Adaptive fuzzy sliding-mode controller of uncertain nonlinear systems

This paper deals with the design of adaptive fuzzy sliding-mode controllers for the T-S fuzzy model based on the Lyapunov function. It is shown that the Lyapunov function can be used to establish fuzzy sliding surfaces by solving a set of linear matrix inequalities (LMIs). The design of the fuzzy sliding surfaces and the adaptive fuzzy sliding-mode controllers is proposed. The adaptive mechanism is also used to deal with unknown parameter perturbations and external disturbances. Two examples illustrate the feasibility of the proposed methods.     

基于T-S模糊模型的非线性系统广义预测控制

针对离散非线性系统,提出一种基于T-S模糊模型的广义预测控制方法。该方法将采样点的T-S模糊模型转化为采样点线性模型与非线性误差叠加的线性形式,通过迭代修正非线性误差,使具有非线性误差的线性模型预测控制律逐渐逼近采样点T-S模糊模型预测控制律。同时,该预测控制方法也能适用于当系统受输入输出约束时的控制。仿真结果验证了所提出的TS模糊模型广义预测方法有效。     

Improved delay-range-dependent robust stability for uncertain systems with interval time-varying delay

This paper is concerned with the improved delay-range-dependent stability and robust stability criteria for linear systems with time-varying delay and norm-bounded uncertainties. In order to obtain much less conservative criteria, a Lyapunov-Krasovskii functional (LKF), which makes use of the information of both the lower and upper bounds of the interval time-varying delay, is proposed to derive new stability criteria. By using delayed decomposition approach (DDA), a tighter upper bound of the derivative of Lyapunov functional can be obtained, and thus the proposed criteria give results with less conservatism compared with some previous ones. The resulting criteria have advantages over some previous ones in that it involves fewer matrix variables but has less conservatism, which are established theoretically. We show, by four well known examples, that our result overcomes the previous allowable maximum admissible upper bound (MAUB) of the time-delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time delay.     

T-S region-based fuzzy control with multiple performance constraints

Takagi-Sugeno fuzzy control problems with minimizing H2/Hinfinity norm are investigated in this paper. A redesigned T-S fuzzy model and controller are called a T-S Region-based Fuzzy Model (TSRFM) and a T-S Region-based Fuzzy Controller (TSRFC), respectively, which are derived from the fuzzy region concept and the robust control technique. The fuzzy region concept is used to divide the general plant rules into several fuzzy regions and the robust control technique is used to stabilize all plant rules of each fuzzy region. In this case, the stability conditions with H2/Hinfinity performance are derived from Lyapunov criterion, which are expressed in terms of LMIs. For the fuzzy model involving large plant rules, the proposed idea greatly reduces the total number of LMIs and controller rules so that TSRFC is easy to implement with simple hardware. Although the controller rules are reduced, TSRFC is able to provide performance as good as former designs.     

Interval type-2 fuzzy PID controller for uncertain nonlinear inverted pendulum system

In this paper, the interval type-2 fuzzy proportional–integral–derivative controller (IT2F-PID) is proposed for controlling an inverted pendulum on a cart system with an uncertain model. The proposed controller is designed using a new method of type-reduction that we have proposed, which is called the simplified type-reduction method. The proposed IT2F-PID controller is able to handle the effect of structure uncertainties due to the structure of the interval type-2 fuzzy logic system (IT2-FLS). The results of the proposed IT2F-PID controller using a new method of type-reduction are compared with the other proposed IT2F-PID controller using the uncertainty bound method and the type-1 fuzzy PID controller (T1F-PID). The simulation and practical results show that the performance of the proposed controller is significantly improved compared with the T1F-PID controller.     

Covariance control with observed-state feedback gains for continuous nonlinear systems using T-S fuzzy models

The design problem of state variance constrained control for stochastic systems has received rather extensive attention in recent years. This paper solves the state variance constrained controller design problem by using the covariance control theory, with observed-state feedback gains for continuous Takagi-Sugeno (TS) fuzzy models. By incorporating the technique of state estimation into the practical covariance control theory, a variance constrained control methodology is developed for the continuous TS fuzzy models. Finally, a numerical example is shown to demonstrate the efficiency and applicability of the proposed approach.     

Improved results on delay-interval-dependent robust stability criteria for uncertain neutral-type systems with time-varying delays

In this paper, we consider the problem of delay-interval-dependent robust stability and stabilization of a class of linear uncertain neutral-type systems with time-varying delay. By constructing a candidate Lyapunov–Krasovskii functional (LKF), that takes into account the delay-range information appropriately, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMIs) to compute the maximum allowable upper bounds (MAUB) for the delay-interval within which the uncertain neutral-type system under consideration remains asymptotically stable. The verifiable stabilizability conditions and memoryless state feedback control design are stated. Finally, numerical examples are also designated to demonstrate the effectiveness and reduced conservatism of the developed results.     

