Takagi-Sugeno Model Research Articles

New Criteria of Passivity Analysis for Fuzzy Time-Delay Systems With Parameter Uncertainties

This paper investigates the passivity problem for a class of uncertain stochastic fuzzy nonlinear systems with mixed delays and nonlinear noise disturbances by employing an improved free-weighting matrix approach. The fuzzy system is based on the Takagi–Sugeno 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, the parameter uncertainties, the stochastic disturbances, and nonlinearities are considered, where the parameter uncertainties enter into all the system matrices, the stochastic disturbances are given in the form of a Brownian motion. The mixed delays comprise both discrete and distributed time-varying delays. By taking the relationship among the time delays, their lower and upper bounds into account, some less conservative linear-matrix-inequality-based delay-dependent passivity criteria are obtained without ignoring any useful terms in the derivative of Lyapunov functional. Finally, numerical examples are given to demonstrate the effectiveness and merits of the proposed methods.

A robust predictive actuator fault-tolerant control scheme for Takagi-Sugeno fuzzy systems

Abstract The paper deals with the problem of robust predictive fault-tolerant control for nonlinear discrete-time systems described by the Takagi-Sugeno models. The proposed approach is based on a triple stage procedure, i.e. it starts from fault estimation while the fault is compensated with a robust controller. The robust controller is designed without taking into account the input constraints related with the actuator saturation that may change due to its faulty behaviour. Thus, to check the compensation feasibility, the robust invariant set is developed, which takes into account the input constraints. If the current state does not belong to the robust invariant set, then suitable predictive control actions are performed in order to enhance the invariant set. This appealing phenomenon makes it possible to enlarge the domain of attraction, which makes the proposed approach an efficient solution for the fault-tolerant control. The final part of the paper shows an illustrative example regarding the application of the proposed approach to the twin-rotor system.

Progressively better estimates of the domain of attraction for nonlinear systems via piecewise Takagi–Sugeno models: Stability and stabilization issues

This paper introduces a novel approach for stability analysis and controller design of nonlinear models, both continuous- and discrete-time, based on an exact piecewise Takagi–Sugeno representation which generalizes the sector nonlinearity methodology. The motivation behind this work lies on the fact that piecewise-induced Takagi–Sugeno representations have smaller variations than single ones covering the whole modeling area, thus increasing the chances of finding piecewise solutions for stability analysis or controller synthesis. Moreover, this relaxation is shown to produce progressively better estimations of the domain of attraction via easy-to-implement algorithms that demand much less computational effort than other recent approaches in the literature. Examples are provided to highlight the advantages of the contributions over the existing methods.

Multi-source information fusion model in rule-based Gaussian-shaped fuzzy control inference system incorporating Gaussian density function

An increasing number of applications require the integration of data from various disciplines, which leads to problems with the fusion of multi-source information. In this paper, a special information structure formalized in terms of three indices (the central presentation, population or scale, and density function) is proposed. Single and mixed Gaussian models are used for single source information and their fusion results, and a parameter estimation method is also introduced. Furthermore, fuzzy similarity computing is developed for solving the fuzzy implications under a Mamdani model and a Gaussian-shaped density function. Finally, an improved rule-based Gaussian-shaped fuzzy control inference system is proposed in combination with a nonlinear conjugate gradient and a Takagi-Sugeno (T-S) model, which demonstrated the effectiveness of the proposed method as compared to other fuzzy inference systems.

Nonquadratic Controller and Observer Design for Continuous TS Models: A Discrete-Inspired Solution

This work deals with controller and observer design for continuous-time Takagi–Sugeno models based on a new nonquadratic Lyapunov function. The proposed technique intends to attain the level of development reached by its discrete-time counterpart by suitably adapting one of its key ideas: the inclusion of former values of the premise variables. The proposed approach naturally overcome the problem of dealing with the time-derivatives of the membership functions, thus providing a simplified as well as easier alternative to recent results on this matter. Moreover, thanks to the Finsler’s Lemma and a Tustin-like transformation, controller and observer gains are decoupled from the proposed Lyapunov function. The results are expressed as linear matrix inequalities which are efficiently solved by commercially available software implementing convex optimization techniques.

