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Multi-label classification can effectively identify the relevant labels of an instance from a given set of labels. However, the modeling of the relationship between the features and the labels is critical to the classification performance. To this end, we pro-pose a new multi-label classification method, called Multi-Label Takagi-Sugeno-Kang Fuzzy System (ML-TSK FS), to improve the classification performance. The structure of ML-TSK FS is designed using fuzzy rules to model the relationship between features and labels. The fuzzy system is trained by integrating fuzzy inference based multi-label correlation learning with mul-ti-label regression loss. The proposed ML-TSK FS is evaluated by experimentally on 12 benchmark multi-label datasets. The results show that the performance of ML-TSK FS is competitive with existing methods in terms of various evaluation metrics, indicating that it is able to model the feature-label relationship effectively using fuzzy inference rules and enhances the classifi-cation performance.

While input or output-perturbation-based adversarial training techniques have been exploited to enhance the generalization capability of a variety of nonfuzzy and fuzzy classifiers by means of dynamic regularization, their performance may perhaps be very sensitive to some inappropriate adversarial samples. In order to avoid this weakness and simultaneously ensure enhanced generalization capability, this work attempts to explore a novel knowledge adversarial attack model for the zero-order Tagaki-Sugeno-Kang (TSK) fuzzy classifiers. The proposed model is motivated by exploiting the existence of special knowledge adversarial attacks from the perspective of the human-like thinking process when training an interpretable zero-order TSK fuzzy classifier. Without any direct use of adversarial samples, which is different from input or output perturbation-based adversarial attacks, the proposed model considers adversarial perturbations of interpretable zero-order fuzzy rules in a knowledge-oblivion and/or knowledge-bias or their ensemble to mimic the robust use of knowledge in the human thinking process. Through dynamic regularization, the proposed model is theoretically justified for its strong generalization capability. Accordingly, a novel knowledge adversarial training method called KAT is devised to achieve promising generalization performance, interpretability, and fast training for zero-order TSK fuzzy classifiers. The effectiveness of KAT is manifested by the experimental results on 15 benchmarking UCI and KEEL datasets.

This work addresses the nonfragile H∞ controller design problem for a class of discrete-time uncertain nonlinear systems. The norm-bounded uncertainty is contained in the nonlinear plant, which is described by the well-known Takagi-Sugeno (T-S) fuzzy model. The controller gain perturbation is also considered. When the input signal is transmitted from the controller to the system through the digital communication channels, it will be quantized by a static quantizer. The main attention is to design the nonfragile H∞ state-feedback controller for the closed-loop quantized uncertain T-S fuzzy system. By introducing some auxiliary scalars and the fuzzy basis-dependent Lyapunov function approach, sufficient conditions are established in the form of linear matrix inequalities (LMIs). The construction for the nonfragile H∞ controller can be completed by solving these LMIs. In the end, the applicability and effectiveness of the proposed method have been illustrated by two simulation examples.

This work addresses the problem of aperiodically sampled control for the networked Takagi-Sugeno (T-S) fuzzy systems, where the aperiodically sampled input is generated by a periodic sampler and an event-triggered mechanism (ETM). The purpose of ETM is used to reduce the computational and communication burdens. For guaranteeing controller robustness, the practical stability of T-S fuzzy systems is considered by using the Lyapunov method and linear matrix inequality (LMI) technique. As one of the most powerful inequalities for deriving stability criteria using LMIs, Jensen's inequality has recently been improved by various authors for the stability analysis of delayed systems. However, these results are conservative to obtain lower bounds for integrals with an exponential term. Inspired by this, improved integral inequalities are derived in this work, and they are applied to obtain practical stability criteria for aperiodically sampled control. Finally, a numerical example on flight control of a helicopter is given to illustrate the effectiveness of the obtained practical stability criteria. Furthermore, the effectiveness of the improved Jensen inequalities on the exponential stability criteria is illustrated by numerical comparisons.

The problems of impulse controllability and impulse elimination are investigated based on sliding mode control(SMC) for Takagi-Sugeno(T-S) fuzzy singular systems(FSSs) in this paper. Necessary and sufficient conditions for T-S FSSs to be impulse controllable are obtained based on the rank of matrices of system equivalent form. The relationship between impulses and fuzzy membership functions is given. The linear switching function(LSF) and SMC law are designed to be applied to the impulse elimination of T-S FSSs. The main contributions of this approach are to design a SMC law which can not only effectively eliminate impulses of T-S FSSs but also make the system asymptotically stable and give the principle of SMC to eliminate the impulse. Finally, The proposed method is applied to three examples. Example 1 and 3 are to illustrate that SMC can effectively eliminate impulses of T-S FSSs. Example 2 verifies the superiority of this method by comparing with P-D feedback control law(FCL).

