Constrained predictive control based on T-S fuzzy model for nonlinear systems

A constrained generalized predictive control （GPC） algorithm based on the T-S fuzzy model is presented for the nonlinear system. First, a Takagi-Sugeno （T-S） fuzzy model based on the fuzzy cluster algorithm and the orthogonalleast square method is constructed to approach the nonlinear system. Since its consequence is linear, it can divide the nonlinear system into a number of linear or nearly linear subsystems. For this T-S fuzzy model, a GPC algorithm with input constraints is presented. This strategy takes into account all the constraints of the control signal and its increment, and does not require the calculation of the Diophantine equations. So it needs only a small computer memory and the computational speed is high. The simulation results show a good performance for the nonlinear systems.

Statistic PID Tracking Control for Non-Gaussian Stochastic Systems Based on T-S Fuzzy Model

A new robust proportional-integral-derivative （PID） tracking control framework is considered for stochastic systems with non-Gaussian variable based on B-spline neural network approximation and T-S fuzzy model identification. The tracked object is the statistical information of a given target probability density function （PDF）, rather than a deterministic signal. Following B-spline approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. Different from the previous related works, the time delay T-S fuzzy models with the exogenous disturbances are applied to identify the nonlinear weighting dynamics. Meanwhile, the generalized PID controller structure and the improved convex linear matrix inequalities （LMI） algorithms are proposed to fulfil the tracking problem. Furthermore, in order to enhance the robust performance, the peak-to-peak measure index is applied to optimize the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.

Controller design of uncertain nonlinear systems based on T-S fuzzy model

A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input variables adopting standard fuzzy partitions, the efficient maximal overlapped-rules group （EMORG） is presented, and a new sufficient condition to check the stability of T-S fuzzy system with uncertainty is derived, which is expressed in terms of Linear Matrix Inequalities. The derived stability condition, which only requires a local common positive definite matrix in each EMORG, can reduce the conservatism and difficulty in existing stability conditions. Finally, a simulation example shows the proposed approach is effective.

Impulsive Control for T-S Fuzzy Model Based Chaotic Systems Consisting of Van der Pol Oscillators Coupled to Linear Oscillators

This paper proposes an impulsive control scheme for chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators （VDPL） based on their Takagi-Sugeno （T-S） fuzzy models. A T-S fuzzy model is utilized to represent the chaotic VDPL system. By using comparison method, a general asymptotical stability criterion by means of linear matrix inequality （LMI） is derived for the T-S fuzzy model of VDPL system with impulsive effects. The simulation results demonstrate the effectiveness of the proposed scheme.

Generating Li-Yorke chaos in a stable continuous-time T-S fuzzy model via time-delay feedback control

This paper investigates the chaotification problem of a stable continuous-time T S fuzzy system. A simple nonlinear state time-delay feedback controller is designed by parallel distributed compensation technique. Then, the asymptotically approximate relationship between the controlled continuous-time T-S fuzzy system with time-delay and a discrete-time T-S fuzzy system is established. Based on the discrete-time T-S fuzzy system, it proves that the chaos in the discrete- time T-S fuzzy system satisfies the Li-Yorke definition by choosing appropriate controller parameters via the revised Marotto theorem. Finally, the effectiveness of the proposed chaotic anticontrol method is verified by a practical example.

Predictive Control Algorithm for Urban Rail Train Brake Control System Based on T-S Fuzzy Model

Urban rail transit has the advantages of large traffic capacity,high punctuality and zero congestion,and it plays an increasingly important role in modern urban life.Braking system is an important system of urban rail train,which directly affects the performance and safety of train operation and impacts passenger comfort.The braking performance of urban rail trains is directly related to the improvement of train speed and transportation capacity.Also,urban rail transit has the characteristics of high speed,short station distance,frequent starting,and frequent braking.This makes the braking control system constitute a time-varying,time-delaying and nonlinear control system,especially the braking force changes directly disturb the parking accuracy and comfort.To solve these issues,a predictive control algorithm based on T-S fuzzy model was proposed and applied to the train braking control system.Compared with the traditional PID control algorithm and self-adaptive fuzzy PID control algorithm,the braking capacity of urban rail train was improved by 8%.The algorithm can achieve fast and accurate synchronous braking,thereby overcoming the dynamic influence of the uncertainty,hysteresis and time-varying factors of the controlled object.Finally,the desired control objectives can be achieved,the system will have superior robustness,stability and comfort.

