Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying delays

This paper investigates delay-dependent robust exponential state estimation of Markovian jumping fuzzy neural networks with mixed random time-varying delay. In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the robust exponential state estimation of Markovian jumping Hopfield neural networks with mixed random time-varying delays. Moreover probabilistic delay satisfies a certain probability-distribution. By introducing a stochastic variable with a Bernoulli distribution, the neural networks with random time delays is transformed into one with deterministic delays and stochastic parameters. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time delays, the dynamics of the estimation error is globally exponentially stable in the mean square. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, several delay-dependent robust state estimators for such T–S fuzzy Markovian jumping Hopfield neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving a delay-dependent LMI. Finally some numerical examples are provided to demonstrate the effectiveness of the proposed method.     

一类不确定非线性系统的执行器故障模糊容错控制

针对一类状态不完全可测的不确定非线性系统,研究了带有执行器故障的容错控制问题.采用 T-S模型对非线性系统进行模糊建模,利用并行分布补偿(PDC)算法设计了状态现潮器和基于状态现 潮器的客错控制,给出了保证该模糊容错控制系统稳定的充分条件.根据李雅普诺夫稳定性理论和线性 矩阵不等式(LMI),证明了所提出的模糊容错控制方法不但使得模糊控制系统渐近稳定,而且能够取得 H∞性能指标.计算机仿真结果进一步验证了所提出方法的正确性.     

Improved stability criteria for time-varying delayed T-S fuzzy systems via delay partitioning approach

This paper focuses on the stability analysis for uncertain Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. The uncertainties of system parameter matrices are assumed to be time-varying and norm-bounded. Some new Lyapunov-Krasovskii functionals (LKFs) are constructed by nonuniformly dividing the whole delay interval into multiple segments and choosing different Lyapunov functionals to different segments in the LKFs. By employing these LKFs, some new delay-derivative-dependent stability criteria are established for the nominal and uncertain T-S fuzzy systems in a convex way. These stability criteria are derived that depend on both the upper and lower bounds of the time derivative of the delay. By employing the new delay partitioning approach, the obtained stability criteria are stated in terms of linear matrix inequality (LMI). They are equivalent or less conservative while involving less decision variables than the existing results. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results.     

Indirect adaptive fuzzy observer and controller design based on interval type-2 T-S fuzzy model

This paper presents the design scheme of the indirect adaptive fuzzy observer and controller based on the interval type-2 (IT2) T-S fuzzy model. The nonlinear systems can be well approximated by IT2 T-S fuzzy model, in which the fuzzy rules’ antecedents are interval type-2 fuzzy sets and consequents are linear state equations. The proposed IT2 T-S fuzzy model is a combination of IT2 fuzzy system and T-S fuzzy model, and also inherits the benefits of type-2 fuzzy logic systems, which is able to directly handle uncertainties and can minimize the effects of uncertainties in rule-based fuzzy system. These characteristics can improve the accuracy of the system modeling and reduce the number of system rules. The proposed method using feedback control, adaptive laws, and on-line object parameters are adjusted to ensure observation error bounded. In addition, using Lyapunov synthesis approach and Lipschitz condition, the stability analysis is conducted. The simulation results show that the proposed method can handle unpredicted disturbance and data uncertainties very well in advantage of the effectiveness of observation and control.     

Dynamics of fuzzy impulsive bidirectional associative memory neural networks with time-varying delays

Complex nonlinear systems can be represented to a set of linear sub-models by using fuzzy sets and fuzzy reasoning via ordinary Takagi-Sugeno (TS) fuzzy models. In this paper, the exponential stability of TS fuzzy bidirectional associative memory (BAM) neural networks with impulsive effect and time-varying delays is investigated. The model of fuzzy impulsive BAM neural networks with time-varying delays established as a modified TS fuzzy model is new in which the consequent parts are composed of a set of impulsive BAM neural networks with time-varying delays. Further the exponential stability for fuzzy impulsive BAM neural networks is presented by utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) technique without tuning any parameters. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.     

Stability analysis of fuzzy Markovian jumping Cohen–Grossberg BAM neural networks with mixed time-varying delays

In this paper, we investigate the robust stability of uncertain fuzzy Markovian jumping Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. A new delay-dependent stability condition is derived under uncertain switching probabilities by Takagi–Sugeno fuzzy model. Based on the linear matrix inequality (LMI) technique, upper bounds for the discrete and distributed delays are calculated using the LMI toolbox in MATLAB. Numerical examples are provided to illustrate the effectiveness of the proposed method.     

Adaptive compensation of uncertain Euler–Lagrange systems with multiple time-varying actuator faults

This work proposes the command tracking problem for uncertain Euler–Lagrange (EL) systems with multiple partial loss of effectiveness (PLOE) actuator faults. Compared to existing fault-tolerant controllers for EL systems, the proposed adaptive controller accounts for parametric uncertainties in the system and multiple time-varying actuator fault parameters. The proposed method can also handle an infinite number of fault cases. The closed-loop fault-tolerant system is treated as a switched dynamical system, and a switched system stability is established using multiple Lyapunov functions. It is shown that all signals are bounded in each sub-interval and at the switching instances, and asymptotic tracking can be obtained only for a finite number of fault occurrences, whereas tracking error is bounded for the infinite case. Finally, a simulation example on a robotic manipulator is presented to show the effectiveness of the proposed method.     