The problem of enhanced stabilization of discrete-time Takagi-Sugeno fuzzy system is investigated in depth via proposing a new way to employ much more information implied in various time-varying differences of multi-instant normalized fuzzy weighting functions. Benefit from the given comprehensive real-time scheduling model, these time-varying differences on time vertical dimension and two different transverse dimensions are for the first time integrated into fuzzy stabilization and two key alterable weights are also introduced. Consequently, much considerable freedom can be produced and, thus, it brings much less conservative results than the reported ones in recent literature. More importantly, a very simple workable way has been provided to online recognize the specific enabled mode at each sampling instant so that those existing time-consuming online operations in referred literature can be avoided to ease online implementation costs. Indeed, this feature is very beneficial to the practical application of our theoretical results. Finally, the superiority of our developed method over previous ones is validated adequately via two benchmark simulations.

This article deals with the problem of H∞ and l2-l∞ filtering for discrete-time Takagi-Sugeno fuzzy nonhomogeneous Markov jump systems with quantization effects, respectively. The time-varying transition probabilities are in a polytope set. To reduce conservativeness, a mode-dependent logarithmic quantizer is considered in this article. Based on the fuzzy-rule-dependent Lyapunov function, sufficient conditions are given such that the filtering error system is stochastically stable and has a prescribed H∞ or l2-l∞ performance index, respectively. Finally, a practical example is provided to illustrate the effectiveness of the proposed fuzzy filter design methods.

In the recently published paper, a switching method has been proposed to deal with the time derivative of the membership functions and less conservative results can be obtained due to this method; however, this method is based on the assumption that the switching times are finite. In this article, this method is further studied and the average dwell-time (ADT) switching technique is applied to ensure the stability if there is no such assumption. In addition, an algorithm is proposed to find the switching controller gains. The final simulation demonstrates the effectiveness of the developed new results.

The main objective of this work is to propose two fuzzy controllers: one based on the Mamdani inference method and another controller based on the Takagi- Sugeno inference method, both will be designed for application in a position control system of a servomechanism. Some comparations between the methods mentioned above will be made with regard to the performance of the system in order to identify the advantages of the Takagi- Sugeno method in relation to the Mamdani method in the presence of disturbances and nonlinearities of the system. Some results of simulation and practical application are presented and results obtained showed that controllers based on Takagi- Sugeno method is more efficient than controllers based on Mamdani method for this specific application.

In data-driven modeling besides the point estimate of the model parameters, an estimation of the parameter uncertainty is of great interest. For this, bounded error parameter estimation methods can be used. These are particularly interesting for problems where the stochastical properties of the random effects are unknown and cannot be determined. In this paper, different methods for obtaining a feasible parameter set are evaluated for the use with Takagi-Sugeno models. Case studies with simulated data and with measured data from a manufacturing process are presented.

The aim of this paper is to present a robust anti-windup compensator methodology to deal with the stabilization of nonlinear time-varying delay systems, which are described by Takagi–Sugeno (T–S) fuzzy models. Given a stabilizing output feedback fuzzy controller, an anti-windup control approach is developed to estimate the domain of attraction. Based on the Lyapunov–Krasovskii functional and delay-dependent analysis, sufficient conditions for the robust stabilization via anti-windup controller are derived in terms of linear matrix inequalities. In addition, an algorithm is provided to optimize the anti-windup gain and reduce the conservatism. Numerical examples illustrate the effectiveness of our methodology and show the improvements over the existing ones.

This paper focuses on the issue of two-objec-tive filtering for Takagi–Sugeno fuzzy Hopfield neural networks with time-variant delay. The intention is to design a fuzzy filter subject to random occurring gain perturbations to make sure that the filtering-error system achieves a pre-defined $${\mathscr {H}}_{\infty }$$ and $${\mathscr {L}}_{2}\mathscr {-L}_{\infty }$$ disturbance attenuation level in mean square simultaneously. Without imposing any additional constraints on the differentiability of the time-delay function, a criterion of the mean-square $${\mathscr {H}}_{\infty }$$ and $${\mathscr {L}}_{2}\mathscr {-L} _{\infty }$$ performance analysis for the filtering-error system is derived by means of an augmented Lyapunov functional and the second-order Bessel–Legendre inequality. Then, a numerically tractable design scheme is developed for the desired non-fragile $${\mathscr {H}}_{\infty }$$ and $$ {\mathscr {L}}_{2}\mathscr {-L}_{\infty }$$ filter, where the gains are able to be determined by the solution of some linear matrix inequalities. At last, a numerical example with simulations is provided to illustrate the applicability and superiority of the present $${\mathscr {H}}_{\infty }$$ and $$ {\mathscr {L}}_{2}\mathscr {-L}_{\infty }$$ filtering method.

