Takagi-Sugeno Fuzzy Model Research Articles

Pantograph Catenary Contact Force Regulation Based on Modified Takagi-Sugeno Fuzzy Models

In this paper, a new contact force control technique, based on the modified Takagi-Sugeno model and the parallel distributed compensation concept is developed to suppress vibrations between the pantograph and the catenary by regulating the contact force to a reference value, thereby achieving stable current collection. The proposed method uses simple and standard PID and modified Takagi-Sugeno fuzzy controllers. The two controllers guarantee the designed system's robust stability. Furthermore, based on a simplified pantograph–catenary system model, the comparative simulation results show that variations of the contact force can be almost attenuated. As a result, the system stability is guaranteed, and the performance robustness is verified.

Iterative Nonlinear Fuzzy Modeling of Lithium-Ion Batteries

Electric vehicles (EVs), in their pure and hybrid variants, have become the main alternative to ensure the decarbonization of the current vehicle fleet. Due to its excellent performance, EV technology is closely linked to lithium-ion battery (LIB) technology. A LIB is a complex dynamic system with extraordinary nonlinear behavior defined by electrical, thermal and electrochemical dynamics. To ensure the proper management of a LIB in such demanding applications as EVs, it is crucial to have an accurate mathematical model that can adequately predict its dynamic behavior. Furthermore, this model must be able to iteratively adapt its parameters to accommodate system disturbances during its operation as well as performance loss in terms of efficiency and nominal capacity during its life cycle. To this end, a methodology that employs the extended Kalman filter to iteratively improve a fuzzy model applied to a real LIB is presented in this paper. This algorithm allows to improve the classical Takagi–Sugeno fuzzy model (TSFM) with each new set of data obtained, adapting the model to the variations of the battery characteristics throughout its operating cycle. Data for modeling and subsequent validation were collected during experimental tests on a real LIB under EVs driving cycle conditions according to the “worldwide harmonised light vehicle test procedure” (WLTP) standard. The TSFM results allow the creation of an accurate nonlinear dynamic model of the LIB, even under fluctuating operating conditions, demonstrating its suitability for modeling and design of model-based control systems for LIBs used in EVs applications.

Robust fault detection for delta operator switched fuzzy systems with bilateral packet losses

Considering packet losses, time-varying delay, and parameter uncertainty in the switched fuzzy system, this paper designs a robust fault detection filter at any switching rate and analyzes the H performance of the system. Firstly, the Takagi-Sugeno (T-S) fuzzy model is used to establish a global fuzzy model for the uncertain nonlinear time-delay switched system, and the packet loss process is modeled as a mathematical model satisfying Bernoulli distribution. Secondly, through the average dwell time method and multiple Lyapunov functions, the exponentially stable condition of the nonlinear network switched system is given. Finally, specific parameters of the robust fault detection filter can be obtained by solving linear matrix inequalities (LMIs). The effectiveness of the method is verified by simulation results.

Robust fault-tolerant tracking control for a class of T-S fuzzy systems subject to actuator failure and external disturbance

Based on the Takagi-Sugeno (T-S) fuzzy model approach, this study discusses the robust fault-tolerant tracking controller design for non-linear systems affected by external disturbances, uncertainties, and actuator failures. In contrast to existing results, this study assumes the actuator fault model includes linear and nonlinear terms, and a state feedback controller is designed to improve the tracking and stability of the system when actuators fail. Using a non-quadratic Lyapunov function, new sufficient conditions for L_2-gain tracking performance analysis are derived to determine simultaneously the minimal level of the L_2-gain and controller gains. The robustness of the proposed approach is also investigated. An illustration of the theoretical developments is provided by a Duffing forced oscillation system.

Neural-network based adaptive sliding mode control for Takagi-Sugeno fuzzy systems

In the present study, the adaptive sliding mode control (ASMC) strategy is investigated for a class of complex nonlinear systems with matched and unknown nonlinearities and external disturbances. The nonlinearities and external disturbances are approached by a Gaussian radial basic neural network. A Takagi-Sugeno (T-S) fuzzy model based integral switching function is introduced to solve the ASMC problem, which eliminates the constrain that input gains required to share a common matrix in all fuzzy rules. Then, the switching control term is represented as a proportional integral (PI) control format to reduce the chattering phenomenon. Based on the Lyapunov theory, a set of existence conditions of the sliding mode controller are given such that the stability of the control systems can be guaranteed. Finally, a experimental simulation is utilized to verify the effectiveness of the proposed sliding mode control (SMC) strategy.

