Impulsive control for a Takagi-Sugeno fuzzy model with time-delay and its application to chaotic systems

A control approach where the fuzzy logic methodology is combined with impulsive control is developed for controlling some time-delay chaotic systems in this paper. We first introduce impulses into each subsystem with delay of the Takagi-Sugeno （TS） fuzzy IF-THEN rules and then present a unified TS impulsive fuzzy model with delay for chaos control. Based on the new model, a simple and unified set of conditions for controlling chaotic systems is derived by the Lyapunov Razumikhin method, and a design procedure for estimating bounds on control matrices is also given. Several numerical examples are presented to illustrate the effectiveness of this method.

Exponential stability of Takagi-Sugeno fuzzy systems with impulsive effects and small delays

This paper deals with the exponential stability of impulsive Takagi-Sugeno fuzzy systems with delay. Impulsive control and delayed fuzzy control are applied to the system, and the criterion on exponential stability expressed in terms of linear matrix inequalities （LMIs） is presented.

基于TS模糊神经网络的Fuzzy规则自动获取研究

Fuzzy规则的获取一直是模糊智能系统的一个瓶颈 .本文在深入研究 TS模糊神经网络的物理意义的基础上 ,给出了使用遗传算法优化模糊规则集的算法并提出了从训练后的 TS模糊神经网络中抽取 Fuzzy规则的可操作方法 .分析和实验证明 ,这种方法可以实现且是有效的 ,对于 Fuzzy规则自动获取的研究具有积极的借鉴意义 .

基于改进TS模糊的直流电弧炉闪变抑制优化

为提高静止无功补偿器(static var compensator,SVC)应对直流电弧炉等冲击性负载的闪变抑制性能,文中在改进Takagi-Sugeno(TS)模糊算法的基础上,提出一种SVC滚动预测控制方法。首先,建立直流电弧炉电气模型并仿真分析其无功特性;然后,针对经典TS模糊预测算法应用于波动负荷时出现的输出异常置0情况,提出一种范围自适应修正的改进方法,该方法能消除一类算法应用机理导致的异常值,从而提高TS模糊算法对波动负荷无功功率预测的可靠性和准确性;最后,基于模型训练时间约束,建立无功功率半周期滚动预测控制模型,提前10 ms预测无功功率,改善了SVC传统控制系统响应的滞后特性。仿真结果表明,相比于SVC传统控制方法,所提方法的平均闪变改善率提高了54.17%,验证了所提方法对闪变现象的抑制效果提升显著。

Stabilization design for continuous-time Takagi-Sugeno fuzzy systems based on new relaxed conditions

This paper deals with the problem of stabilization design for a class of continuous-time Takagi-Sugeno（T-S）fuzzy systems.New stabilization conditions are derived based on a relaxed approach in which both fuzzy Lyapunov functions and staircase membership functions are used.Through the staircase membership functions approximating the continuous membership functions of the given fuzzy model,the information of the membership functions can be brought into the stabilization design of the fuzzy systems,thereby significantly reducing the conservativeness in the existing stabilization conditions of the T-S fuzzy systems.Unlike some previous fuzzy Lyapunov function approaches reported in the literature,the proposed stabilization conditions do not depend on the time-derivative of the membership functions that may be the main source of conservatism when considering fuzzy Lyapunov functions analysis.Moreover,conditions for the solvability of the controller design are written in the form of linear matrix inequalities,but not bilinear matrix inequalities,which are easier to be solved by convex optimization techniques.A simulation example is given to demonstrate the validity of the proposed approach.

Hybrid TS fuzzy modelling and simulation for chaotic Lorenz system

The projection of the chaotic attractor observed from the Lorenz system in the X-Z plane is like a butterfly, hence the classical Lorenz system is widely known as the butterfly attractor, and has served as a prototype model for studying chaotic behaviour since it was coined. In this work we take one step further to investigate some fundamental dynamic behaviours of a novel hybrid Takagi-Sugeno （TS） fuzzy Lorenz-type system, which is essentially derived from the delta-operator-based TS fuzzy modelling for complex nonlinear systems, and contains the original Lorenz system of continuous-time TS fuzzy form as a special case. By simply and appropriately tuning the additional parametric perturbations in the two-rule hybrid TS fuzzy Lorenz-type system, complex （two-wing） butterfly attractors observed from this system in the three dimensional （3D） X-Y-Z space are created, which have not yet been reported in the literature, and the forming mechanism of the compound structures have been numerically investigated.

Controlling chaos using Takagi-Sugeno fuzzy model and adaptive adjustment

In this paper, an approach to the control of continuous-time chaotic systems is proposed using the Takagi-Sugeno （TS） fuzzy model and adaptive adjustment. Sufficient conditions are derived to guarantee chaos control from Lyapunov stability theory. The proposed approach offers a systematic design procedure for stabilizing a large class of chaotic systems in the literature about chaos research. The simulation results on Rossler＇s system verify the effectiveness of the proposed methods.

