the approximated model. The simulation results show that the type‐2 fuzzy control rules can effectively stabilize the car model.

Observer based (Q,V,R)-α-dissipative control for TS fuzzy descriptor systems with time delay

This paper is concerned with the design of (Q,V,R)-α-dissipative control for continuous TS fuzzy descriptor systems with unmeasurable states and time-varying delay. Our attention is focused on the design of the fuzzy controller and the fuzzy observer such that the closed loop fuzzy descriptor system with time delay is not only regular, impulse-free and stable but also (Q,V,R)-α-dissipative. By using the matrix decoupling technique, new delay dependent stabilization conditions are presented in terms of Linear Matrix Inequalities (LMI). As a particular case, observer-based H∞ control is deduced from the proposed observer-based dissipative control result. Finally, a numerical example is given to demonstrate the effectiveness of our results.

TS-fuzzy modeling based on ε-insensitive smooth support vector regression

This paper establishes a connection between Takagi-Sugeno TS fuzzy systems and e-insensitive smooth support vector regression e-SSVR, a smooth strategy for solving e-SVR. In previous e-SVR-based fuzzy models, the form of membership functions is restricted by the Mercer condition. The e-SSVR formulation puts no restrictions on the kernel. Therefore, the proposed e-SSVR-based TS-fuzzy modeling method relaxes the restriction on membership functions. By applying the reduced kernel technique, the number of fuzzy rules is reduced without scarifying the generalization ability. The computational complexity is also reduced by the reduced kernel technique. The performance of our method is illustrated by extensive experiments and comparisons.

Identification and Control Design of Fuzzy Takagi-Sugeno Model for Pressure Process Rig

The design of an intelligent controller based on fuzzy TS model for a pressure process rig is presented. The proposed controller consists of a fuzzy TS model, a feedback fuzzy TS model, and a low pass filter combined in an internal model control structure. The identification of the fuzzy TS model uses fuzzy clustering technique to mimic the nonlinearity characteristic of the process. Instead of least-squares algorithm, the instrumental variable method is used to estimate the consequent parameters of the fuzzy TS model in order to avoid inconsistency problem. The identified model is validated with the performance indicators variance-accounted-for and root mean square. By using the technique of inverse fuzzy model analytically, the feedback fuzzy controller is designed based on the identified fuzzy TS model. The performance of the proposed controller is verified through experiments at various operating points.

Motion control of planar parallel robot using the fuzzy descriptor system approach

This work presents the control of a two-degree of freedom parallel robot manipulator. A quasi-LPV approach, through the so-called TS fuzzy model and LMI constraints problems is used. Moreover, in this context a way to derive interesting control laws is to keep the descriptor form of the mechanical system. Therefore, new LMI problems have to be defined that helps to reduce the conservatism of the usual results. Some relaxations are also proposed to leave the pure quadratic stability/stabilization framework. A comparison study between the classical control strategies from robotics and the control design using TS fuzzy descriptor models is carried out to show the interest of the proposed approach.

Investigation of the near-grazing behavior in hard-impact oscillators using model-based TS fuzzy approach

An impact oscillator is a non-smooth dy- namical system with discontinuous state jumps whose dynamical behavior illustrates a variety of non-linear phenomena including a grazing bifurcation. This spe- cific phenomenon is difficult to analyze because it co- incides with an infinite stretching of the phase space in the neighborhood of the grazing orbit, resulting in the well-known problem of the square-root singular- ity of the Jacobian of the discrete-time map. A novel Takagi-Sugeno fuzzy model-based approach is pre- sented in this paper to model a hard impacting system as a non-smooth dynamical system including discon- tinuous jumps. Employing non-smooth Lyapunov the- ory, the structural stability of the system is analyzed to predict the onset of the destabilizing chaotic be- havior. The proposed stability results, formulated as a Linear Matrix Inequality (LMI) problem, demonstrate how the new method can detect the loss of stability just before the grazing bifurcation.

A Reduced‐Order TS Fuzzy Observer Scheme with Application to Actuator Faults Reconstruction

This paper focuses on the principle for designing reduced‐order fuzzy‐observer‐based actuator fault reconstruction for a class of nonlinear systems. The problem addressed can be indicated as an approach for a kind of reduced‐order fuzzy observer design with special gain matrix structure that depends on a given matching condition specification. Using the Lyapunov theory, the stability conditions are obtained and expressed in terms of linear matrix inequalities, and the conditions for asymptotic estimation of actuator faults are derived. Simulation results illustrate the observer design procedure and demonstrate the actuator fault reconstruction effectiveness and performance.

Introducing evolving Takagi–Sugeno method based on local least squares support vector machine models

In this study, an efficient local online identification method based on the evolving Takagi–Sugeno least square support vector machine (eTS-LS-SVM) for nonlinear time series prediction is introduced. As an innovation, this paper has applied the nonlinear models, i.e. local LS-SVM models, as the consequence parts of the fuzzy rules, instead of the linear models used in the conventional evolving TS fuzzy models. In each step, the proposed learning approach includes two phases. The fuzzy rules (rule premise) are first created and updated adaptively based on a sequential clustering technique to obtain the structure of TS model. Then, the parameters of each local LS-SVM model (rule consequence) are recursively updated by deriving a new recursive algorithm (a local decremental and incremental procedure) to minimize the local modelling error and trace the process’s dynamics. Besides, a new learning algorithm based on the recursive gradient-based method is used to adaptively update the meta-parameters of the LS-SVM models. Comparison of the suggested method with some of the previous approaches based on the online prediction of the nonlinear time series has shown that the introduced identification algorithm has a proper performance in terms of learning and generalization abilities while having a lower redundancy.