Special issue on “Optimal design and operation of energy systems”

Special issue on “Optimal design and operation of energy systems”

Robust fuzzy stabilization control for the traction converters in high-speed train

High-speed railways have quickly gained popularity as an environmentally beneficial mode of transportation. In addition, converters and electric motors are becoming more widely used. However, power converters and motors can act as constant power loads when tightly controlled, making the source converters unstable. In this article, robust fuzzy control is proposed for stabilizing power electronic converters feeding a constant power load in a high-speed train. The negative incremental resistance characteristics of the trains are first investigated. Then, utilizing the Takagi–Sugeno fuzzy model and the parallel distributed compensation approach, a robust stabilizing controller is constructed to ensure asymptotic descent of the dynamic system state trajectories toward the equilibrium position. Moreover, using linear matrix inequalities, the intended control gain can be automatically computed. The critical adjustment time of the controller and total harmonic distortions of the line currents are selected to measure and compare the dynamic stability of the designed controller. The suggested technique not only maintains global stability in the face of considerable changes in the constant power loads, but it also offers a fast dynamic reaction time and precise tracking over a wide operating range. Finally, simulations and experiments are performed to validate the proposed approach.

Extended Dissipativity Analysis for Delayed Fuzzy Systems using Polynomial Based Integral Inequality

This study addresses the problem of extended dissipativity analysis for nonlinear time-delay systems represented by Takagi–Sugeno fuzzy model. Different from the existing schemes in the literature, this paper aims to solve the dissipativity problem by considering the H∞, L2 -L∞ and dissipative performance constraints in a unified framework. Additionally, to estimate the single integral terms in the derivative of the Lyapunov–Krasovskii functional, a polynomial-based integral inequality is used.The advantage of the proposed method is demonstrated numerically with the well-known benchmark of a truck-trailler model drawn from the literature.

Harmonic Disturbance Suppression for High-Performance Nonlinear Repetitive-Control Systems

This study focuses on the performance design issue of nonlinear repetitive control (RC) systems subject to harmonic disturbances. First, a Takagi-Sugeno fuzzy model is used to describe a nonlinear plant. Then, a repetitive controller featuring a harmonic disturbance period is integrated with an EID estimator to form an RC-EID structure. The structure has a learning feature that gradually reduces the harmonic disturbance estimation error by self-learning. The linear inequality matrices guarantee the stability of nonlinear RC systems. A case study with two permanent magnet synchronous motors shows that the presented RC-EID estimator enhances the harmonic disturbance-suppression performance while compensating for the phase lag caused by the conventional EID filter.

Vehicle Actuator Fault Detection With Finite-Frequency Specifications via Takagi-Sugeno Fuzzy Observers: Theory and Experiments

This article presents a new nonlinear observer-based method to detect the faults of both steering and torque actuators of autonomous ground vehicles. To this end, the nonlinear vehicle system is reformulated in a Takagi-Sugeno (TS) fuzzy model with both measured and unmeasured nonlinear consequents, called N-TS fuzzy model. Differently from the classical TS fuzzy technique with linear consequents, this N-TS fuzzy reformulation enables an effective use of differential mean value theorem to deal with unmeasured nonlinearities, which is known as a major challenge in TS fuzzy observer design. Moreover, the N-TS fuzzy form also allows reducing not only the design conservatism but also the numerical complexity of the design conditions as well as the observer structure, which is crucial for real-time vehicle application. To minimize the disturbance effect with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {H}_\infty$</tex-math></inline-formula> performance and maximize the fault sensibility with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {H}_-$</tex-math></inline-formula> performance, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information on the disturbance/fault frequency ranges is taken into account in the N-TS fuzzy observer design via the generalized Kalman–Yakubovich–Popov (KYP) lemma. Based on Lyapunov stability theory, the design of the proposed multiobjective <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {H}_-/\mathscr {H}_\infty$</tex-math></inline-formula> N-TS fuzzy fault detector is recast as an optimization problem with strict linear matrix inequality (LMI) constraints, which can be effectively solved with numerical solvers. Both numerical and experiments are performed under realistic driving conditions to demonstrate the theoretical and practical interests of the new finite-frequency fuzzy fault detection method.

Adaptive control of T-S fuzzy systems with Markov switching parameters through observer-based sliding mode approach

This paper addresses the problem of observer-based adaptive sliding mode control (SMC) for nonlinear Markov jump systems (MJSs), using a Takagi-Sugeno (T-S) fuzzy model with the premise variables of fuzzy rules depend on system state. Firstly, an integral sliding surface is designed based on fuzzy observer system; Secondly, sufficient conditions for stochastic stability and $ H_{\infty} $ perturbation attenuate level are provided for the obtained sliding mode dynamics and error systems using linear matrix inequality techniques. Furthermore, an adaptive SMC law is combined with the observed state variables to ensure finite time reachability of the sliding surface. Lastly, the theory is validated with simulations based on a practical example.

