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.

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.

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.

Angular velocity dynamics identification of small unmanned helicopter using fuzzy model

Attitude identification method for unmanned helicopter based on fuzzy model at hovering is presented. The dynamical attitude model is considered as basis for attitude control and it is very complex. To reduce the complexity of model, nonlinear model of unmanned helicopter with unknown parameters are to be determined by fuzzy system first and then derivative based gradient method is used to identify unknown parameters of model. Gradient method is used due to ability that fuzzy system is not necessarily to be linear in parameters, therefore all fuzzy sets for input and output can be adjusted. The validity of the proposed model was verified using experimental data obtained by the commercially available flight simulator X-Plane. The simulation results showed high accuracy of the modeling method and attitude dynamics data matched well with experimental data.

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.

Fuzzy rule-based support vector regression system

In this paper, we design a fuzzy rule-based support vector regression system. The proposed system utilizes the advantages of fuzzy model and support vector regression to extract support vectors to generate fuzzy if-then rules from the training data set. Based on the first-order hnear Tagaki-Sugeno （TS） model, the structure of rules is identified by the support vector regression and then the consequent parameters of rules are tuned by the global least squares method. Our model is applied to the real world regression task. The simulation results gives promising performances in terms of a set of fuzzy hales, which can be easily interpreted by humans.

Active fault tolerant control design for stochastic Interval Type-2 Takagi-Sugeno fuzzy model

Purpose-The purpose of this paper is to look at the problem of fault tolerant control(FTC)for discrete time nonlinear system described by Interval Type-2 Takagi–Sugeno(IT2 TS)fuzzy model subjected to stochastic noise and actuator faults.Design/methodology/approach–An IT2 fuzzy augmented state observer is first developed to estimate simultaneously the system states and the actuator faults since this estimation is required for the design of the FTC control law.Furthermore,based on the information of the states and the faults estimate,an IT2 fuzzy state feedback controller is conceived to compensate for the faults effect and to ensure a good tracking performance between the healthy system and the faulty one.Sufficient conditions for the existence of the IT2 fuzzy controller and the IT2 fuzzy observer are given in terms of linear matrix inequalities which can be solved using a two-step computing procedure.Findings–The paper opted for simulation results which are applied to the three-tank system.These results are presented to illustrate the effectiveness of the proposed FTC strategy.Originality/value–In this paper,the problem of active FTC design for noisy and faulty nonlinear system represented by IT2 TS fuzzy model is treated.The developed IT2 fuzzy fault tolerant controller is designed such that it can guarantee the stability of the closed-loop system.Moreover,the proposed controller allows to accommodate for faults,presents a satisfactory state tracking performance and outperforms the traditional type-1 fuzzy fault tolerant controller.

Decay rate performance approach for stabilization continuous fuzzy models using their discretized forms

Purpose–The purpose of this paper is to deal with the stabilization of the continuous Takagi Sugeno(TS)fuzzy models using their discretized forms based on the decay rate performance approach.Design/methodology/approach–This approach is structured as follows:first,a discrete model is obtained from the discretization of the continuous TS fuzzy model.The discretized model is obtained from the Euler approximation method which is used for several orders.Second,based on the decay rate stabilization conditions,the gains of a non-PDC control law ensuring the stabilization of the discrete model are determined.Third by keeping the values of the gains,the authors determine the values of the performance criterion and the authors check by simulation the stability of the continuous TS fuzzy models through the zero order hold.Findings–The proposed idea lead to compare the performance continuous stability results with the literature.The comparison is,also,taken between the quadratic and non-quadratic cases.Originality/value–Therefore,the originality of this paper consists in the improvement of the continuous fuzzy models by using their discretized models.In this case,the effect of the discretization step on the performances of the continuous TS fuzzy models is studied.The usefulness of this approach is shown through two examples.

Improving the Performance of DC Microgrids by Utilizing Adaptive Takagi-Sugeno Model Predictive Control

In naval direct current(DC)microgrids,pulsed power loads(PPLs)are becoming more prominent.A solar sys-tem,an energy storage system,and a pulse load coupled directly to the DC bus compose a DC microgrid in this study.For DC mi-crogrids equipped with sonar,radar,and other sensors,pulse load research is crucial.Due to high pulse loads,there is a possibility of severe power pulsation and voltage loss.The original contribution of this paper is that we are able to address the nonlinear problem by applying the Takagi-Sugeno(TS)model formulation for naval DC microgrids.Additionally,we provide a nonlinear power observer for estimating major disturbances affecting DC microgrids.To demonstrate the TS-potential,we examine three approaches for mitigating their negative effects:instantaneous power control(IPC)control,model predictive control(MPC)formulation,and TS-MPC approach with compensated PPLs.The results reveal that the TS-MPC approach with adjusted PPLs effectively shares power and regulates bus voltage under a variety of load conditions,while greatly decreasing detrimental impacts of the pulse load.Additionally,the comparison confirmed the efficiency of this technique.Index Terms-DC microgrids(MG),model predictive control(MPC),pulsed power loads(PPLs),nonlinear power observer,Takagi-Sugeno(TS)fuzzy model.