Takagi-Sugeno Fuzzy Research Articles

Observer‐based PID control for fuzzy dynamic systems with memory triggering protocol

AbstractThis paper addresses the issue of observer‐based proportional–integral–derivative control for Takagi–Sugeno fuzzy dynamic systems using a memory triggering protocol. To tackle the challenges of managing nonlinear systems, the Takagi–Sugeno fuzzy approach is employed to approximate these systems with a series of local linear models. A novel memory event‐triggering mechanism is introduced, utilizing a computer's storage unit to store historical data and adjust the triggering threshold based on this data, thereby reducing unnecessary network resource usage. Given that the system state can be affected by external disturbances and become unpredictable, an observer‐based proportional–integral–derivative controller is designed to manage these uncertainties. Finally, a car‐damper‐spring model is presented to validate the proposed methodology.

State and Fault Interval Estimation for Discrete-Time Takagi–Sugeno Fuzzy Systems via Intermediate Observer Base on Zonotopic Analysis

State and Fault Interval Estimation for Discrete-Time Takagi–Sugeno Fuzzy Systems via Intermediate Observer Base on Zonotopic Analysis

Fractional Caputo Operator and Takagi–Sugeno Fuzzy Modeling to Diabetes Analysis

Diabetes is becoming more and more dangerous, and the effects continue to grow due to the population’s ignorance of the seriousness of this phenomenon. The studies that have been carried out have not been able to follow the phenomenon more precisely, which has led to the use of the fractional derivative tool, which has a very great capability to study real problems and phenomena but is somewhat limited on nonlinear models. In this work, we will develop a new fractional derivative model of a diabetic population, the Takagi–Sugeno fractional fuzzy model, which will enable us to study the phenomenon with these nonlinear terms in order to obtain greater precision in the results. We will study the existence and uniqueness of the solution using the Lipschizian theorem and then turn to the new fuzzy model, which leads us to four dynamical systems. The interpretation results show the quality of fuzzy membership in tracking the malleable phenomena of nonlinear terms existing in the system.

A Fractional-Order Model Predictive Control Strategy with Takagi–Sugeno Fuzzy Optimization for Vehicle Active Suspension System

Aiming at the problem of system controller performance failure caused by improperly setting the value of each weighting coefficient of the model predictive control (MPC), a fractional-order MPC strategy with Takagi–Sugeno fuzzy optimization (T–SFO MPC) is proposed for a vehicle active suspension system. Firstly, the fractional-order model predictive control framework for active suspension systems is designed based on a 1/4 vehicle model. Then, we analyze the influence of different weighting coefficients on the suspension performance and introduce the Takagi–Sugeno fuzzy optimization theory to adaptively adjust the weighting coefficients of the fractional-order MPC controller. Finally, the system responses of the T–SFO MPC, traditional MPC, linear quadratic regulator (LQR), and passive suspension control are numerically analyzed under various road conditions. Simulation results show that suspension response with the T–SFO MPC is significantly improved compared with passive suspension control, traditional MPC control, and LQR control, and the weight coefficients of the T–SFO MPC can be adaptively adjusted according to the dynamic changes of suspension response. Compared with passive suspension, the root mean square (RMS) value of the vertical acceleration of the T–SFO MPC under various roads decreased by a maximum of 37.97%, and the RMS value of suspension dynamic deflection and tire dynamic load decreased by a maximum of 32.94% and 37.8%, respectively. These results validate that the proposed control method can achieve coordinated optimization of vehicle comfort and handling stability.

Design of extended dissipative-based composite anti-disturbance reliable tracking control for stochastic Takagi–Sugeno fuzzy systems

This study focuses on examining the issues of extended dissipative-based composite anti-disturbance reliable tracking control for stochastic Takagi–Sugeno fuzzy systems afflicted by sensor faults and multiple disturbances. Explicitly, the multiple disturbances include the autonomous Wiener process and non random noises with partly known information that are generated by an exogenous plant. To address the difficulty of estimating the non random disturbance while considering the partially known information, the study incorporates a fuzzy stochastic disturbance observer. Furthermore, to solve the output tracking issue of the system under consideration, a modified repetitive tracking control is implemented. Then, combining the methodologies of disturbance observer-based control technique with modified repetitive control, a composite anti-disturbance reliable tracking control strategy is developed for achieving the intended tracking goal despite the multiple disturbances and sensor faults encountered. Additionally, the proposed approach involves extended dissipativity scheme, which includes H ∞ , passivity, dissipativity, and L 2 − L ∞ performances in a unified framework. In particular, by employing Lyapunov–Krasovskii functional approach, the essential stability criteria for the proposed closed-loop system are articulated in the form of linear matrix inequalities. Additionally, numerical illustrations are presented to exemplify the application and efficiency of the developed control protocol.