Filter design for continuous-discrete Takagi-Sugeno fuzzy system with finite frequency specifications

&lt;abstract&gt;&lt;p&gt;This paper was concerned with the problem of filter design for the continuous-discrete system in the Takagi-Sugeno (T-S) fuzzy model. In a known finite frequency (FF) domain, an FF $ H_\infty $ performance was defined for the nonlinear continuous-discrete system. With the designed filter, sufficient conditions were then established for the filtering error system to be asymptotically stable and having a prescribed FF $ H_\infty $ performance. After that, a systematic method for the filter design was proposed. Finally, an example was provided to check effectiveness of the derived results.&lt;/p&gt;&lt;/abstract&gt;

Stability and Stabilization of Polynomial Fuzzy-Model-Based Switched Nonlinear Systems Under MDADT Switching Signal

This article proposes a novel Lyapunov stability analysis for a class of switched nonlinear systems under the mode-dependent average dwell time (MDADT) switching signals. For the first time, a polynomial fuzzy model is used to describe the nonlinearity of the switched systems instead of a Takagi–Sugeno fuzzy model, which can represent a wider range of nonlinear plants. As existing advanced results are relatively conservative and lead to that tighter bounds on the dwell time are not easy to be obtained, therefore, the stability analysis for switched systems is still quite challenging. In this article, to tackle this problem, by developing a polynomial multiple Lyapunov function (MLF) approach and exploring the feature of the membership functions, relaxed stability conditions are derived for the switched polynomial fuzzy-model-based control systems. In particular, the polynomial MLF is guaranteed radially unbounded by a two-step procedure, making traditional quadratic MLF a specific case, thereby improved stability conditions can be established in the form of sum-of-squares. Moreover, the new algorithm for multivariate Chebyshev membership functions based on linear programming is proposed to introduce the information of membership functions and further relax the stability conditions to obtain tighter bounds on MDADT. Finally, a simulation example demonstrates the effectiveness of the developed techniques.

System decomposition-based stability criteria for Takagi-Sugeno fuzzy uncertain stochastic delayed neural networks in quaternion field

&lt;abstract&gt;&lt;p&gt;Stochastic disturbances often occur in real-world systems which can lead to undesirable system dynamics. Therefore, it is necessary to investigate stochastic disturbances in neural network modeling. As such, this paper examines the stability problem for Takagi-Sugeno fuzzy uncertain quaternion-valued stochastic neural networks. By applying Takagi-Sugeno fuzzy models and stochastic analysis, we first consider a general form of Takagi-Sugeno fuzzy uncertain quaternion-valued stochastic neural networks with time-varying delays. Then, by constructing suitable Lyapunov-Krasovskii functional, we present new delay-dependent robust and global asymptotic stability criteria for the considered networks. Furthermore, we present our results in terms of real-valued linear matrix inequalities that can be solved in MATLAB LMI toolbox. Finally, two numerical examples are presented with their simulations to demonstrate the validity of the theoretical analysis.&lt;/p&gt;&lt;/abstract&gt;

Direct quaternion method-based stability criteria for quaternion-valued Takagi-Sugeno fuzzy BAM delayed neural networks using quaternion-valued Wirtinger-based integral inequality

&lt;abstract&gt;&lt;p&gt;This paper investigates the global asymptotic stability problem for a class of quaternion-valued Takagi-Sugeno fuzzy BAM neural networks with time-varying delays. By applying Takagi-Sugeno fuzzy models, we first consider a general form of quaternion-valued Takagi-Sugeno fuzzy BAM neural networks with time-varying delays. Then, we apply the Cauchy-Schwarz algorithm and homeomorphism principle to obtain sufficient conditions for the existence and uniqueness of the equilibrium point. By utilizing suitable Lyapunov-Krasovskii functionals and newly developed quaternion-valued Wirtinger-based integral inequality, some sufficient criteria are obtained to guarantee the global asymptotic stability of the considered networks. Further, the results of this paper are presented in the form of quaternion-valued linear matrix inequalities, which can be solved using the MATLAB YALMIP toolbox. Two numerical examples are presented with their simulations to demonstrate the validity of the theoretical analysis.&lt;/p&gt;&lt;/abstract&gt;

Output Feedback Control of TS Fuzzy Systems with Unmeasured Nonlinearities via a Local Separation Principle

This paper presents a fuzzy observer-based control framework for TS fuzzy models with nonlinear consequents (N-TS). The N-TS fuzzy model is constructed such that only measured nonlinearities are considered to obtain the fuzzy membership functions, and all unmeasured nonlinearities are modeled as local consequent parts. Based on the differential mean value theorem, the closed-loop system is rewritten in an adequate format, which allows proving the separation principle for asymptotic TS fuzzy observer-based control design. Sufficient design conditions, expressed in terms of linear matrix inequalities, are derived via delayed nonquadratic Lyapunov functions for the synthesis of both stabilizing fuzzy controller and Luenberger-like fuzzy observer. Using Lyapunov-based arguments of a local separation principle, a constructive procedure is provided to maximize the closed-loop domain of attraction (DoA) estimation, which is guaranteed to be included inside the predefined fuzzy modeling region. Numerical examples are given to illustrate the effectiveness of the proposed approach.