Fuzzy horizon group shift FIR filtering for nonlinear systems with Takagi–Sugeno model

In recent years, the Takagi–Sugeno (T–S) fuzzy model has been commonly used for the approximation of nonlinear systems. Using the T–S fuzzy model, nonlinear systems can be converted into linear time-varying systems, which can reduce approximation errors compared with the conventional Taylor approximation. In this paper, we propose a new nonlinear filter with a finite impulse response (FIR) structure based on the T–S fuzzy model. We firstly derive the fuzzy FIR filter and combine it with the horizon group shift (HGS) algorithm to manage the horizon size, which is an important design parameter of FIR filters. The resulting filter is called the fuzzy HGS FIR filter (FHFF). Due to the FIR structure, the FHFF has robustness against model parameter uncertainties. We demonstrate the performance of the FHFF in comparison with existing nonlinear filters, such as the fuzzy Kalman filter and the particle filter.

A New Robust Adaptive Fuzzy Sliding Mode Controller for a Variable Speed Wind Turbine

In this paper, we present a novel adaptive fuzzy sliding mode controller without reaching phase and chattering problems for a variable speed wind turbine with unknown dynamic parts. The approach is based on modifying the sliding domain equation through the use of logarithmic functions. The adaptive fuzzy law Takagi-Sugeno (TS) model is used to approximate the unknown dynamic parts. In this model, only the rotor speed is available, an asymptotic fuzzy observer is used to approximate the unknown rotor acceleration which is needed to synthesize the control law. The stability and effectiveness of the proposed control law are proved and the simulation is given to demonstrate the superiority of the proposed approach in comparison with the previous one, in terms of settling time, tracking accuracy, energy consumption and smoothness of the control input.

A Combined Methodology of H∞ Fuzzy Tracking Control and Virtual Reference Model for a PMSM

The aim of this paper is to present a new fuzzy tracking strategy for a permanent magnet synchronous machine (PMSM) by using Takagi-Sugeno models (T-S). A feedback-based fuzzy control with h-infinity tracking performance and a concept of virtual reference model are combined to develop a fuzzy tracking controller capable to track a reference signal and ensure a minimum effect of disturbance on the PMSM system. First, a T-S fuzzy model is used to represent the PMSM nonlinear system with disturbance. Next, an integral fuzzy tracking control based on the concept of virtual desired variables (VDVs) is formulated to simplify the design of the virtual reference model and the control law. Finally, based on this concept, a two-stage design procedure is developed: i) determine the VDVs from the nonlinear system output equation and generalized kinematics constraints ii) calculate the feedback controller gains by solving a set of linear matrix inequalities (LMIs). Simulation results are provided to demonstrate the validity and the effectiveness of the proposed method.

Diagnosis of companies’ bankruptcy using Takagi-Sugeno model

Diagnosis of companies’ bankruptcy using Takagi-Sugeno model

Intelligent Ratio Control in Presence of Pneumatic Control Valve Stiction

The presence of hard nonlinearities, such as control valve stiction, may severely degrade the plant profitability by introducing limit cycles in the process variable. This paper presents an innovative use of a recently developed intelligent controller for effective ratio control in the presence of a sticky control valve. The intelligent controller, stiction combating intelligent controller (SCIC), is inherently a fuzzy controller which makes use of Takagi–Sugeno model and changes its gain in run time to deal with stiction nonlinearity. Some of the various advantages which SCIC controller offers are, its simple structure, non-requirement of process parameters’ estimation and its capability to provide standalone solution to stiction nonlinearity. These qualities of SCIC controller make it a front runner among other solutions, for the effective ratio control in the presence of a sticky pneumatic control valve. The efficacy of the SCIC controller in ratio control is experimentally verified on a laboratory scale plant with uncertain parameters. A performance comparison between SCIC and linear proportional integral (PI) controller is also made for their setpoint tracking, disturbance rejection and trajectory tracking capabilities at various operating points. Based on extensive experimental studies, it can be concluded that SCIC controller, undoubtedly, outperformed the linear PI controller for all investigated cases and also efficiently handled uncertainties in the plant parameters.