Finite Time Stability Analysis and Feedback Control for Takagi–Sugeno Fuzzy Time Delay Fractional-Order Systems

This study treats the problem of Finite Time Stability Analysis (FTSA) and Finite Time Feedback Control (FTFC), using a Linear Matrix Inequalities Approach (LMIA). It specifically focuses on Takagi–Sugeno fuzzy Time Delay Fractional-Order Systems (TDFOS) that include nonlinear perturbations and interval Time Varying Delays (ITVDs). We consider the case of the Caputo Tempered Fractional Derivative (CTFD), which generalizes the Caputo Fractional Derivative (CFD). Two main results are presented: a two-step procedure is provided, followed by a more relaxed single-step procedure. Two examples are presented to show the reduction in conservatism achieved by the proposed methods. The first is a numerical example, while the second involves the FTFC of an inverted pendulum, which exhibits both symmetrical dynamics for small angular displacements and asymmetrical dynamics for larger deviations.

Stabilization of Continuous Two Dimensional Fractional order Positive Takagi-Sugeno Fuzzy Systems with Delays

Stabilization of Continuous Two Dimensional Fractional order Positive Takagi-Sugeno Fuzzy Systems with Delays

Fault detection observer design for Takagi–Sugeno fuzzy systems with finite-frequency specifications

This paper addresses robust fault detection observer design for a class of discrete-time Takagi–Sugeno fuzzy systems with finite-frequency specifications. A novel design method is presented based on finite-frequency H−/H∞ indices and peak-to-peak analysis. The finite-frequency H− and H∞ indices are utilized to characterize fault sensitivity and disturbance robustness, respectively. Peak-to-peak analysis is used to derive a dynamic threshold. To further reduce the conservatism caused by predefined parameters, an iterative algorithm is developed. Both theoretical proof and simulation results show that the performance of the proposed method is not worse than the existing works.

Stability Analysis and Stabilization of General Conformable Polynomial Fuzzy Models with Time Delay

This paper introduces a sum-of-squares (S-O-S) approach to Stability Analysis and Stabilization (SAS) of nonlinear dynamical systems described by General Conformable Polynomial Fuzzy (GCPF) models with a time delay. First, we present GCPF models, which are more general compared to the widely recognized Takagi–Sugeno Fuzzy (T-SF) models. Then, we establish SAS conditions for these models using a Lyapunov–Krasovskii functional and the S-O-S approach, making the SAS conditions in this work less conservative than the Linear Matrix Inequalities (LMI)-based approach to the T-SF models. In addition, the SAS conditions are found by satisfying S-O-S conditions dependent on membership functions that are reliant on the polynomial fitting approximation algorithm. These S-O-S conditions can be solved numerically using the recently developed SOSTOOLS. To demonstrate the effectiveness and practicality of our approach, two numerical examples are provided to demonstrate the effectiveness and practicality of our approach.

Takagi–Sugeno Fuzzy Parallel Distributed Compensation Control for Low-Frequency Oscillation Suppression in Wind Energy-Penetrated Power Systems

In this paper, a Takagi–Sugeno fuzzy parallel distributed compensation control (TS-PDCC) is proposed for low-frequency oscillation (LFO) suppression in wind energy-penetrated power systems. Firstly, the fuzzy C-mean algorithm (FCMA) is applied to cluster the daily average wind speed of the wind farm, and the obtained wind speed clustering center is used as the premise variable of TS-PDCC, which increases the freedom of parameter setting of the TS fuzzy model and is closer to the actual working environment. Secondly, based on the TS fuzzy model, the TS-PDCC is designed to adjust the active power output of the wind turbine for LFO suppression. To facilitate the computation of controller parameters, the stability conditions are transformed into a set of Linear Matrix Inequalities (LMIs) via the Schur complement. Subsequently, a Lyapunov function is designed to verify the stability of the wind energy-penetrated power system and obtain the parameter ranges. Simulation cases are conducted to verify the validity and superior performance of the proposed TS-PDCC under different operating conditions.

