Takagi-Sugeno Fuzzy Research Articles

Takagi–Sugeno fuzzy based power system fault section diagnosis models via genetic learning adaptive GSK algorithm

To effectively deal with the operating uncertainties of protective relays and circuit breakers existing in the power system faults, an improved fault section diagnosis (FSD) method is proposed by using Takagi–Sugeno fuzzy neural networks (T–S FNN). In this method an optimal T–S FNN-based diagnosis model is built with the idea of distributed parallel processing for each section instead of the whole power system. To obtain accurate T–S FNN-based diagnosis models, a genetic learning adaptive gaining-sharing knowledge-based algorithm (GLAGSK) is designed to optimize their structure parameters and consequent parameters. GLAGSK combines an adaptive knowledge ratio and a genetic learning strategy to balance population diversity and convergence speed to boost the optimization ability. After a fault occurs, selective optimal T–S FNN-based diagnosis models are triggered according to the alarm information. They work in parallel to improve the fault diagnosis efficiency. Simulation results of three test systems including an actual fault event show that, compared with other peer algorithms, GLAGSK can obtain more accurate T–S FNN-based diagnosis models with faster global convergence. Besides, compared with the BP and RBF neural networks and other FSD methods, the proposed FSD method based on optimal T–S FNN-based diagnosis models can diagnose different complex faults successfully with higher fault credibility.

Sampled-Data Control for a Class of Singular Takagi-Sugeno Fuzzy Systems with Application in Truck-Trailer System

In order to solve the admissibility problem for a class of nonlinear singular systems with sampling, nonlinearity, and external disturbances, a sample-data control algorithm based on input delay methodology is proposed in this paper. Firstly, the system is converted to a time-delay system based on Takagi–Sugeno fuzzy models via an input delay approach, with many novel time-delay methods being used to deal with the sampled-data control problem. Secondly, both the upper and lower bounds of the sampling period are considered, which has a wider application scope. Thirdly, to obtain less conservative results, an appropriate Lyapunov–Krasovskii function, which involves several symmetric positive definite matrices, is established, and a relaxation variable is introduced by the method of reciprocally convex inequality. Then the conditions of admissibility are given, and the design method of the sampled-data controller is introduced. Finally, a truck-trailer example and two numerical examples are given to prove that the proposed approaches are valid and applicable.

Hidden Markov model based non-fragile sampled-data control design for mode-dependent fuzzy systems with actuator faults

This paper investigates the dissipativity-based asynchronous sampled-data control design for a class of Takagi–Sugeno fuzzy Markovian jump systems along with time delay, gain fluctuations, and actuator failures. To do this, the hidden Markov model is introduced to describe the phenomenon of asynchronization between the controller and the given fuzzy jump systems. Then, a novel mode-dependent Lyapunov–Krasovskii functional is constructed to achieve the stability conditions and expand the maximum sampling period of fuzzy systems. The main purpose of this study is to design the asynchronous non-fragile reliable control with sampled-data information such that the mode-dependent fuzzy system is stochastically stable and possesses the dissipativity performance. For this, a sufficient condition is derived for the proposed system in the form of linear matrix inequalities. Meanwhile, the less conservative results and the desired controller are attained by solving the inequalities. At last, the validity and the superiority of our design technique are demonstrated by numerical examples.

Lagrange Stability of Fuzzy Memristive Neural Networks on Time Scales With Discrete Time Varying and Infinite Distributed Delays

The existing results of Lagrange stability for neural networks with distributed time delays are scale-free, which introduces conservativeness naturally. A class of Takagi–Sugeno fuzzy memristive neural networks (FMNNs) on time scales with discrete time-varying and infinite distributed delays is brought in this article. First, a new scale-limited Halanay inequality is demonstrated by timescale theory. Next, on the basis of inequality techniques on time scales, some new scale-limited algebraic criteria and linear matrix inequality criteria of Lagrange stability are obtained by comparison strategy and generalized Halanay inequality. All scale-limited sufficient criteria of Lagrange stability for FMNNs not only apply to continuous-time FMNNs and their discrete-time analogs, but also could deal with the arbitrary combination of them. Finally, two numerical simulations are given to verify the validity of the obtained theoretical results.