Reconfigurable Controller Based on Fuzzy Descriptor Observer for Nonlinear Systems with Sensor Faults

In this paper, the FTC system for multiple operating condition nonlinear systems subjected to sensor faults is developed by applying reconfigurable control scheme. The scheme generates any modified control signal using appropriate additive reference signal to the nominal control system. The proposed observer is developed based on descriptor approach in the fuzzy Takagi-Sugeno model configuration in order to accommodate some operating conditions of a nonlinear system. The simulation result shows that the proposed method has capability to compensate more than one sensor fault occurred in a three-tank benchmark system even there is a change in condition operation as well as in reference signal.

Contraction scour estimation using data-driven methods

The paper presents an artificial neural network (ANN) and an adaptive neuro-fuzzy inference system (ANFIS), which could accurately estimate the maximum equilibrium depth of the contraction scour. The developed networks have been trained using the data set conducted by different investigators for long contractions under clear-water conditions. The designed multilayer perceptron (MLP) ANN includes one hidden layer and seven nodes within that layer. Its hidden neurons use a hyperbolic tangent sigmoidal transfer function. The ANN model was implemented using the MATLAB software package. The importance of the individual input parameters was tested with a sensitivity analysis. This revealed the contraction ratio to be by far the most sensitive parameter, followed by the effect of armor layer formation for nonuniform sediments. For the designed MLP–ANN network, the training was based on the Levenberg–Marquardt back-propagation algorithm in batch mode. The designed ANFIS was the zero-order Takagi–Sugeno model with four bell-shaped membership functions for each input and applied the Levenberg–Marquardt algorithm for network training. The ANFIS model was implemented using a FORTRAN-based computer code. The calculated results show that the selected networks estimate the equilibrium maximum scour depth under clear-water conditions within the range of the used data set significantly better than other conventional methods.

Evolving Fuzzy Rules for Anomaly Detection in Data Streams

Evolvable Takagi-Sugeno (T-S) models are fuzzy-rule-based models with the ability to continuously learn and adapt to incoming samples from data streams. The model adjusts both premise and consequent parameters to enhance the performance of the model. This paper introduces a new methodology for the estimation of the premise parameters in the evolvable T-S (eTS) model. Incremental updates for the weighted sample mean and inverse of the covariance matrix enable us to construct an evolvable fuzzy rule base that is used to detect outliers and regime changes in the input stream. We compare our model with Angelov's eTS+ model with artificial and real data.

Sensor fault tolerant control of nonlinear Takagi-Sugeno systems. Application to vehicle lateral dynamics

This paper presents a new scheme for sensor fault tolerant control for nonlinear systems based on the Takagi–Sugeno modeling. First, a structured residual generator aimed at detecting and isolating sensor faults is designed. A bank of observers controlled either by only one system output or a set of outputs is then implemented, leading to a set of state estimates. The parallel distributed compensation structure is adopted to design the fault tolerant controller. The novelty in this paper is that the estimated state used in the controller is a weighted state vector obtained from all the estimated states provided by the different observers. The weighting functions depend on the residual vector signals delivered by the residual generator. They are designed to avoid crisp switches in the control law. Indeed, the interesting feature of the proposed approach is to avoid the commonly used switching strategy. For each residual component, the greater its magnitude is, the less the weight affected to the corresponding state estimate is. Consequently, the controller only uses estimations computed on the basis of healthy measurements. The closed-loop stability is studied with the Lyapunov theory, and the obtained conditions are expressed as a set of linear matrix inequalities. The proposed residual generation and fault tolerant controller are applied to a vehicle lateral dynamics affected by sensor faults. Copyright © 2015 John Wiley & Sons, Ltd.