Synchronization of Takagi–Sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays

In this paper, we propose and investigate a new general model of fuzzy stochastic discrete-time complex networks (SDCNs) described by Takagi–Sugeno (T–S) fuzzy model with discrete and distributed time-varying delays. The proposed model takes some well-studied models as special cases. By employing a new Lyapunov functional candidate, we utilize some stochastic analysis techniques and Kronecker product to deduce delay-dependent synchronization criteria that ensure the mean-square synchronization of the proposed T–S fuzzy SDCNs with mixed time-varying delays. These sufficient conditions are computationally efficient as it can be solved numerically by the LMI toolbox in Matlab. A numerical simulation example is provided to verify the effectiveness and the applicability of the proposed approach.     

T-S模糊系统的脉冲稳定性

针对模糊控制系统提出了一种新的稳定性设计方法.该方法在传统T-S模型的局部子系统中引入脉冲控制项,构造了具有脉冲影响的模糊控制系统.然后,通过去模糊化技术,把具有脉冲影响的模糊系统转化为脉冲微分系统.这样,借助脉冲微分方程的比较原理和线性矩阵不等式技术,给出了模糊系统的脉冲稳定的充分条件.从而建立了模糊系统的简单脉冲控制策略.     

Robust control for Takagi–Sugeno fuzzy systems with time-varying state and input delays

The paper investigates the robust control for uncertain Takagi–Sugeno (T–S) fuzzy systems with time-varying state and input delays. Delay-dependent stabilization criterion is proposed to guarantee the asymptotic stabilization of fuzzy systems with parametric uncertainties. The result of [Lee HJ, Park JB, Joo YH. Robust control for uncertain Takagi–Sugeno fuzzy systems with time-varying input delay. ASME J Dyn Syst Meas Control 2005;127:302–6] is extended to uncertain fuzzy systems with time-varying state and input delays. Simulations show that significant improvement over the previous results can be obtained.     

基于模糊与神经网络技术的复杂非线性跟踪控制

针对一类具有不确定性、多重时延和状态未知的复杂非线性系统,把模糊T-S模型和RBF神经网络结合起来,提出了一种基于观测器的跟踪控制方案.首先,应用模糊T-S模型对非线性系统建模,设计观测器用来观测系统状态,并由线性矩阵不等式得到模糊模型的控制律;其次,构建了自适应RBF神经网络,应用自适应RBF神经网络作为补偿器来补偿建模误差和不确定非线性部分.证明了闭环系统满足期望的跟踪性能.示例仿真结果表明了该方案的有效性.     

Delay decomposition approach to stability analysis for uncertain fuzzy Hopfield neural networks with time-varying delay

This paper is concerned with delay-dependent stability analysis for uncertain Tagaki–Sugeno (T-S) fuzzy Hopfield neural networks (UFHNNs) with time-varying delay. By decomposing the delay interval into multiple equidistant subintervals, Lyapunov–Krasovskii functionals (LKFs) are constructed on these intervals. Employing these LKFs, a new stability criterion is proposed in terms of Linear Matrix Inequalities (LMIs), which is dependent on the size of the time delay and can be easily verified by MATLAB LMI toolbox. Numerical examples are given to illustrative the effectiveness of the proposed method.     

Reliable controller for nonlinear multiagent system with additive time varying delay and nonlinear actuator faults

In this paper, the problem of nonlinear multiagent system with reliable control is taken into account. The prescribed system consists of additive time-varying delay, actuator faults with both linear and nonlinear functions. The main focus of this paper is to design a reliable control which guarantees the stability and consensus condition of the proposed system. Actuator faults with linear and nonlinear functions are considered in the control input. From the implementation of integral inequality, the linear matrix inequality format is derived by constructing the suitable Lyapunov Krasovskii functional for the specified system. Terminally numerical examples are furnished for the efficiency of the specified method.     

Cluster synchronization for T–S fuzzy complex networks using pinning control with probabilistic time‐varying delays

In this article, cluster synchronization problem for Lur'e type Takagi–Sugeno (T–S) fuzzy complex networks with probabilistic time‐varying delays is considered. Pinning control strategy is proposed. The probability distribution of the time‐varying delay is considered. In terms of the probability distribution of the delays, a new type of system model with probability‐distribution‐dependent parameter matrices is proposed. Moreover, probabilistic delay is assumed to satisfy certain probability distribution and the probability of the delay takes values in some intervals. By constructing a suitable Lyapunov–Krasovskii functional involving triple integral terms and using Kronecker product with convex combination technique, some sufficient conditions are derived to ensure the cluster synchronization of designed networks such that the linear feedback controller can be used to every cluster. The problem of controller design is converted into solving a series of linear matrix inequalities. The effectiveness of our results is verified through numerical examples and simulations. © 2014 Wiley Periodicals, Inc. Complexity 21: 59–77, 2015     