An Enhanced Input-Delay Approach to Sampled-Data Stabilization for Nonlinear Stochastic Singular Systems Based on T-S Fuzzy Models

The sampled-data stabilization problem of nonlinear stochastic singular systems on the basis of the Takagi–Sugeno fuzzy models under variable samplings is discussed in this article. A new piecewise Lyapunov–Krasovskii functional is constructed, which can capture the actual sampling mode’s available features more fully, and an enhanced input-delay method is presented. By using the proper augmented scheme based on the auxiliary vector function, the new mean square admissibility criteria are derived by making good use of the convex combination techniques and the free weighting matrix approach. It is shown that the obtained results in this article contain less conservatism when compared with the existing ones. The superiority and correctness of our results are verified by an application example of a truck–trailer model.

Human-Machine Shared Steering Control for Vehicle Lane Keeping Systems via a Fuzzy Observer-Based Event-Triggered Method

This paper is concerned with the human-machine shared control issue for vehicle lane keeping systems via a new fuzzy observer-based event-triggered method. In order to capture system nonlinear and uncertain characteristics such as nonlinear tire dynamics, varying velocity and driver behavioral uncertainties, Takagi-Sugeno fuzzy approach is employed to model the global driver-vehicle-road system. After system modeling, the fuzzy observer-based control structure is considered because a full states information is not available in practical driving environment. Then, most existing human-machine shared control methods are based on the periodic sampling communication mechanism. However, since the network bandwidth is limited, the above mechanism may cause oversampling and communication congestion. Thus, an adaptive event-triggered mechanism is introduced between the observer and the controller to mitigate the communication burden and improve the bandwidth utilization. Based on Lyapunov functional theory, a set of sufficient conditions are given to calculate desired human-machine shared controllers. Finally, simulation tests are implemented on Matlab/Simulink-CarSim platform and simulation results illustrate that the proposed method can achieve a favorable improvement in the lane keeping capability, the driver handling comfort and the network bandwidth utilization.

LMI-Based Robust Fuzzy Model Predictive Control of Discrete-Time Fuzzy Takagi-Sugeno Large-Scale Systems Based on Hierarchical Optimization and H∞ Performance

This paper studies robust fuzzy model predictive control of discrete-time fuzzy Takagi-Sugeno large-scale systems based on hierarchical optimization and H_[Formula: see text] Performance. The considered system in this paper is a large-scale system. So, the Takagi-Sugeno (T-S) fuzzy approach which uses nonlinear local models is applied to estimate the nonlinear system to reduce the burden of modeling. The model predictive control (MPC) is a practical application that is useful for all systems but the problem is the online computational cost. For large-scale systems, this problem is the online computational burden. Besides, it leads to conservative or even no solution. By the proposed method, more relaxed solutions are achieved. First, the T-S system with nonlinear local models is adopted. Second, the hierarchical optimization scheme is considered for the optimization part of the MPC. Third, by inspiring the [Formula: see text] performance, uncertainties and disturbances that are appeared are reduced. Moreover, the linear matrix inequalities (LMIs) are used to solve the proposed method that the computational burden significantly is reduced at the same time. Simulation results are finally presented to show the effectiveness of the proposed controller.