State constrained tracking control for nonlinear systems

This work addresses the model reference tracking control problem. It aims to highlight the encountered difficulties and the proposed solutions to achieve the tracking objective.Based on a literature overview of linear and nonlinear reference tracking, the achievements and the limitations of the existing strategies are highlighted. This motivates the present work to propose clear control algorithms for perfect and approximate tracking controls of nonlinear systems described by Takagi–Sugeno models. First, perfect nonlinear tracking control is addressed and necessary structural conditions are stated. If these conditions do not hold, approximate tracking control is proposed and the choice of the reference model to be tracked as well as the choice of the criterion to be minimized are discussed with respect to the desired objectives. The case of constrained control input is also considered in order to anticipate and counteract the effect of the control saturation.

Evolving Takagi–Sugeno model based on online Gustafson-Kessel algorithm and kernel recursive least square method

In this paper, we introduce an evolving Takagi-Sugeno model which utilizes an online Gustafson-Kessel algorithm for structure identification and sparse weighted kernel least square as local models. Our online clustering algorithm can form elliptical clusters which leads to creating less but more complex clusters than spherical ones. The proposed clustering method is capable of determining number of required clusters and reducing the complexity of model by merging similar clusters. Moreover, we propose weighted kernel recursive least square method with a new sparsification procedure based on instant prediction error. This sparsification procedure enhances kernel recursive least square performance. To illustrate our methodology, we apply the introduced algorithm to online identification of nonlinear and time varying system. Finally, to show the superiority of our approach in comparison to some known online approaches two different case studies are considered: Mackey-Glass and electrical load time series.

Parameter estimation for uncertain systems based on fault diagnosis using Takagi–Sugeno model

The paper addresses a systematic procedure to deal with state and parameter uncertainty estimation for nonlinear time-varying systems. A robust observer with respect to states, inputs and perturbations is designed, using a Takagi–Sugeno (T–S) approach with unknown premise variables. Tools of the linear automatic to the nonlinear systems are applied, using the Linear Matrix Inequalities optimization. The observer estimates the uncertainties, the states and minimizes the effect of external disturbances on the estimation error. The uncertainties are modelled in a polynomial way which allows considering the uncertainty estimation as a fault detection problem. The residual sensitivity to faults while maintaining robustness according to a noise signal is handled by H∞/H− approach. The method performance is illustrated using the three-tank system.

Automated generation and comparison of Takagi–Sugeno and polytopic quasi-LPV models

In the last decades, gain-scheduling control techniques have consolidated as an efficient answer to analysis and synthesis problems for non-linear systems. Among the approaches proposed in the literature, the linear parameter varying (LPV) and Takagi–Sugeno (TS) paradigms have proved to be successful in dealing with the different trials that the analyzer, or the designer, of a gain-scheduled control system has to face. Despite the strong similarities between the two paradigms, research on LPV and TS systems has been performed in an independent way and some results that could be useful for both paradigms were obtained only for one of them. However, in recent works, some clues that there is a very close connection between LPV and TS worlds have been presented. The present paper openly addresses the presence of strong analogies between LPV and TS models, in an attempt to establish a bridge between these two worlds, so far considered different. In particular, this paper addresses the modeling problem, presenting two methods for the automated generation of LPV and TS systems, and introducing some measures in order to compare the obtained models. A mathematical example is used to illustrate the proposed methods.

Nonlinear Adaptive Predictive Functional Control Based on the Takagi–Sugeno Model for Average Cracking Outlet Temperature of the Ethylene Cracking Furnace

The conventional PID control has been proven insufficient and incapable for this particular petro-chemical process. This paper proposes a nonlinear adaptive predictive functional control (NAPFC) algorithm based on the Takagi–Sugeno (T-S) model for average cracking outlet temperature (ACOT) of the ethylene cracking furnace. In this algorithm, in order to overcome the effect on system performance under model mismatch, the structure parameters of the T-S fuzzy model are confirmed, and the model consequent parameters are identified online using the forgetting factor least-square method. Prediction output is calculated according to the identified parameters instead of computing the Diophantine equation, thereby obtaining directly the predictive control law and avoiding the complex computation of the inverse of the matrix. Application results on ACOT of the ethylene cracking furnace show the proposed control strategy has strong tracking ability and robustness.

Формирование оптимального управления нелинейным динамическим объектом на основе модели Такаги-Сугено

Формирование оптимального управления нелинейным динамическим объектом на основе модели Такаги-Сугено