New sufficient conditions for general linear SISO Takagi-Sugeno fuzzy systems as universal approximators

By the best approximation theory, it is first proved that the SISO （single-input single-output） linear Takagi-Sugeno （TS） fuzzy systems can approximate an arbitrary polynomial which, according to Weierstrass approximation theorem, can uniformly approximate any continuous functions on the compact domain. Then new sufficient conditions for general linear SISO TS fuzzy systems as universal approximators are obtained. Formulae are derived to calculate the number of input fuzzy sets to satisfy the given approximation accuracy. Then the presented result is compared with the existing literature＇s results. The comparison shows that the presented result needs less input fuzzy sets, which can simplify the design of the fuzzy system, and examples are given to show its effectiveness.

Adaptive predictive functional control based on Takagi-Sugeno model and its application to pH process

In order to obtain accurate prediction model and compensate for the influence of model mismatch on the control performance of the system and avoid solving nonlinear programming problem,an adaptive fuzzy predictive functional control(AFPFC) scheme for multivariable nonlinear systems was proposed.Firstly,multivariable nonlinear systems were described based on Takagi-Sugeno(T-S) fuzzy models;assuming that the antecedent parameters of T-S models were kept,the consequent parameters were identified on-line by using the weighted recursive least square(WRLS) method.Secondly,the identified T-S models were linearized to be time-varying state space model at each sampling instant.Finally,by using linear predictive control technique the analysis solution of the optimal control law of AFPFC was established.The application results for pH neutralization process show that the absolute error between the identified T-S model output and the process output is smaller than 0.015;the tracking ability of the proposed AFPFC is superior to that of non-AFPFC(NAFPFC) for pH process without disturbances,the overshoot of the effluent pH value of AFPFC with disturbances is decreased by 50% compared with that of NAFPFC;when the process parameters of AFPFC vary with time the integrated absolute error(IAE) performance index still retains to be less than 200 compared with that of NAFPFC.

Robust stability analysis of Takagi-Sugeno uncertain stochastic fuzzy recurrent neural networks with mixed time-varying delays

In this paper, the global stability of Takagi-Sugeno （TS） uncertain stochastic fuzzy recurrent neural networks with discrete and distributed time-varying delays （TSUSFRNNs） is considered. A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSUSFRNNs. The proposed stability conditions are demonstrated through numerical examples. Furthermore, the supplementary requirement that the time derivative of time-varying delays must be smaller than one is removed. Comparison results are demonstrated to show that the proposed method is more able to guarantee the widest stability region than the other methods available in the existing literature.

Robust stabilization of state delayed discrete-time Takagi-Sugeno fuzzy systems with input saturation via an anti-windup fuzzy design

We consider the robust stabilization problem for discrete-time Takagi-Sugeno （T S） fuzzy systems with time- varied delays subjected to input saturation. We design static and dynamic anti-windup fuzzy controllers to ensure the convergence of all admissible initial states within the domain of attraction. Based on the project lemma and classical sector conditions, the conditions for the existence of solutions to this problem are obtained and expressed in terms of a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design approach.

Analytical Structures of Typical Takagi-Sugeno Fuzzy PID Gain Scheduling Controllers

The analytical structure of a class of typical Takagi Sugeno (TS) fuzzy controllers is revealed in this paper.The TS fuzzy controllers consist of three or more trapezoidal input fuzzy sets, Zadeh fuzzy logic AND operator,fuzzy rules with linear consequent, and the centriod defuzzifier. The TS fuzzy controllers are proved to be accurately nonlinear PID controllers with gains continuously changing with process output. The analytical expressions of the variable gains of the TS fuzzy controllers are derived and their mathematical characteristics including the bounds and geometrical shape of the gain variation are analyzed. The resulting explicit structures show that the TS fuzzy controllers are inherently nonlinear PID gain scheduling controllers with variable gains in different regions of input space.

New Approach of Stability for Time-Delay Takagi-Sugeno Fuzzy System Based on Fuzzy Weighting-Dependent Lyapunov Functionals

This paper deals with the stability of Takagi-Sugeno fuzzy models with time delay. Using fuzzy weighting- dependent Lyapunov-Krasovskii functionals, new sufficient stability criteria are established in terms of Linear Matrix Inequality;hence the stability bound of upper bound delay time can be easily estimated. Finally, numeric simulations are given to validate the developed approach.

Robust fuzzy control of Takagi-Sugeno fuzzy neural networks with discontinuous activation functions and time delays

The problem of global robust asymptotical stability for a class of Takagi-Sugeno fuzzy neural networks（TSFNN） with discontinuous activation functions and time delays is investigated by using Lyapunov stability theory.Based on linear matrix inequalities（LMIs）,we originally propose robust fuzzy control to guarantee the global robust asymptotical stability of TSFNNs.Compared with the existing literature,this paper removes the assumptions on the neuron activations such as Lipschitz conditions,bounded,monotonic increasing property or the right-limit value is bigger than the left one at the discontinuous point.Thus,the results are more general and wider.Finally,two numerical examples are given to show the effectiveness of the proposed stability results.