Multiple delay-dependent guaranteed cost control for uncertain switched random nonlinear systems against intermittent sensor and actuator faults

In this paper, guaranteed cost control is investigated for switched random nonlinear systems against multiple state delays, model uncertainties, intermittent sensor and actuator faults. Other factors containing nonlinear dynamics, external disturbances as well as measurement noise are also considered. This is the first try to realize guaranteed cost control for uncertain switched random nonlinear systems against multiple time delays. In practice, color noise is more common than white noise in some specific situations. Thus, this paper considers random systems with color noise. In contrast to the previous study works, the suggested system can be applied to a wider range. First, a dynamic full-order output feedback controller is established to make the system stable. And an entire closed-loop system is got to achieve guaranteed cost control. Then, the multiple delay-dependent sufficient conditions are acquired through the piecewise Lyapunov function in the framework of linear matrix inequalities (LMIs). In the meantime, controller gain matrices are obtained. At last, two simulation examples are presented to verify the availability of the suggested approach.     

模糊Delta算子系统的鲁棒镇定

研究一类基于Delta算子描述的T-S模糊模型状态反馈镇定设计问题。首先将全局模糊模型按隶属函数划分成若干子空间,并被表示成不确定系统的形式;采用分段Lyapunov函数法,得到鲁棒稳定化控制律存在的充分条件．该条件被进一步等价表示成一组线性矩阵不等式的可解性问题。克服了以往设计法中需要求解一公共正定矩阵P的不足,也无需求解繁琐的Riccati方程。所得结果可将连续和离散模糊系统的有关结论统一到Delta算子框架内。     

Sampled‐data reliable stabilization of T‐S fuzzy systems and its application

In this article, based on sampled‐data approach, a new robust state feedback reliable controller design for a class of Takagi–Sugeno fuzzy systems is presented. Different from the existing fault models for reliable controller, a novel generalized actuator fault model is proposed. In particular, the implemented fault model consists of both linear and nonlinear components. Consequently, by employing input‐delay approach, the sampled‐data system is equivalently transformed into a continuous‐time system with a variable time delay. The main objective is to design a suitable reliable sampled‐data state feedback controller guaranteeing the asymptotic stability of the resulting closed‐loop fuzzy system. For this purpose, using Lyapunov stability theory together with Wirtinger‐based double integral inequality, some new delay‐dependent stabilization conditions in terms of linear matrix inequalities are established to determine the underlying system's stability and to achieve the desired control performance. Finally, to show the advantages and effectiveness of the developed control method, numerical simulations are carried out on two practical models. © 2016 Wiley Periodicals, Inc. Complexity 21: 518–529, 2016     

基于T-S模型的不确定时滞系统的保代价控制

基于T—S模糊模型，研究具有范数有界、时变参数不确定性和时滞的非线性系统的保代价控制问题，得到存在稳定模糊保代价控制器的充分条件，并推算出相应的线性矩阵不等式(LMI)形式。     

Detection,isolation and identification of multiple actuator and sensor faults in nonlinear dynamic systems: Application to a waste water treatment process

The goal in many fault detection and isolation schemes is to increase the isolation and identification speed. This paper, presents a new approach of a nonlinear model based adaptive observer method, for detection, isolation and identification of actuator and sensor faults. Firstly, we will design a new method for the actuator fault problem where, after the fault detection and before the fault isolation, we will try to estimate the output of the instrument. The method is based on the formation of nonlinear observer banks where each bank isolates each actuator fault. Secondly, for the sensor problem we will reformulate the system by introducing a new state variable, so that an augmented system can be constructed to treat sensor faults as actuator faults. A method based on the design of an adaptive observers’ bank will be used for the fault treatment. These approaches use the system model and the outputs of the adaptive observers to generate residues. Residuals are defined in such way to isolate the faulty instrument after detecting the fault occurrence. The advantages of these methods are that we can treat not only single actuator and sensor faults but also multiple faults, more over the isolation time has been decreased. In this study, we consider that only abrupt faults in the system can occur. The validity of the methods will be tested firstly in simulation by using a nonlinear model of waste water treatment process with and without measurement noise and secondly with the same nonlinear model but by using this time real data.     

Robust reliable control for uncertain switched nonlinear systems with time delay under asynchronous switching

This paper investigates the problem of robust reliable control for a class of switched nonlinear systems with time delay and actuator failures under asynchronous switching. When the switching instants of the controller experience delays with respect to those of the system, a kind of reliable controller design method is proposed, and the dwell time approach is utilized for the stability analysis. Sufficient conditions for the existence of the reliable controller are formulated in terms of a set of LMIs. Then the proposed approach is extended to take into account switched delay systems with Lipschitz nonlinearities and structured uncertainties. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.