Discrete-Time System Conditional Optimization Based on Takagi–Sugeno Fuzzy Model Using the Full Transfer Function

The study proposes a novel method for synthesis of a discrete-time parallel distributed compensation (PDC) controller for the nonlinear discrete-time Takagi–Sugeno (TS) fuzzy plant model. For each of the fuzzy plant model linear subsystems, a local linear first order proportional-sum (PS) controller is designed. The algebraic technique is used in two-dimensional parameter space, utilizing the characteristic polynomial of the row nondegenerate full transfer function matrix. Each system’s relative stability is accomplished in relation to the selected damping coefficient. The supplementary criterion is the minimal value of the performance index in the form of the sum of squared errors (SSE). However, unlike the traditional technique, output error is impacted by all simultaneous actions on the system: nonzero inputs and nonzero initial conditions. The full transfer function matrix of the system allows for the treatment of simultaneous actions of the input vector and unknown unpredictable initial conditions. In order to show the improvement caused by the application of a new optimization method that considers nonzero initial conditions, a comparison of PDC controllers designed under zero and nonzero initial conditions is given, where the system in both cases starts from the same nonzero initial conditions, which is often the case in practice. The simulation and experimental results on a DC servo motor are shown to demonstrate the suggested method efficiency.

Improved Control Design for Autonomous Vehicles

In this paper, the autonomous vehicle presented as a discrete-time Takagi-Sugeno fuzzy (T-S) model. We used the discrete-time T-S model since it is ready for the implementation unlike the continuous T-S fuzzy model. The main goal is to keep the autonomous vehicle in the centreline of the lane regardless the external disturbances. These disturbances are the wind force and the unknown curvature; they are applied to test if the autonomous vehicle moves from the centreline. To ensure that the autonomous vehicle remain on the centreline we propose two discrete-time fuzzy lateral controllers called also steering controllers.

A switched system approach to exponential filtering design for Takagi–Sugeno fuzzy systems with sampled‐data measurements subject to packet dropouts

AbstractThis article studies the problem of exponential filtering design for Takagi–Sugeno fuzzy systems with sampled‐data measurements under the data packet dropout phenomenon. A novel switched system approach is developed, and thus the resulting filtering error system is rewritten in a time‐varying delayed switched system form. Based on novel piecewise time‐dependent Lyapunov functionals, sufficient conditions are obtained to guarantee the exponential stability with performance of the filtering error system. The full‐/reduced‐order filter design results in the form of solving a set of linear matrix inequalities are obtained. Finally, simulation results are provided to show the effectiveness of the method.

Extended Kalman filter and Takagi-Sugeno fuzzy observer for a strip winding system

This paper proposes two nonlinear estimation approaches, namely based on Extended Kalman Filter (EKF) and a Takagi-Sugeno Fuzzy Observer with 32 rules (TSFO-32), for a Strip Winding System (SWS) characterized by variable reference input, variable moment of inertia with constant increasing tendency and variable parameters. The SWS is a complex and nonlinear mechatronic system viewed as a controlled process, which wraps a strip with constant linear velocity on a reel, and the variable radius modifies both the angular velocity and the moment of inertia. The motivation of using EKF is the zero stationary error at low speeds. The motivation of using TSFO-32 is that once the Takagi-Sugeno fuzzy models are obtained, various analysis and design tools initially developed for linear systems, which facilitate the observation and/or synthesis of the controller for complex nonlinear systems, can be adapted appropriately and used in these nonlinear systems. Therefore, these tools simplify the design as well-established approaches and algorithms are available. The fuzzy control system stability and observer design conditions are derived and expressed as linear matrix inequalities. The efficiency of TSFO-32 is discussed in this paper in terms of setting a certain convergence rate. The performance of the two nonlinear estimation approaches is validated by means of digital simulations conducted for three values of the moment of inertia.

State and static output feedback control of singular Takagi–Sugeno fuzzy systems with time-varying delay via proportional plus derivative feedback

This paper investigates the problems of state and static output feedback control for a class of singular Takagi–Sugeno fuzzy systems with time-varying delay. Two kinds of controllers are considered: one is the proportional plus derivative state feedback controller, the other is the proportional plus derivative static output feedback controller. The augmented Lyapunov–Krasovskii functional is chosen to analyze the stabilization of the considered system and the sufficient conditions are proposed based on the Lyapunov stability theory. In order to solve the controller gains, two iterative algorithms are built. Two persuasive examples are given to show the effectiveness of our methods.