Takagi-Sugeno Fuzzy Regulator Design for Nonlinear and Unstable Systems Using Negative Absolute Eigenvalue Approach

This paper introduces a Takagi-Sugeno(T-S)fuzzy regulator design using the negative absolute eigenvalue(NAE)approach for a class of nonlinear and unstable systems.The open-loop system is initially embodied by the traditional T-S fuzzy model and then,all closed-loop subsystems are combined using the proposed Max-Min operator in place of traditional weighted average operator from the controller side to lessen the coupling virtually and simplify the proposed regulator design.For each virtually decoupled closed-loop subsystem,the composite regulators(i.e.,primary and secondary regulators)are designed by the NAE approach based on the enhanced eigenvalue analysis.The Lyapunov function is utilized to guarantee the asymptotic stability of the overall T-S fuzzy control system.The most popular and widely used nonlinear and unstable systems like the electromagnetic levitation system(EMLS)and the inverted cart pendulum(ICP)are simulated for the wide range of the initial conditions and the enormous variation in the disturbance.The transient and steady-state performance of the considered systems using the proposed design are analyzed in terms of the decay rate,settling time and integral errors as IAE,ISE,ITAE,and ITSE to validate the effectiveness of the proposed approach compared to the most popular and traditional parallel distributed compensation(PDC)approach.

Inverse Model Control for a Quad-rotor Aircraft Using TS-fuzzy Support Vector Regression

An inverse model control based on TS-fuzzy support vector regression( TS-fuzzy SVR) for a quadrotor aircraft is developed. The TS-kernel is the product of linear combination of input and a cluster of output corresponding to a cluster of TS-type fuzzy rules. The output of TS-fuzzy SVR is a linear weighted sum of the TSkernels. The dynamical model of the quad-rotor aircraft is derived. A new control scheme combined with TSfuzzy SVR inverse model control and PID control is presented so that the TS-fuzzy SVR inverse model control enhances capabilities of disturbance rejection and the robustness while the PID control enhances fast responsiveness and reliability of the system. Simulation results show the capabilities of the developed control for the attitude system of quad-rotor aircraft.

基于TS模糊控制的双馈风力发电机低电压穿越技术研究

建立了变速恒频双馈感应风力发电机数学模型。为提高双馈感应发电机(Double Fed Induction Geneator,DFIG)机组的低电压穿越(LVRT)能力,设计了TakagiSugeno(TS)模糊PI控制器。以某风电场为对象建立了DFIG多机互联仿真模型。仿真结果表明,相比传统PI控制器,TS模糊PI控制器可以有效抑制电网故障时DFIG有功功率和变流器直流母线电压震荡,从而提高系统的低电压穿越能力。

基于TS模型的分数阶混沌系统同步

提出一种基于TS模糊模型的分数阶混沌系统的同步算法.利用TS模型将分数阶混沌系统模糊化,设计并行分布式补偿模糊控制器,以线性矩阵不等式的形式给出分数阶混沌系统同步的充分条件,将模糊控制器的设计问题转化为求解线性矩阵不等式问题,并通过Matlab数值仿真验证了该方法的可行性和有效性.

基于鲁棒模糊C-均值回归的TS建模方法及其在热工过程中的应用

热工过程往往具有强耦合、大惯性和非线性等特点,且在运行过程中易受到诸种不确定性因素的干扰,导致常规建模方法难以获得令人满意的效果。针对非线性热工对象特性建模问题,文中改进了模糊C均值回归算法（FCR）的误差函数,提出一种鲁棒模糊C均值回归算法（RFCR）,并将其用于热工对象的TS建模前件辨识过程中。一方面,相比于FCM聚类算法,RFCR作为一种超平面型聚类算法,更加符合TS建模局部线性化的特点,能够更加精确地辨识TS模型的前件参数;另一方面,RFCR算法能够克服离群点和噪音点的影响,增强了TS模糊辨识的鲁棒性,从而更加适宜于热工过程建模。仿真实例表明,应用文中新算法所建立的煤气炉及机炉协调系统的TS模型具有精确性高、鲁棒性强的特点,证明了算法的有效性和实用性。

基于TS模糊模型的热工过程建模方法

热工过程对象通常具有复杂的动态特性和非线性、强耦合、不确定性等特征,从而使得常规建模方法难以取得满意的效果,因此提出一种改进型TS模糊模型在线建模方法。此建模方法基于以下思想,首先提出基于中心粒群算法的截集模糊C-均值聚类算法并对TS模糊模型进行模型结构离线辨识,确定模型的结构和前件部分参数的初始值;然后应用解耦扩展卡尔曼滤波算法进行后件参数在线辨识,同时对前件辨识结果进行精确修正。最后,对煤气炉、500MW机组及气化炉等热工过程进行仿真计算表明本方法具有精度高、计算量小等优点。