This work deals with the design of fuzzy controllers for stabilization of continuous-time nonlinear systems subject to L 2 disturbances, which are represented by nonlinear Takagi–Sugeno fuzzy models, i.e. , Takagi–Sugeno fuzzy models with nonlinear consequents. A nonquadratic Lyapunov function is used to derive sufficient design conditions based on linear matrix inequality constraints as well as to reduce the conservativeness when compared to existing control approaches in the literature. Furthermore, the nonquadratic Lyapunov function is defined in terms of an integral membership function, which leads to a delayed nonquadratic L 2 -stabilization condition. This condition avoids the well-known difficulties in dealing with time derivatives of membership functions and/or path-independent conditions, found in most of the nonquadratic control approaches for continuous-time Takagi–Sugeno fuzzy models. Two numerical examples are performed to illustrate the reduction in conservativeness provided by the proposed approach.

This paper is concerned with the analysis of optimization procedures for optimal experiment design for locally affine Takagi-Sugeno (TS) fuzzy models based on the Fisher Information Matrix (FIM). The FIM is used to estimate the covariance matrix of a parameter estimate. It depends on the model parameters as well as the regression variables. Due to the dependency on the model parameters good initial models are required. Since the FIM is a matrix, a scalar measure of the FIM is optimized. Different measures and optimization goals are investigated in three case studies.

This article concerns the event‐triggered fuzzy filter design for Takagi‐Sugeno (T‐S) fuzzy systems subject to deception attacks under the stochastic multiple time‐varying delays. A sequen...

This article focuses on the stabilization conditions of fractional order fuzzy singularly perturbed systems via state and static output feedback control with order 0 < α < 1, respectively. First, by an equivalent transformation, fractional order singularly perturbed systems are transformed into fractional order singular systems. Second, three stabilizing conditions under state feedback control are proposed. Then, based on the introduction of intermediate variables, static output feedback control condition in terms of strict linear matrix inequalities which guarantee the fractional order Takagi–Sugeno fuzzy singularly perturbed system to be stable is obtained. And the proposed conditions can overcome some drawbacks in the existing work. Finally, two examples are provided to show the effectiveness of the results in this study.

Over the last several decades, neuro-fuzzy systems (NFS) have been widely analyzed and described in the literature because of their many advantages. They can model the uncertainty characteristic of human reasoning and the possibility of a universal approximation. These properties allow, for example, for the implementation of nonlinear control and modeling systems of better quality than would be possible with the use of classical methods. However, according to the authors, the number of NFS applications deployed so far is not large enough. This is because the implementation of NFS on typical digital platforms, such as, for example, microcontrollers, has not led to sufficiently high performance. On the other hand, the world literature describes many cases of NFS hardware implementation in programmable gate arrays (FPGAs) offering sufficiently high performance. Unfortunately, the complexity and cost of such systems were so high that the solutions were not very successful. This paper proposes a method of the hardware implementation of MRBF-TS systems. Such systems are created by modifying a subclass of Takagi-Sugeno (TS) fuzzy-neural structures, i.e. the NFS group functionally equivalent to networks with radial basis functions (RBF). The structure of the MRBF-TS is designed to be well suited to the implementation on an FPGA. Thanks to this, it is possible to obtain both very high computing efficiency and high accuracy with relatively low consumption of hardware resources. This paper describes both, the method of implementing MRBFTS type structures on the FPGA and the method of designing such structures based on the population algorithm. The described solution allows for the implementation of control or modeling systems, the implementation of which was impossible so far due to technical or economic reasons.

Although the Takagi–Sugeno fuzzy model is effective for representing the dynamics of a plant to be controlled, two main questions arise when using it just as other models: 1) how to deal with the gap, which is referred to as uncertainty in this study, between the model and the concerned plant, and how to estimate the state information when it cannot be obtained directly, especially with the existence of uncertainty; 2) how to design a controller that guarantees a stable control system where only the estimated state is available and an uncertainty exists. While the existing studies cannot effectively observe the state and the resulting control systems can only be managed to be uniformly stable, this study first presents a state observer capable of precisely estimating the state regardless of the existence of uncertainty. Then, based on the state observer, an uncertainty observer is derived, which can track the trajectory of uncertainty whenever it occurs in a real system. Finally, a controller based on both observers is presented, which guarantees the asymptotic stability of the resulting control system.