Observer-based sliding mode control for discrete-time nonlinear system with time-varying delay

This work deals with the design observer-based sliding mode control for discrete-time Takagi–Sugeno fuzzy models with time-varying delay and subject to measurement noises. The sliding surface is developed by introducing the state and input vectors to overcome the restrictive assumption in most existing sliding mode control schemes which forces the input matrices of all linear subsystems to be equal. Sufficient stability conditions of the error system and sliding mode dynamics with disturbance attenuation level are developed using the augmented Lyapunov–Krasovskii functional and free-weighting matrix. Finally, a simulation example is presented to demonstrate the efficiency of the proposed results.

Zonotopic observer designs for uncertain Takagi–Sugeno fuzzy systems

This paper addresses the zonotopic observer design for nonlinear systems affected by uncertainties, i.e., state disturbances and measurement noises using Takagi–Sugeno (TS) fuzzy technique. The system uncertainties are considered as unknown but bounded, which are handled via a set-membership framework. For state estimation purposes, we develop an algorithm to recursively compute the zonotope containing the mismatching nonlinear term caused by unmeasured nonlinearities. Then, two methods are proposed to design the zonotopic observer gains. The first method is based on the minimization of the F−radius of zonotopes, for which the membership-function-dependent observer gain must be completely computed online. For the second method, an ℋ∞ approach is used together with a nonquadratic Lyapunov function to determine the observer gain. Then, the zonotopic observer design is reformulated a convex optimization problem under linear matrix inequalities (LMIs), which can be effectively solved with numerical solvers. An autonomous vehicle application is provided to demonstrate and analyze the effectiveness of both proposed methods.

Aperiodic Sampled-Data Takagi–Sugeno Fuzzy Extended State Observer for a Class of Uncertain Nonlinear Systems With External Disturbance and Unmodeled Dynamics

For the extended state observer (ESO) design, the most challenging issue is to exploit efficient nonlinear observation performance, while maintaining desirable linear numerical tractability under noncontinuous transmission. In this article, in order to address this issue, the sampled-data ESO design is investigated for a class of uncertain nonlinear systems. First, based on the fuzzy modeling approach with reasonable fuzzy rules and sets, the nonlinear functions of the ESO are suitably approximated by several local linear models weighted by membership functions. Then, a novel methodology of Takagi–Sugeno fuzzy extended state observer (TSFESO) is developed for the first time. By virtue of fuzzy membership functions, the estimating action is implemented in a nonlinear pattern, while taking advantages of Takagi–Sugeno fuzzy formulation, the observer gains can be calculated in a linear manner. As a result, the nonlinear estimating efficiency and linear numerical tractability are integrated in a unified framework. Second, for the aperiodic sampling case, the exponential convergence criterion for the TSFESO is presented by constructing a sampling- and time-dependent Lyapunov functional, in which the information on sampling action is taken into full consideration for desirable feasibility. Moreover, the observer design approach is also put forward. Finally, the superiorities and effectiveness of the proposed approaches are demonstrated by numerical examples.

Tuning Parameters-Based Fault Estimation Observer for Time-Delay Fuzzy Systems Over a Finite Horizon

In this work, the problem of fault and state estimation is studied for Takagi–Sugeno fuzzy systems with time-varying delay and external disturbance over a finite horizon. A fuzzy rule-based fault estimator with two tuning parameters, including the current system output information, is designed. Based on which, the Luenberger state observer is then considered to estimate the immeasurable states of the system addressed. The aim of taking into account the tuning parameters in the estimator design is to improve the accuracy of the fault estimation. More precisely, by defining error variables in accordance with actual and estimated system states and faults, an augmented system is formulated to achieve the desired results. By using the existing stability theory and integral inequality, a delay-dependent criterion for ensuring that the states of the augmented system are bounded over a finite horizon is derived. Subsequently, conditions for determining the observer gain matrices are presented. Two simulation examples, including an application example of the truck-trailer model, are provided to demonstrate the advantages of the theoretical results that have been established. In particular, the importance of the use of tuning parameters is discussed.