Limiting State Estimation of Switched Interval Systems with Metzler-Takagi-Sugeno Models

The paper deals with interval observer design for fuzzy switched positive systems. The systems are represented by the Takagi-Sugeno fuzzy models, with premise variables depending on a measurable part of the state vector. Stability conditions for the proposed interval observer structure are formulated via linear matrix inequalities to ensure nonnegative system state estimation. The proposed method allows to compute the lower and upper bounds of the system state under the assumption that the system disturbance are bounded. The properties of proposed approach are illustrated in numerical example.

A Study on Dynamic Motion Planning for Autonomous Vehicles Based on Nonlinear Vehicle Model

Autonomous driving technology, especially motion planning and the trajectory tracking method, is the foundation of an intelligent interconnected vehicle, which needs to be improved urgently. Currently, research on path planning methods has improved, but few of the current studies consider the vehicle's nonlinear characteristics in the reference model, due to the heavy computational effort. At present, most of the algorithms are designed by a linear vehicle model in order to achieve the real-time performance at the cost of lost accuracy. To achieve a better performance, the dynamics and kinematics characteristics of the vehicle must be simulated, and real-time computing ensured at the same time. In this article, a Takagi-Sugeno fuzzy-model-based closed-loop rapidly exploring random tree algorithm with on-line re-planning process is applied to build the motion planner, which effectively improves the vehicle performance of dynamic obstacle avoidance, and plans the local obstacle avoidance path in line with the dynamic characteristics of the vehicle. A nonlinear vehicle model is integrated into the motion planner design directly. For fast local path planning mission, the Takagi-Sugeno fuzzy modelling method is applied to the modeling process in the planner design, so that the vehicle state can be directly utilized into the path planner to create a feasible path in real-time. The performance of the planner was evaluated by numerical simulation. The results demonstrate that the proposed motion planner can effectively generate a reference trajectory that guarantees driving efficiency with a lower re-planning rate.

Model predictive control for Takagi–Sugeno fuzzy model-based Spacecraft combined energy and attitude control system

A Combined Energy and Attitude Control System (CEACS) is a dual system in which flywheels are used as energy storage and attitude control devices. This work is a progress on CEACS for small satellites to improve the attitude accuracy. In this maiden work, the Fuzzy–MPC controller is introduced to regulate the CEACS attitude with both linear and nonlinear initial angles, and in the presence of actuator constraints. The nonlinear attitude model is transformed into a set of linear subsystems using the Takagi–Sugeno fuzzy modeling approach. The subsystem is designed with a MPC controller and a total control action is summed up using the parallel distributed compensation approach. The numerical results have been analyzed in terms of attitude pointing accuracies, actuator constraints, and energy consumed by the actuators. A performance comparison between the Fuzzy–MPC and Fuzzy–LQR controllers has also been done. The results validate that the Fuzzy-MPC controller achieves the desired CEACS attitude pointing accuracy of 0.0010° with a zero steady-state error and keeps the control torques within the actuator constraints. On the other hand, the Fuzzy–LQR controller gives some measurable steady-state error and achieves the CEACS attitude pointing accuracy of 0.0012°. Therefore, the Fuzzy–MPC based CEACS architecture not only achieves the desired pointing accuracies but also produces ten times smaller control torques than the Fuzzy–LQR controller, which result in a lower onboard power consumption.

Intelligent power control of wind conversion system based on Takagi–Sugeno fuzzy model

SummaryThis paper comes up with a novel fuzzy control design for a wind conversion system (WCS). To do this, a boost converter is employed to adjust the rectified voltage under different wind speed levels. Initially, the boost converter model is well presented via the Takagi–Sugeno approach. Then, a T‐S fuzzy controller is designed to promptly calculate the duty cycle required for an optimal power operation. Afterward, the optimal DC current is determined and then transferred to the reference model to instantly determine the desired trajectories. These latter should be preserved so as to reach the maximum power. Following that, linear matrix inequalities (LMIs) are also used to guarantee the stability analyses and the performance. Finally, the sound performance and the validity of the suggested control schema are both proved by a numerical and some experimental results.