This paper studies the H ∞ filtering problem for continuous-time T-S fuzzy Markov jump systems with time-varying delay. A switched fuzzy filter approach is proposed for the first time to improve the previous filter solutions independent of the derivative of fuzzy membership functions (FMFs). Furthermore, a novel delay-product-type FMFs-dependent Lyapunov-Krasovskii functional (LKF) is constructed to make full use of the information on FMFs and time delay simultaneously. A parameter-dependent reciprocally convex inequality (PDRCI) is proposed to more accurately estimate the delay-product-type FMFs-dependent LKF. Based on these ingredients, the existence condition and explicit design method of fuzzy H ∞ filter are both given. Two examples are employed to illustrate the effectiveness of the proposed methods.

Summary In the network environment, the single time‐triggered scheme wastes limited bandwidth resources due to all the sampled data are transmitted to the networks, and the single event‐triggered s...

This article analyzes the integral sliding mode control (ISMC) problem for the nonlinear stochastic system by employing the fuzzy approach. Firstly, the Takagi‐Sugeno (T‐S) fuzzy stochasti...

Summary In this article, by using singular perturbation theory, reinforcement learning (RL), and Takagi–Sugeno (T‐S) fuzzy methods, a RL‐fuzzy‐based composite suboptimal control method is proposed ...

Forecasting is a method of predicting past and current data, most often by pattern analysis. A Fuzzy Takagi Sugeno Kang (TSK) study can predict Indonesia's inflation rate, yet with too high error. This study proposes an accuracy improvement based on Evolution Strategies (ES), a specific evolutionary algorithm with good performance optimization problems. ES algorithm used to determine the best coefficient values on consequent fuzzy rules. This research uses Bank Indonesia time-series data as in the previous study. ES algorithm uses the popSize test to determine the number of initial chromosomes to produce the best optimal solution for this problem. The increase of popSize creates better fitness value due to the ES's broader search area. The RMSE of ES-TSK is 0.637, which outperforms the baseline approach. This research generally shows that ES may reduce repetitive experiment events due to Fuzzy coefficients' manual setting. The algorithm complexity may cost to the computing time, yet with higher performance.

This article investigates the problem of multistability of almost-periodic solutions of Takagi–Sugeno fuzzy neural networks with nonmonotonic discontinuous activation functions and time-varying delays. Based on the geometrical properties of nonmonotonic activation functions, by using the Ascoli–Arzela theorem and the inequality techniques, it is demonstrated that under some reasonable conditions, the addressed networks have a locally exponentially stable almost-periodic solution in some hyperrectangular regions. We also estimate the attraction basins of the locally stable almost-periodic solutions, which indicates that the attraction basins of the locally exponentially stable almost-periodic solution can be larger than original hyperrectangular regions. These results, which include boundedness, globally attractivity, multiple stability, and attraction basins, generalize and improve the earlier publications, and can be extended to monostability and multistability of Takagi–Sugeno fuzzy neural networks with nonmonotonic discontinuous activation functions. Finally, several numerical examples are given to show the feasibility, the effectiveness, and the merits of the theoretical results.

Presented in this research paper is an integrated direct yaw moment control (DYC) and active front steering (AFS) for an uncertain vehicle lateral dynamics model considering network-induced communication delay, which is a time-varying continuous function with a known upper bound. Firstly, we consider tire cornering stiffness as a non-linear norm-bounded uncertain system that is modeled by fuzzy membership functions, and then vehicle lateral dynamics model is expressed by a set of linear Takagi-Sugeno (T-S) uncertain fuzzy models. Secondly, since the network-induced communication delay in vehicle control system is an inherent reason for stability and performance degradation, we derive a robust delay-dependent [Formula: see text] control methodology via the Lyapunov-Krasovskii functional for stability and performance conditions of the closed-loop system. For the synthesis, the robust control method is employed within the T-S fuzzy-model-based analysis framework and formulations are performed based on the solution of delay-dependent linear matrix inequalities (LMIs). The simulation study is presented using MATLAB/Simulink to show the achieved improvements in tracking variables via the designed robust fuzzy [Formula: see text] state-feedback controller. The proposed fuzzy robust delay-dependent controller is compared with a linear robust delay-dependent controller to clearly show the tracking improvements for different road conditions. Moreover, a performance-based analysis is carried out to demonstrate the advantage of the design with respect to different delay values. It is confirmed from the analysis results that the proposed fuzzy controller can successfully stabilize and possess improved tracking performance for vehicle lateral motion control.