Controller Design for Electric Power Steering System Using T-S Fuzzy Model Approach

Pressure ripples in electric power steering （EPS） systems can be caused by the phase lag between the driver s steering torque and steer angle, the nonlinear frictions, and the disturbances from road and sensor noise especially during high-frequency maneuvers. This paper investigates the use of the robust fuzzy control method for actively reducing pressure ripples for EPS systems. Remarkable progress on steering maneuverability is achieved. The EPS dynamics is described with an eight-order nonlinear state-space model and approximated by a Takagi-Sugeno （T-S） fuzzy model with time-varying delays and external disturbances. A stabilization approach is then presented for nonlinear time-delay systems through fuzzy state feedback controller in parallel distributed compensation （PDC） structure. The closed-loop stability conditions of EPS system with the fuzzy controller are parameterized in terms of the linear matrix inequality （LMI） problem. Simulations and experiments using the proposed robust fuzzy controller and traditional PID controller have been carried out for EPS systems. Both the simulation and experiment results show that the proposed fuzzy controller can reduce the torque ripples and allow us to have a good steering feeling and stable driving.

Fault tolerant synchronization of chaotic systems based on T-S fuzzy model with fuzzy sampled-data controller

In this paper the fault tolerant synchronization of two chaotic systems based on fuzzy model and sample data is investigated. The problem of fault tolerant synchronization is formulated to study the global asymptotical stability of the error system with the fuzzy sampled-data controller which contains a state feedback controller and a fault compensator. The synchronization can be achieved no matter whether the fault occurs or not. To investigate the stability of the error system and facilitate the design of the fuzzy sampled-data controller, a Takagi Sugeno （T-S） fuzzy model is employed to represent the chaotic system dynamics. To acquire good performance and produce a less conservative analysis result, a new parameter-dependent Lyapunov-Krasovksii functional and a relaxed stabilization technique are considered. The stability conditions based on linear matrix inequality are obtained to achieve the fault tolerant synchronization of the chaotic systems. Finally, a numerical simulation is shown to verify the results.

Pendulation reduction on ship-mounted container crane via T-S fuzzy model

Ship-mounted container cranes are challenging industrial applications of nonlinear pendulum-like systems with oscillating disturbance which can cause them unstable.Since wave-induced ship motion causes the hoisted container to swing during the transfer operation,the swing motion may be dangerously large and the operation must be stopped.In order to reduce payload pendulation of ship-mounted crane,nonlinear dynamics of ship-mounted crane is derived and a control method using T-S fuzzy model is proposed.Simulation results are given to illustrate the validity of the proposed design method and pendulation of ship-mounted crane is reduced significantly.

Robust State Feedback H_∞Control for Dynamic Biped Robot Based on T-S Fuzzy Model

T-S fuzzy model was applied to describe nonlinear system and global fuzzy model was expressed by the form of uncertain system.Based on robust state feedback H_∞control strategy,designed a global asymptotic steady fuzzy model.This control system can use the experimental input-output data pairs for the biped robot learning and walking with dynamic balance.It is proved by simulation result that robust state feedback H_∞control method based on T-S fuzzy model can effectively restrain the effect of model uncertainties and external disturbance acting on biped robot.From these works,we showed the satisfactory performance of joint tracking without any chattering.

Output regulation of nonlinear singularly perturbed systems based on T-S fuzzy model

Based on the T-S model, the output regulation of nonlinear singularly perturbed systems via state feedback is discussed. It is shown that, under standard assumptions, this problean is solvable if and only if certain linear matrix equations are solvable. Once these equations are solvable, the state feedback regulator can easily be constructed.

Modeling and Stability Analysis for Non-linear Network Control System Based on T-S Fuzzy Model

Based on the T-S fuzzy model,this paper presents a new model of non-linear network control system with stochastic transfer delay.Sufficient criterion is proposed to guarantee globally asymptotically stability of this two-levels T-S fuzzy model.Also a T-S fuzzy observer of NCS is designed base on this two-levels T-S fuzzy model.All these results present a new approach for networked control system analysis and design.

Hybrid Dynamic Variables-Dependent Event-Triggered Fuzzy Model Predictive Control

This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance.

Predictive functional control based on fuzzy T-S model for HVAC systems temperature control

In heating, ventilating and air-conditioning （HVAC） systems, there exist severe nonlinearity, time-varying nature, disturbances and uncertainties. A new predictive functional control based on Takagi-Sugeno （T-S） fuzzy model was proposed to control HVAC systems. The T-S fuzzy model of stabilized controlled process was obtained using the least squares method, then on the basis of global linear predictive model from T-S fuzzy model, the process was controlled by the predictive functional controller. Especially the feedback regulation part was developed to compensate uncertainties of fuzzy predictive model. Finally simulation test results in HVAC systems control applications showed that the proposed fuzzy model predictive functional control improves tracking effect and robustness. Compared with the conventional PID controller, this control strategy has the advantages of less overshoot and shorter setting time, etc.

Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

基于概率信息与协作学习的鲁棒T-S模糊建模方法

T-S模糊建模方法在非线性系统建模中取得了大量的应用.然而,T-S模型在参数辨识过程中忽略了结构风险项,同时没有考虑各个规则之间的联系,因此在数据受到非高斯噪声和异常点的影响时,模型容易失效.针对以上不足,提出了基于概率信息与协作学习的模糊建模方法.该方法建立了规则之间协作学习机制以保证模型的连续性、平滑性与鲁棒性,并进一步构建了包含正则化项、误差项、规则概率信息及规则之间协作关系项的目标函数,用于提高模型的泛化能力和建模性能.除此之外,建立了空间投影机制,将数据低维特征空间的非线性关系转换为高维投影空间的线性关系,以增强规则之间的协作性.针对该模型,建立了基于最小二乘的求解方法,获得了可靠的模型参数.数学算例仿真和实际锻压实验表明:所提出的方法在面对噪声以及强非线性影响时,依然能在规则数较低的情况下保持优秀的建模性能.对比其他优秀的模糊建模方法,该模型有着更强的抗干扰能力,且建模均方根误差(RMSE)远低于其他建模方法.综上所述,所提出的方法对传统方法和建模理论进行了改进,即使面对强非线性系统拥有较强的泛化能力、鲁棒性以及优秀的建模能力,并且能够以较少的模糊规则对工程当中非线性、不确定性系统建模.

Computation Tree Logic Model Checking of Multi-Agent Systems Based on Fuzzy Epistemic Interpreted Systems

Model checking is an automated formal verification method to verify whether epistemic multi-agent systems adhere to property specifications.Although there is an extensive literature on qualitative properties such as safety and liveness,there is still a lack of quantitative and uncertain property verifications for these systems.In uncertain environments,agents must make judicious decisions based on subjective epistemic.To verify epistemic and measurable properties in multi-agent systems,this paper extends fuzzy computation tree logic by introducing epistemic modalities and proposing a new Fuzzy Computation Tree Logic of Knowledge(FCTLK).We represent fuzzy multi-agent systems as distributed knowledge bases with fuzzy epistemic interpreted systems.In addition,we provide a transformation algorithm from fuzzy epistemic interpreted systems to fuzzy Kripke structures,as well as transformation rules from FCTLK formulas to Fuzzy Computation Tree Logic(FCTL)formulas.Accordingly,we transform the FCTLK model checking problem into the FCTL model checking.This enables the verification of FCTLK formulas by using the fuzzy model checking algorithm of FCTL without additional computational overheads.Finally,we present correctness proofs and complexity analyses of the proposed algorithms.Additionally,we further illustrate the practical application of our approach through an example of a train control system.

Finite-Time H_(∞)Sampled-Data Reliable Control for a Class of Markovian Jump Systems with Randomly Occurring Uncertainty via T-S Fuzzy Model

The paper analyzes finite-time H_(∞)sampled-data reliability control for nonlinear continuous time Markovian jump systems with randomly occurring uncertainty on account of T-S fuzzy model.In particular,the transition rates of the Markovian jump systems have both the upper bound and lower bound.Meanwhile,a new Lyapunov-Krasovskii functional(LKF)is considered,which fully captures the available characteristics of real sampling period,and a sampled-data controller with nonlinear actuator failures is designed.Based on the integral inequality technique,some less conservative conditions are proposed such that the stochastic fuzzy system is reliable in the sense,which satisfies finite-time bounded and certain H_(∞)performance levelγ.Additionally,some numerical examples can illustrate the effectiveness of the results.

T-S Fuzzy Model-Based Depth Control of Underwater Vehicles

A T-S fuzzy model with two rules is established to exactly describe the nonlinear uncertain heave dynamics of underwater vehicles with bounded heave speed.A single linear-matrix-inequality-based (LMI-based) state feedback controller is then synthesized to guarantee the global stability of the depth control system.Simulation results verify the effectiveness of the proposed approach in comparison with linear-quadratic regulator (LQR) method.Nonlinear disturbance observer is appended to the system when the underwater vehicles are affected by the gravity-buoyancy imbalance.The two-stage control method is effective to stabilize an uncertain system with both parameter uncertainties and external disturbances.