Intermittent dynamic event-triggered control for synchronization of Takagi–Sugeno fuzzy competitive neural networks with leakage delay and different time scales

Because competitive neural networks (CNNs) can simulate the phenomena of lateral inhibition among neurons, their dynamics are attracting increasing attention, which motives us to investigate the global exponential synchronization issue of multiple time-delays fuzzy CNNs (MDFCNNs) with different time scales in this article. Firstly, to solve the significant resource wastage problem caused by the time-triggered mechanism previously adopted in CNNs, a novel intermittent dynamic event-triggered mechanism is proposed. It is worth mentioning that the fuzzy logic systems are also utilized in this model and controller, effectively handling the uncertainties and nonlinearities in practical problems. Secondly, by designing the intermittent static/dynamic event-triggered mechanism, we derive the global exponential synchronization conditions for MDFCNNs with different time scales under a simpler and more implementable controller composed of a linear negative feedback control term. We also utilize the reduction to absurdity to demonstrate the nonexistence of Zeno behavior for the error system of master-slave CNNs. Furthermore, we provide several corollaries to further indicate the generality of the model and the cost savings of the control mechanism. Finally, we provide an example and some comparisons to demonstrate the efficiency of the derived theoretical findings.

On soft measurement modeling for predicting photovoltaic power with uncertainty based on the Takagi–Sugeno model

Abstract Accurate solar power forecast is becoming more essential for safe and reliable power grid operation with the increasing number of grid-connected photovoltaic (PV) power production units. However, PV power exhibits significant output fluctuation due to both external inputs and intrinsic stochasticity in system dynamics. Therefore, an efficient and reliable soft measurement model of PV power with uncertainty is demanded in practice applications. The technique described in this paper captures the impacts produced by the fundamental uncertainty observed in the data, instead of relying on unrealistic assumptions about uncertainty. A soft measurement model using the Takagi-Sugeno (TS) Fuzzy Logic System (FLS) based on several input-output time series of PV plants is presented in this study. Chebyshev's inequality from probability theory and statistics is adopted to create the confidence interval-based response envelopes for these time series at each moment. An envelope-based measure of output uncertainty and a center-valued response forecasting model can be obtained by the proposed identification technique. PV datasets are employed to demonstrate the concept, which indicates the proposed soft measurement may outperform existing methods in terms of prediction accuracy. The average values of Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and the Correlation Coefficient (R) are only 0.0787, 0.1113, and 0.9979. The average values of the prediction interval coverage probability (PICP) and the prediction interval normalized average width (PINAW) are 0.9806 and 0.1051.

Membership-Functions-Derivative-Dependent Stability Criteria for Delayed Takagi–Sugeno Fuzzy Systems

Membership-Functions-Derivative-Dependent Stability Criteria for Delayed Takagi–Sugeno Fuzzy Systems

Simplified LMI Conditions for Takagi-Sugeno Fuzzy Observer Design with Unmeasured Premise Variables

Simplified LMI Conditions for Takagi-Sugeno Fuzzy Observer Design with Unmeasured Premise Variables

Stabilization of Takagi–Sugeno fuzzy Hidden Markov Jump Systems with memory sampled-data control

The stability of Takagi–Sugeno fuzzy hidden Markovian jump systems by employing a memory sampled-data control (SDC) scheme that includes a constant signal transmission delay is investigated. The asynchronous situation between the system plant and the controller is represented using the hidden Markov model. The stability of the provided model is ensured by implication of the fuzzy time-scheduled Lyapunov functional (LF), and the sufficient conditions are derived in the form of linear matrix inequalities (LMIs). This simplifies the utilization and generalization of the analysis results, as they exhibit convexity in the subsystem matrix. Additionally, it diminishes the influence of external disturbances by employing the H∞ norm bound. To acquire the required time-dependent memory SDC, it is necessary to solve this set of LMIs. The efficacy and feasibility of the proposed method is established by attaining stability for a chaotic Lorenz system using the T–S fuzzy Hidden Markov Jump Systems with Memory SDC.

