Takagi-Sugeno Model Research Articles

Multi-objective H2/H∞ saturated non-PDC static output feedback control for path tracking of autonomous vehicle

This paper presents a new fuzzy output feedback control design for autonomous vehicle steering under actuator saturation, unavailability of the sideslip angle measurement, unknown road curvature, and lateral wind force. To take into account the actuator constraint, the saturation effect is transformed into dead-zone nonlinearity. A static output controller based on non-compensation parallel distributed technic and a Takagi-Sugeno (T-S) model of vehicle lateral dynamics is proposed to consider the unavailability of some vehicle states. To avoid the problem of imposing bounds on membership functions time derivatives resulting from the use of the fuzzy Lyapunov approach, a proper integral structure based on the non-quadratic Lyapunov approach is investigated. The mixed [Formula: see text] stabilization conditions of the augmented closed-loop system are expressed in terms of linear matrix inequalities (LMIs). Finally, the robustness and the advantages of the proposed approaches are demonstrated through different tests.

A Takagi-Sugeno model approach for robust fuzzy control design for trajectory tracking of non-linear systems

This article investigates the robust fuzzy tracking control design for a class of uncertain nonlinear systems using the Takagi–Sugeno (TS) fuzzy models. The main purpose of this study is to design state feedback and observer-based controllers such that the closed-loop system is asymptotically stable. Based on the Lyapunov theory, sufficient conditions are derived such that the closed-loop system is robustly stable. The linear matrix inequality LMI approach is used to obtain the state-feedback and observer gains. The effectiveness of the proposed design approach is provided via numerical simulations for a pendulum system.

Incremental state model in predictive control: A new fuzzy control proposal for nonlinear systems

In this work, a fuzzy predictive optimal control for multivariable nonlinear systems with pure time delays is presented. Therefore, dynamic local linear state models are used at each point of the state space obtained by fuzzy Takagi-Sugeno (T-S) modelling. The modelling error is considered as white noise, and the state is observed using the Kalman Filter (KF). This method does not take into account possible input constraints. Therefore, it applies to systems where there are no saturation problems. In this work, a new approach in the Model Predictive Control (MPC) method is proposed by calculating the control signal increment as a function of the error between a reference state vector and the prediction at N-steps of the state vector instead of using the traditional MPC approach which is based on calculating the error between a reference and the predicted output. The proposed method has a satisfactory tracking performance. The main feature of the proposed method is that it attains computational savings compared to other methods that have used incremental state models, which making it more appropriate for real-time applications.

Adaptive sliding mode control with fuzzy adjustment of switching term based on the Takagi-Sugeno model for horizontal vibration of the high-speed elevator cabin system

In purpose of reducing the severe horizontal vibration of the high-speed elevator car system which is caused by the excitation of the guide rail, an adaptive sliding mode controller with fuzzy switching gain (FGASMC) is designed in this paper. At first, a 4-DOF active control dynamics model of the horizontal vibration of the elevator car is designed, on which the actuators are symmetrically distributed around the cabin center, and the accuracy of which is demonstrated by experiments. Considering the uncertainty caused by the load conditions, structural mass of the elevator, and the output gain of actuators, a Takagi-Sugeno (TS) model for controlling horizontal vibration of the car system is derived based on the designed 4-DOF dynamics model. Then, based on the TS model mentioned above, an adaptive sliding mode controller (ASMC) for suppressing the horizontal vibration of the car system is designed by a quadratic index method. To ensure the reachability of the sliding mode and keep the chattering smaller, the fuzzy method is utilized to adjust the switching gain of the ASMC. For that, an FGASMC is proposed. Finally, the effectiveness of the proposed controller is verified by MATLAB simulation. The results illustrate that the designed FGASMC can effectively suppress horizontal vibration of the high-speed elevator car system, and the control effect of which is obviously superior than the linear quadratic regulator optimized by genetic algorithm, which provides a new idea for active vibration reduction of high-speed elevator car.