A new stabilization problem for Takagi–Sugeno (T–S) fuzzy systems involving time-varying delay and interval uncertainties is investigated in this paper. Firstly, a new stabilization condition on dynamic output feedback control for T–S fuzzy systems is proposed. Meanwhile, a robust H∞-γ stabilization criterion for T–S fuzzy systems is presented based on Lyapunov–Krasovskii function. In addition, an incremental sampling method based on loss function is developed to deal with interval uncertainties of T–S fuzzy systems. Sequentially, the stabilization problem is calculated by combining a linear matrix inequality approach with the incremental sampling method. Lastly, two numerical examples are provided to illustrate the effectiveness and feasibility of the proposed approach.

International audience; This paper presents a new H∞ anti-windup dynamic output control developed for a class of nonlinear systems subject to both sensors and actuators saturations. First, the nonlinear system under consideration is represented by a Takagi-Sugeno (T-S) fuzzy model. Then, a dynamic output feedback (DOF) control strategy is proposed and the saturation constraints are transformed into dead-zone nonlinearities. Based on this transformation and by using the sector condition, the H∞ dynamic output stabilization conditions of the closed-loop system are given in terms of linear matrix inequalities (LMI). Finally, a numerical example is simulated to demonstrate the efficiency of the proposed design method.

This paper proposes a general robust model predictive control (MPC) approach for the constrained Takagi-Sugeno (T-S) fuzzy model with additive bounded disturbances. We adopt the homogeneous polynomially parameter-dependent (HPP) Lyapunov matrix with the arbitrary complexity degree and the corresponding HPP control law for the controller design. By applying the Polya’s theorem and the extended nonquadratic boundedness property, a systematic approach to construct a set of sufficient conditions for assessing robust stability described by parameter-dependent linear matrix inequalities (LMIs) is established. The proposed approach is an improvement over existing approaches in terms of control performance and stabilizable model range. Numerical examples are provided to show the effectiveness of the proposed robust MPC approach.

Nonlinearities exist everywhere and the investigation on control problems for nonlinear systems is of both theoretical and practical significance. The Takagi-Sugeno (T-S) fuzzy techniques, as one of the powerful model-based tools for dealing with control problems for nonlinear systems, have received considerable and persistent research attention during the recent decades. Based on the T-S fuzzy model, many complicated nonlinear control problems have been addressed in the literature. In this paper, we aim to provide a survey with respect to the T-S fuzzy control problems with complexities that are frequently encountered in the engineering practice. Firstly, the backgrounds of the fuzzy control and engineering-oriented complexities are discussed. The considered complexities are divided into traditional engineering-oriented ones and the network-induced ones. The former mainly includes time-delays, parameter uncertainties, sensor/actuator faults and the latter contains network-induced phenomena, communication protocols, event-triggered schemes and cyber-attacks. Then, the recent progress on the T-S fuzzy control problems subject to these complexities has been reviewed in details. Finally, based on the literature review, the conclusions are drawn and some possible future topics are given.

Modern challenges in a post-industrial society require further development of management systems for complex technical and technological phenomena and processes. Effective control of an object is possible if a controller, or a fuzzy controller, correctly generates the required control action. Recently, fuzzy controllers have been very popular. Fuzzy logical statements in this case help considering various nonlinear relationships. The synthesis of the fuzzy controller parameters allows for more efficient operation of the control system. A possible option for obtaining the best set of parameters for a fuzzy controller is the use of genetic algorithms for its synthesis. The use of genetic algorithms for the fuzzy controllers synthesis can lead to the fact that the elements of its parameters array will change in such a way that an incorrect value of one or more elements will occur. This situation leads to impossibility of composing membership functions for the terms of the variables of the fuzzy controller. Incorrect value formation is excluded by constructing a limited functional dependency. This paper proposes a mathematical model of the parameters of the term-set of variables of a fuzzy controller of the Takagi — Sugeno — Kang type of the zero and first orders. The authors disclose the content of the conditions and conclusions of the rule base for the fuzzy controller of the above type. As a result of the simulation, some operations of the genetic algorithm are implemented using a random number generator. Graphical models of the membership functions of the input variables of the fuzzy controller of the type under consideration clearly illustrate the occurrence of all parameters in their range of possible values. A description of the control system operation with two control parameters and one control action at the specified values of the control parameters is presented.