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

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.

A GMDH-based fuzzy modeling approach for constructing TS model

In this paper, a new learning algorithm based on group method of data handling (GMDH) is proposed for the identification of Takagi–Sugeno fuzzy model. Different from existing methods, the new approach, called TS-GMDH, starts from simple elementary TS fuzzy models, and then uses the mechanism of GMDH to produce candidate fuzzy models of growing complexity until the TS model of optimal complexity has been created. The main characteristic of the new approach is its ability to identify the structure of TS model automatically. Experiments on Box–Jenkins gas furnace data and UCI datasets have shown that the proposed method can achieve satisfactory results and is more robust to noise in comparison with other TS modeling techniques such as ANFIS.

A Fuzzy Multiobjective Particle Swarm Optimized TS Fuzzy Logic Congestion Controller for Wireless Local Area Networks

A Takagi-Sugeno Fuzzy Logic Congestion Detection (TSFLCD) mechanism is proposed for IEEE 802.11 wireless Local Area Networks. A Fuzzy Preference based Multi-Objective Particle Swarm Optimization (FPMOPSO) mechanism, for tuning the input membership functions and the output scalars, is also proposed. An online adaptation mechanism that finetunes the output scalars based on system dynamics is implemented. Compared to the Adaptive Random Early Detection (ARED) and the Mamdani inference based Fuzzy Logic Congestion Detection (FLCD) mechanisms, simulation results show that the TSFLCD mechanism leads to more than 40% reduction in packet loss rate. It also leads to more than 25% and up to 14% reductions in jitter and delay respectively for real time traffic. This work lays a foundation for the development of simple multiobjective fuzzy congestion controllers in wireless LANs.

Improving the stability conditions of TS fuzzy systems with fuzzy Lyapunov functions

AbstractIn this paper, the fuzzy Lyapunov function approach is considered for stabilizing continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing a slack LMI variable into the problem formulation. The stability results are thus used in the state feedback design which is also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilizing conditions presented.

Predicting wave run-up on rubble-mound structures using M5 model tree

Prediction of run-up level is a key task in design of the coastal structures. For the design of the crest level of coastal structures, the wave run-up level with a 2% exceedance probability, R u2% , is most commonly used. In this study, the performance of M5 model tree for prediction of the wave run-up on rubble-mound structures was investigated. The main advantage of model trees, unlike the other soft computing tools, is their easier use and more importantly their understandable mathematical rules. Experimental data set of Van der Meer and Stam was used for developing model trees. The conventional governing parameters were selected as the input variables and the obtained results were compared with Van der Meer and Stam’s formula, recommended by the Coastal Engineering Manual (CEM, 2006). The predictive accuracy of the model tree approach was found to be superior to that of Van der Meer and Stam’s empirical formula. Furthermore, to judge the generalization capability of the model tree method, the model developed based on laboratory data set was validated with the prototype run-up measurements on the Zeebrugge breakwater, Belgium. Results show that the model tree is more accurate than empirical formulas and TS Fuzzy approach in estimating the full-scale run-up.

TS Fuzzy Controller to Stochastic Systems

TS Fuzzy Controller to Stochastic Systems

Weighted Multi-Output Type TS Fuzzy Reasoning Method and Its Application to Fuzzy Discriminant Analysis for Diabetes Diagnostic Data

Weighted Multi-Output Type TS Fuzzy Reasoning Method and Its Application to Fuzzy Discriminant Analysis for Diabetes Diagnostic Data

Reducing conservativeness in recent stability conditions of TS fuzzy systems

In this correspondence a new simple strategy for reducing the conservativeness in stability analysis of continuous-time Takagi–Sugeno fuzzy systems based on fuzzy Lyapunov functions is proposed. This new strategy generalizes previous results.

Adaptive TS‐FNN control for a class of uncertain multi‐time‐delay systems: The exponentially stable sliding mode‐based approach

AbstractThis paper presents an adaptive Takagi–Sugeno fuzzy neural network (TS‐FNN) control for a class of multiple time‐delay uncertain nonlinear systems. First, we develop a sliding surface guaranteed to achieve exponential stability while considering mismatched uncertainty and unknown delays. This exponential stability result based on a novel Lyapunov–Krasovskii method is an improvement when compared with traditional schemes where only asymptotic stability is achieved. The stability analysis is transformed into a linear matrix inequalities problem independent of time delays. Then, a sliding mode control‐based TS‐FNN control scheme is proposed to achieve asymptotic stability for the controlled system. Since the TS‐FNN combines TS fuzzy rules and a neural network structure, fewer numbers of fuzzy rules and tuning parameters are used compared with the traditional pure TS fuzzy approach. Moreover, all the fuzzy membership functions are tuned on‐line even in the presence of input uncertainty. Finally, simulation results show the control performance of the proposed scheme. Copyright © 2008 John Wiley & Sons, Ltd.