Path tracking control for autonomous vehicles with saturated input: A fuzzy fixed‐time learning control approach

This paper presents a fuzzy fixed-time learning path tracking control strategy for autonomous vehicles with saturated input and uncertainties. First, Takagi-Sugeno (T-S) model is designed to realize an accurate description of the nonlinear path tracking systems. The T-S model is the weighted sum of a series of linear dynamics models. The weighting coefficients are described by fuzzy membership functions. Then, with the consideration of the saturated input, a fixed-time learning control is proposed. It contains a learning law to estimate the uncertainties of the system on-line. The fixed-time convergence and the robustness properties are analyzed through Lyapunov stability theory. Finally, the effectiveness of the proposed control method has been verified through the CarSim/Simulink co-simulations under different driving conditions. The results demonstrate that the developed controller significantly improves the performance of path tracking and follows the desired path well even in the case of parameter uncertainties and external disturbances.

Regional T-S Model-based Attitude Tracking Control of a Quadrotor with Input Saturation and External Disturbances

This paper presents a model reference attitude tracking controller design for a quadrotor unmanned aerial vehicle subject to saturated actuators and external disturbances. The dynamical nonlinear model of the quadrotor's attitude is represented by an uncertain-like Takagi-Sugeno model, with exact matching on a compact subset of the state space. The generalized sector condition is employed to deal with the saturated inputs of the quadrotor. LMI conditions are derived for the design of the proposed tracking controller from a quadratic Lyapunov function, together with a performance index used to minimize the L2-norm transfer between the disturbances and the state tracking errors. Because of the input saturation and the validity domain of the Takagi-Sugeno model, the obtained results only hold regionally and an optimization procedure to estimate the closed-loop tracking domain of attraction is proposed. Simulation results are provided to illustrate the effectiveness of the proposed design methodology.

Simulation and Experimental Validation for Takagi-Sugeno Fuzzy-Based Li-ion Battery Model

Simulation and Experimental Validation for Takagi-Sugeno Fuzzy-Based Li-ion Battery Model

Identification and control of a heat flow system based on the Takagi-Sugeno fuzzy model using the grey wolf optimization algorithm

Even though, it is mostly used by process control engineers, the temperature control remains an important task for researchers. This paper addressed two separate issues concerning model optimization and control. Firstly, the linear models for the three different operating points of the heat flow system were found. From these identified models a Takagi-Sugeno model is obtained using fixed membership functions in the premises of the rules. According to the chosen objective function, parameters in the premise part of Takagi-Sugeno fuzzy model were optimized using the grey wolf algorithm. Furthermore, by using the parallel distributed compensation a fuzzy controller is developed via the fuzzy blending of three proportional + sum controllers designed for each of the operating points. In order to evaluate performance, a comparison is made between the fuzzy controller and local linear controllers. Moreover, the fuzzy controllers from the optimized and initial Takagi-Sugeno plant models are compared. The experimental results on a heat flow platform are presented to validate efficiency of the proposed method.

Model-based wind turbine control design with power tracking capability: A wind-tunnel validation

Owing to the aerodynamic conversion process, wind turbines exhibit a nonlinear behavior and encounter turbulent operating conditions that demand well-defined closed-loop dynamics to withstand accumulated loading over the lifetime. Wind excitation is the main disturbance and driving force for the system and determines the necessary operating strategy, but it usually represents an unmeasurable quantity. In this study, we used a linear-matrix-inequalities-based control and observer design to operate a variable-speed, variable-pitch wind turbine in a wind tunnel experiment at different reproducible inflow conditions while relying on a wind speed estimate obtained from a disturbance observer. The computational complexity of the stability framework incorporating the reconstruction of the unknown wind speed is reduced by exploiting characteristics of the modeling approach based on a convex combination of linear submodels. The assumption used in the proposed stability consideration is evaluated based on measurement data. We introduced an extended operating range compared to the commonly considered operating trajectory of wind turbines in the control design. A controller based on Takagi–Sugeno modeling is used to operate the turbine at challenging power tracking requirements demonstrating the capability to support fast stabilization of the electrical grid while discussing the loading and operational constraints observed during the experiments.

Takagi‐Sugeno exact model and linear matrix inequalities for an active power filter control

In order to take advantage of the capabilities of a shunt active power filter (SAPF), the design of an adequate control scheme must be developed; generally, the SAPF control scheme corresponds to a cascade control composed of an inner loop and an outer loop. This article approaches the design of an inner loop control based on linear matrix inequalities (LMIs) for a SAPF with LCL coupling filter. The control design begins with the system rewriting in exact Takagi-Sugeno (TS) models, in the sequel, through the use of a quadratic energy function, and considering the closed-loop system, the Lyapunov direct method to establish LMI conditions is used. This proposal of inner loop control is called TSLMI, and in conjunction with a PI control, a PI-TSLMI cascade control scheme is configured. The SAPF objectives are the reduction of the total harmonic distortion (THD) in the mains current, the power factor (PF) correction, and facing load changes. The results show a correct performance of the proposed PI-TSLMI for both simulation and experimental tests.