Internal Model Control Design for Nonlinear Systems Based on Inverse Dynamic Takagi–Sugeno Fuzzy Model

Internal Model Control Design for Nonlinear Systems Based on Inverse Dynamic Takagi–Sugeno Fuzzy Model

Adaptive fuzzy integrated LMS based control strategy for voltage power quality enhancement

In this paper, an adaptive Takagi Sugeno (TS) Fuzzy integrated Mixed Order Normalized Least Mean Square/Fourth Algorithm (MONLMS/F) is proposed for the unresolved voltage power quality issues in distribution system. The proposed control utilizes the cost function of mixed order of errors, which are based on second and fourth order and the feature of cost function overcomes the demerit of traditional basic least mean square method, which is based on second-order error. The implemented control technique has two main objectives. Firstly, the fundamental estimation of correct active and reactive signals from polluted grid voltage for computing the reference load voltages and second is the DC link voltage regulation. A correct weight estimation is achieved by Mixed Order Normalized Least Mean Square/Fourth Algorithm (MONLMS/F) and voltage regulation is performed by Takagi Sugeno Fuzzy (TSF) approach. The proposed integrated control enhances the capability of system against voltage deviation from the reference voltage and successfully eliminates the harmonics from polluted grid voltages. A bio-inspired optimizer like Spotted Hyena (SH) is integrated with TSF for self-tuning of the membership functions (MFs) and fuzzy rule to adapt the system variations and regulate fluctuations in the DC link for dynamic conditions. However, auto-tunned TS-Fuzzy have a fast transient response of DC and AC link voltage based on dynamic indicators like settling time (ts=0.12 s), undershoot (Us=3.4 %) and peak overshoot (Mp=5.6 %) are compared to classical PI controller. Nonetheless, the proposed TS-MONLMS/F control strategy outperforms the other classical control with low oscillations at any power quality scenario with improved dynamic response. The significant MATLAB simulation and experimental results are evaluated, and its performance is demonstrated with the dSPACE (DS1202) processor for experimental realization.

Fixed Time Synchronization of Stochastic Takagi–Sugeno Fuzzy Recurrent Neural Networks with Distributed Delay under Feedback and Adaptive Controls

In this paper, the stochastic Takagi–Sugeno fuzzy recurrent neural networks (STSFRNNS) with distributed delay is established based on the Takagi–Sugeno (TS) model and the fixed time synchronization problem is investigated. In order to synchronize the networks, we design two kinds of controllers: a feedback controller and an adaptive controller. Then, we obtain the synchronization criteria in a fixed time by combining the Lyapunov method and the related inequality theory of the stochastic differential equation and calculate the stabilization time for the STSFRNNS. In addition, to verify the authenticity of the theoretical results, we use MATLABR2023A to carry out numerical simulation.

Monotonic Fuzzy Systems With Goniometric Membership Functions

AbstractFuzzy logic-based systems are nowadays commonly used in nonlinear function approximation when incoming data are available. Their main advantage is that the resulting rules can be interpreted understandably. Nevertheless, when the data are noisy an overfitting may occur which leads to poor accuracy and generalization ability. Prior information about the nonlinear function may improve fuzzy system performance. In this paper the case when the function is monotonic with respect to some or all variables is considered. Sufficient conditions for the monotonicity of first-order Takagi–Sugeno fuzzy systems with raised cosine membership functions are derived. Performance of the proposed fuzzy system is tested on two benchmark datasets

A membership function-dependent L∞ performance based output interval estimation method for discrete-time Takagi–Sugeno fuzzy systems applied to fault detection

In the design process of traditional L∞ methods, a common performance index is often considered in different fuzzy rules. This may introduce a certain conservatism when most of the whole fuzzy system operates under a certain fuzzy rule or a few fuzzy rules. Therefore, this paper focuses on robust interval estimation problems for discrete-time Takagi–Sugeno fuzzy systems, and a new membership function-dependent L∞ performance index is proposed. The proposed L∞ performance can ensure better results in practical engineering applications by using the priori knowledge that the model works most of the time on some specific fuzzy systems to design performance index. By means of fuzzy basis-dependent Lyapunov functions, a membership function-dependent L∞ performance based interval estimation strategy applied to fault detection is presented. Through simulation analysis, the L∞ index in this paper is better than the conventional one and a tighter interval estimation is obtained leading to more accurate and faster fault detection effects. Meanwhile, the simulation results of this method also reflect the membership function-dependent property well.