Multi-Instant Gain-Scheduling Stabilization of Discrete-Time Takagi–Sugeno Fuzzy Systems Based on a Time-Variant Balanced Matrix Approach

This article is devoted to the development of multi-instant gain-scheduling stabilization of discrete-time Takagi–Sugeno fuzzy systems by developing a time-variant balanced matrix approach. Many of the reported advances have provided more and more relaxed results via choosing higher order dependent gain matrices, which will be a trouble in the case of real-time implementation. Therefore, a multi-instant gain-scheduling fuzzy state-feedback controller with different working modes is given to stabilize the closed-loop systems by updating the enabled pair of lower order gain matrices in cycle. For each possible working mode, the real-time situation information of the normalized fuzzy weighting functions can be fully considered by using a set of time-variant balanced matrices in accordance to certain rules and, thus, much freedom is introduced for proposing less conservative results. More importantly, our relaxed result is obtained without requiring higher order dependent gain matrices than the existing ones, i.e., its conservatism is reduced in a more meaningful way and thus it is more conducive to real-time implementation. Finally, both the effectiveness and the superiority of the proposed results are discussed and validated in the numerical section.

Impulsive Consensus of Fractional-Order Takagi–Sugeno Fuzzy Multiagent Systems With Average Dwell Time Approach and Its Applications: Achieving Finite-Time Consensus

The Takagi–Sugeno (T–S) fuzzy-based impulsive consensus problem of a fractional-order multiagent system (FOMAS) with an average dwell time (ADT) is investigated. FOMASs are nonlinear systems, and they are modeled as linear subsystems using a T–S fuzzy model. We study a T–S fuzzy FOMAS subject to a class of impulse time sequences with the ADT approach. In this article, an impulsive control scheme is proposed to make the tracking error converge in a finite-time consensus into a small neighborhood of origin. Based on impulsive fractional differential equations theory, the Lyapunov functional approach, and the ADT technique, an impulsive controller is designed to achieve finite-time consensus of a T–S fuzzy FOMAS. Finally, through numerical as well as practical examples, the effectiveness and superiority of the proposed approach are validated.

New Results on Dissipative Control for a Class of Singular Takagi–Sugeno Fuzzy Systems With Time Delay

This article studies the problem of dissipative control for singular Takagi–Sugeno fuzzy systems with time delay. In order to reduce the conservatism brought by the time delay, we choose a proper augmented Lyapunov–Krasovskii functional and the auxiliary-function-based integral inequality to analyze the admissibility and dissipativity of the system. The singularity of the derivative matrix of the system leads to the matrix coupling terms, which are difficult to handle in the controller design by using the common controller design methods, so we propose an iterative algorithm to solve the controller parameters. The sufficient conditions of ensuring that the closed-loop system is admissible and dissipative are presented. Finally, three persuasive examples are given to demonstrate the effectiveness of the proposed method.

Relaxed Conditions of Observer Design of Discrete-Time Takagi–Sugeno Fuzzy Systems via a New Multi-Instant Gain-Scheduling Scheme

A novel multi-instant gain-scheduling scheme is proposed in order to further improve the state estimation performance of discrete-time Takagi–Sugeno fuzzy systems in this article. Different from those existing methods, the enabled working pattern at each sampling instant can be determined in cycle according to utilization of the updated information of adjacent normalized fuzzy weighting functions in depth, and then the featured time-varying free matrices are introduced for each working pattern, which can remove those existing constraints on traditional free matrices. Consequently, the conservatism can be reduced significantly and it does broaden the range of application for observer-based fuzzy state estimation. Despite the fact that the quantity of the free matrices becomes much bigger than before, it needs to be pointed out that the actual computational complexity only increases by a small amount through depressing the number of cycles. Given that the developed designing process belongs to an offline computation, it is an acceptable tradeoff between the increasement of computational burdens and the reduction of conservatism. In the end, the effectiveness of the developed method is illustrated through the detailed analysis of numerical simulations.