Robust static output-feedback vaccination policy design for an uncertain SIR epidemic model with disturbances: Positive Takagi–Sugeno model approach

An analytic vaccination policy is established for a nonlinear susceptible–infected–recovered (SIR) epidemic model involving uncertainties and disturbances by using only the inaccurate information of the infected through the positive Takagi–Sugeno (T–S) fuzzy approach. The SIR model is exactly represented as the fuzzy model in the T–S form. Two conditions for fuzzy static output-feedback controllers are formulated using the symmetric and diagonal Lyapunov matrices. These controllers exhibit L∞–L∞ disturbance attenuation performance, are robust against norm-bounded parametric uncertainties, and preserve closed-loop positivity. The case study for the positive stabilization of the uncertain nonlinear SIR model demonstrates the effectiveness of the proposed methodology.

Monotonic Takagi–Sugeno models with cubic spline membership functions

In the paper we present sufficient monotonicity conditions for zero order Takagi–Sugeno fuzzy systems with cubic spline membership functions. Those fuzzy models have some advantages comparing with commonly used membership functions. In contrast to triangular membership functions the corresponding mapping is smooth. Comparing to Gaussian membership functions the monotonicity conditions are less conservative, more intuitive and admit membership functions with different width. Finally, the derived monotonicity conditions are formulated as linear constraints on the parameters of fuzzy system that can be easily incorporated into related optimization problems solvable by efficient algorithms. Performance of the proposed fuzzy system is tested on two benchmark datasets and output prediction of a nonlinear dynamical system.

Evaluation of methods for feasible parameter set estimation of Takagi-Sugeno models for nonlinear regression with bounded errors

Abstract 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.

Stability Analysis and Robust Stabilization of Uncertain Fuzzy Time-Delay Systems

New sufficient conditions for delay-independent and delay-dependent robust stability of uncertain fuzzy time-delay systems based on uncertain fuzzy Takagi-Sugeno (T-S) models are presented by using the properties of matrix and norm measurements. Further sufficient conditions are formulated, in terms of the linear matrix inequalities (LMIs) of robust stabilization, and are developed via the technique of parallel distributed compensation (PDC), and then the simplification of the conditions for the controller design of uncertain fuzzy time-delay systems. The proposed methods are simple and effective. Some examples below are presented to illustrate our results.

Finite-time impulsive observers for nonlinear systems represented by Takagi–Sugeno models: Application to a chaotic system

In this paper, observer design for nonlinear systems represented by Takagi Sugeno models (T-S) is investigated. The first main contribution concerns the finite time convergence of the estimations, ensured by an impulsive observer with state updates. The second contribution, lies with taking into account unmeasurable parameters, using the Differential Mean Value Theorem (DMVT) to express the disturbed error dynamics into a Linear Parameter Varying system. The stability conditions are formulated in terms of Linear Matrix Inequalities (LMI). To prove the efficiency of the proposed procedure, applications are performed on a chaotic system. The obtained results are pretty satisfying.

A new imputation-based incomplete data-driven fuzzy modeling for accuracy improvement in ubiquitous computing applications

Purpose In real-world decision-making, high accuracy data analysis is essential in a ubiquitous environment. However, we encounter missing data while collecting user-related data information because of various privacy concerns on account of a user. This paper aims to deal with incomplete data for fuzzy model identification, a new method of parameter estimation of a Takagi–Sugeno model in the presence of missing features. Design/methodology/approach In this work, authors proposed a three-fold approach for fuzzy model identification in which imputation-based linear interpolation technique is used to estimate missing features of the data, and then fuzzy c-means clustering is used for determining optimal number of rules and for the determination of parameters of membership functions of the fuzzy model. Finally, the optimization of the all antecedent and consequent parameters along with the width of the antecedent (Gaussian) membership function is done by gradient descent algorithm based on the minimization of root mean square error. Findings The proposed method is tested on two well-known simulation examples as well as on a real data set, and the performance is compared with some traditional methods. The result analysis and statistical analysis show that the proposed model has achieved a considerable improvement in accuracy in the presence of varying degree of data incompleteness. Originality/value The proposed method works well for fuzzy model identification method, a new method of parameter estimation of a Takagi–Sugeno model in the presence of missing features with varying degree of missing data as compared to some well-known methods.