A novel scheme for current sensor faults diagnosis in the stator of a DFIG described by a T-S fuzzy model

Diagnosis of current sensor faults (CSF) for doubly fed induction generators (DFIGs) is of paramount importance for the reliable power generation of DFIG-based wind turbines (WT). In this paper, a new scheme is developed for current sensors faults diagnosis in the stator of a DFIG-based WT. The nonlinear model of the DFIG is first transformed into an equivalent Takagi-Sugeno (T-S) fuzzy model. Secondly, using this model, a novel fault detection and isolation (FDI) algorithm is proposed. This algorithm is based on a bank of Luenberger observers for residuals generation combined with a new proposed residual vector. Furthermore, a new binary decision logic is used for CSF isolation. Stability analysis of the observer bank is analyzed using a Lyapunov theorem, which allows deriving sufficient stability conditions by solving a system of Linear Matrix Inequalities (LMIs). A simulation study is carried out to assess the performance and the effectiveness of the new FDI scheme.     

Observer-based robust control of one-sided Lipschitz nonlinear systems

This paper presents an observer-based controller design for the class of nonlinear systems with time-varying parametric uncertainties and norm-bounded disturbances. The design methodology, for the less conservative one-sided Lipschitz nonlinear systems, involves astute utilization of Young’s inequality and several matrix decompositions. A sufficient condition for simultaneous extraction of observer and controller gains is stipulated by a numerically tractable set of convex optimization conditions. The constraints are handled by a nonlinear iterative cone-complementary linearization method in obtaining gain matrices. Further, an observer-based control technique for one-sided Lipschitz nonlinear systems, robust against L₂-norm-bounded perturbations, is contrived. The proposed methodology ensures robustness against parametric uncertainties and external perturbations. Simulation examples demonstrating the effectiveness of the proposed methodologies are presented.     

New stability and stabilization conditions for nonlinear systems with time-varying delay based on delay-partitioning approach

This paper focuses on stability analysis and stabilization of nonlinear systems with interval time-varying delay, modeled by Takagi-Sugeno (T-S) fuzzy approach. To achieve more relaxation in the feasibility region, delay-partitioning approach is used for all integral terms in the Lyapunov-Krasovskii functional (LKF). A fuzzy Lyapunov function is proposed instead of non-integral term in LKF, and moreover, some slack matrices variables are offered to enlarge the design space. By doing this, new delay-dependent stability criteria are obtained. During the derivation of stability conditions, Jensen’s integral inequality is applied to deal with integral terms. Furthermore, in this paper the problem of controller design via the parallel distributed compensation (PDC) scheme is studied. Stability and stabilization conditions with less conservative are achieved in terms of linear matrix inequality (LMI). Finally, two numerical examples are presented to show the effectiveness of the proposed results.     

Adaptive fuzzy predictive sliding control of uncertain nonlinear systems with bound-known input delay

In this paper, a new Adaptive Fuzzy Predictive Sliding Mode Control (AFP-SMC) is presented for nonlinear systems with uncertain dynamics and unknown input delay. The control unit consists of a fuzzy inference system to approximate the ideal linearization control, together with a switching strategy to compensate for the estimation errors. Also, an adaptive fuzzy predictor is used to estimate the future values of the system states to compensate for the time delay. The adaptation laws are used to tune the controller and predictor parameters, which guarantee the stability based on a Lyapunov-Krasovskii functional. To evaluate the method effectiveness, the simulation and experiment on an overhead crane system are presented. According to the obtained results, AFP-SMC can effectively control the uncertain nonlinear systems, subject to input delays of known bound.     

蝶形直线电机的模糊Takagi-Sugeno鲁棒控制

为了克服现有双足蝶形直线超声电机驱动的一维平台定位中的摩擦驱动非线性,本文基于电机工作原理和扇形非线性特性建立了电机及平台的模糊Takagi-Sugeno(T-S)模型。基于该T-S模型,采用系统增广的方法设计了无静态误差伺服定位控制算法;设计中考虑了鲁棒H∞性能,使得该非线性系统的模糊控制器具有较好干扰抑制性能和鲁棒性。采用嵌入式微控制器实现了所设计的控制算法,并进行了不同步进值的伺服定位控制实验。实验结果显示,在不同步进值下系统的超调量小于4%;在空载和带载荷的状态下对伺服定位控制实验数据的对比显示,系统最大超调量小于5%。与传统PID控制算法相比,本文提出的控制系统具有较高的定位精度,良好的运动平稳性和鲁棒性。     

Robust Takagi-Sugeno fuzzy control for fractional order hydro-turbine governing system

A robust fuzzy control method for fractional order hydro-turbine governing system (FOHGS) in the presence of random disturbances is investigated in this paper. Firstly, the mathematical model of FOHGS is introduced, and based on Takagi-Sugeno (T-S) fuzzy rules, the generalized T-S fuzzy model of FOHGS is presented. Secondly, based on fractional order Lyapunov stability theory, a novel T-S fuzzy control method is designed for the stability control of FOHGS. Thirdly, the relatively loose sufficient stability condition is acquired, which could be transformed into a group of linear matrix inequalities (LMIs) via Schur complement as well as the strict mathematical derivation is given. Furthermore, the control method could resist random disturbances, which shows the good robustness. Simulation results indicate the designed fractional order T-S fuzzy control scheme works well compared with the existing method.     