An Investigation of Takagi-Sugeno Fuzzy Modeling for Spatial Prediction with Sparsely Distributed Geospatial Data

Fuzzy set theory has shown potential for reducing uncertainty as a result of data sparsity and also provides advantages for quantifying gradational changes like those of pollutant concentrations through fuzzy clustering based approaches. The ability to lower the sampling frequency and perform laboratory analyses on fewer samples, yet still produce an adequate pollutant distribution map, would reduce the initial cost of new remediation projects. To assess the ability of fuzzy modeling to make spatial predictions using fewer sample points, its predictive ability was compared with the ordinary kriging (OK) and inverse distance weighting (IDW) methods under increasingly sparse data conditions. This research used a Takagi–Sugeno (TS) fuzzy modelling approach with fuzzy c-means (FCM) clustering to make spatial predictions of the lead concentrations in soil. The performance of the TS model was very dependent on the number of outliers in the respective validation set. For modeling under sparse data conditions, the TS fuzzy modeling approach using FCM clustering and constant width Gaussian shaped membership functions did not show any advantages over IDW and OK for the type of data tested. Therefore, it was not possible to speculate on a possible reduction in sampling frequency for delineating the extent of contamination for new remediation projects.

Finite-Time Fuzzy Sliding Mode Control for Nonlinear Descriptor Systems

This article addresses the finite-time boundedness (FTB) problem for nonlinear descriptor systems. Firstly, the nonlinear descriptor system is represented by the Takagi-Sugeno (T-S) model, where fuzzy representation is assumed to be appearing not only in both the state and input matrices but also in the derivative matrix. By using a descriptor redundancy approach, the fuzzy representation in the derivative matrix is reformulated into a linear one. Then, we introduce a fuzzy sliding mode control (FSMC) law, which ensures the finite-time boundedness (FTB) of closed-loop fuzzy control systems over the reaching phase and sliding motion phase. Moreover, by further employing the descriptor redundancy representation, the sufficient condition for designing FSMC law, which ensures the FTB of the closed-loop control systems over the entire finite-time interval, is derived in terms of linear matrix inequalities (LMIs). Finally, a simulation study with control of a photovoltaic (PV) nonlinear system is given to show the effectiveness of the proposed method.

Forecasting Models of Daily Energy Generation by PV Panels Using Fuzzy Logic

This paper contains studies of daily energy production forecasting methods for photovoltaic solar panels (PV panel) by using mathematical methods and fuzzy logic models. Mathematical models are based on analytic equations that bind PV panel power with temperature and solar radiation. In models based on fuzzy logic, we use Adaptive-network-based Fuzzy Inference Systems (ANFIS) and the zero-order Takagi-Sugeno model (TS) with specially selected linear and non-linear membership functions. The use of mentioned membership functions causes that the TS system is equivalent to a polynomial and its properties can be compared to other analytical models of PV panels found in the literature. The developed models are based on data from a real system. The accuracy of developed prognostic models is compared, and a prototype software implementing the best-performing models is presented. The software is written for a generic programmable logic controller (PLC) compliant to the IEC 61131-3 standard.

Robust $$H_{\infty }$$ adaptive output feedback sliding mode control for interval type-2 fuzzy fractional-order systems with actuator faults

This paper addresses the $$H_{\infty }$$ adaptive output feedback sliding mode fault-tolerant control problem for uncertain nonlinear fractional-order $$\hbox {systems}$$ (FOSs) with $$0<\alpha <1$$ . The interval type-2 Takagi–Sugeno model is employed to represent the FOSs. Adaptive laws are designed to estimate the upper bounds of the nonlinear terms and mismatched disturbances. A reduced dimension sliding surface is constructed based on system output. A sufficient condition is established in terms of linear matrix inequalities to guarantee the stability of the sliding mode. Then, a control scheme based on fractional-order reaching law is proposed to make the resulting control system reach the sliding mode surface in a finite time. The effectiveness of proposed methods is illustrated by a numerical simulation example.