非线性时滞系统自适应模糊动态面控制

针对含完全未知时滞的不确定非线性系统的控制问题,提出了一种自适应模糊动态面控制方案.首先采用模糊逻辑系统逼近系统的未知时滞函数,进而用参考信号代换逼近器输入中的未知时滞信号,取消了对未知时滞常作的假设,摆脱了控制器构造对时滞假设条件的依赖性.模糊逼近和时滞代换产生的误差则采用自适应边界技术处理.基于Lyapunov-Krasovskii泛函,证明了闭环系统所有信号半全局一致最终有界,通过调节设计参数可以实现任意的跟踪精度.仿真实例进一步说明了该方案的可行性.     

Robust state estimation for a class of uncertain nonlinear systems: Comparison of two approaches

In this paper, two approaches for robust state estimation of a class of Lipschitz nonlinear systems are proposed. First, a novel Unknown Input Observer (UIO) is designed without observer matching condition satisfaction. Then, an $H_{\infty }$ observer for approximate disturbance decoupling is proposed. Sufficient conditions for the existence of both proposed observers are derived based on a Lyapunov function. The achieved conditions are formulated in terms of a set of linear matrix inequalities (LMIs) and optimal gain matrices are obtained. The minimum values of the disturbance attenuation levels for both methods are obtained through solving optimization problems. Finally, the proposed approaches are compared by simulation studies of an automated highway system.     

Robust absolute stability criteria for uncertain Lurie interval time-varying delay systems of neutral type

This study investigates the delay-dependent robust absolute stability analysis for uncertain Lurie systems with interval time-varying delays of neutral type. First, we divide the whole delay interval into two segmentations with an unequal width and checking the variation of the Lyapunov–Krasovskii functional (LKF) for each subinterval of delay, much less conservative delay-dependent absolute and robust stability criteria are derived. Second, a new delay-dependent robust stability condition for uncertain Lurie neutral systems with interval time-varying delays, which expressed in terms of quadratic forms of linear matrix inequalities (LMIs), and has been derived by constructing the LKF from the delayed decomposition approach (DDA) and integral inequality approach (IIA). Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.     

A novel approach for remanufacturing process planning considering uncertain and fuzzy information

Frontiers of Mechanical Engineering - Remanufacturing, as one of the optimal disposals of end-of-life products, can bring tremendous economic and ecological benefits. Remanufacturing process...     

Robust covariance control for discrete system by Takagi-Sugeno fuzzy controllers

Variances of the system states or outputs often play vital roles in the problem for performance requirements of many stochastic control systems. For linear stochastic systems, the covariance control technique has been applied to deal with the variance constrained design problem. This paper extends this technique to a class of discrete-time nonlinear perturbed stochastic systems, which are modeled by the Takagi-Sugeno (TS) fuzzy systems. By fuzzy IF-THEN rules, which represent local linear input-output relations, the nonlinear systems can be described by TS fuzzy models. According to the parallel distributed compensation (PDC) concept, the discrete-time nonlinear perturbed stochastic systems can be driven by the linear feedback gains. The purpose of this paper is to provide a method to design an output feedback fuzzy controller, which is based on the upper bound state covariance control technique and PDC concept, for the discrete-time perturbed stochastic systems using TS fuzzy models.     

Design of robust reliable control for T-S fuzzy Markovian jumping delayed neutral type neural networks with probabilistic actuator faults and leakage delays: An event-triggered communication scheme

This study examines the problem of robust reliable control for Takagi-Sugeno (T-S) fuzzy Markovian jumping delayed neural networks with probabilistic actuator faults and leakage terms. An event-triggered communication scheme. First, the randomly occurring actuator faults and their failures rates are governed by two sets of unrelated random variables satisfying certain probabilistic failures of every actuator, new type of distribution based event triggered fault model is proposed, which utilize the effect of transmission delay. Second, Takagi-Sugeno (T-S) fuzzy model is adopted for the neural networks and the randomness of actuators failures is modeled in a Markov jump model framework. Third, to guarantee the considered closed-loop system is exponential mean square stable with a prescribed reliable control performance, a Markov jump event-triggered scheme is designed in this paper, which is the main purpose of our study. Fourth, by constructing appropriate Lyapunov-Krasovskii functional, employing Newton-Leibniz formulation and integral inequalities, several delay-dependent criteria for the solvability of the addressed problem are derived. The obtained stability criteria are stated in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results over the existing ones, among them one example was supported by real-life application of the benchmark problem.