基于观测器的不确定T-S模糊系统鲁棒镇定

为带有参数不确定性的T-S模糊控制系统提出了新的基于观测器的鲁棒输出镇定条件. 该条件用来设计模糊控制器和模糊观测器. 为了设计模糊控制器和模糊观测器, 用T-S模糊模型来表示非线性系统, 并运用平行分布补偿观念. 充分条件基于二次Lyapunov函数, 通过将模糊系统的鲁棒镇定条件表述为一系列矩阵不等式, 比以往文献中列出的条件具有更小的保守性. 该不等式为双线性矩阵不等式, 可分两步骤先后解得使T-S模糊系统镇定的控制器增益和观测器增益. 最后, 通过对一个具有不确定性的连续时间非线性系统控制的例子证明了提出方法比以往方法更宽松.     

Polynomial Fuzzy Observer Designs: A Sum-of-Squares Approach

This paper presents a sum-of-squares (SOS) approach to polynomial fuzzy observer designs for three classes of polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results with respect to a polynomial fuzzy system that is a more general representation of the well-known T-S fuzzy system. Next, we propose polynomial fuzzy observers to estimate states in three classes of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions for the first two classes (Classes I and II) is that they realize the so-called separation principle, i.e., the polynomial fuzzy controller and observer for each class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. Although, for the last class (Class III), the separation principle does not hold, we propose an algorithm to design polynomial fuzzy controller and observer satisfying the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. All the design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program solver, respectively. To illustrate the validity and applicability of the proposed approach, three design examples are provided. The examples demonstrate the advantages of the SOS-based approaches for the existing LMI approaches to T-S fuzzy observer designs.     

Takagi-Sugeno fuzzy model based indirect adaptive fuzzy observer and controller design

This paper proposes the design scheme of the alternative adaptive observer and controller based on the Takagi-Sugeno (T-S) fuzzy model. The T-S fuzzy modeling and the state feedback control technique are adopted for the simple structure. The proposed method maintains consistent performance in the presence of parameter uncertainties and incorporates linguistic fuzzy information from human operators. In addition, with the simple adaptive state feedback controller, it solves the singularity problem, which occurs in the inverse dynamics based on the feedback linearization method. Using Lyapunov theory and Lipschitz condition, the stability analysis is conducted, and the adaptive law is derived. The proposed method is applied to the stabilization problem of a flexible joint manipulator in order to guarantee its performance.     

前件变量未知的T-S模糊系统输出反馈控制

针对一类带有未知前件变量的T-S模糊系统,提出一种新的观测器-控制器设计方法.首先,在前件变量完全未知的情况下,将观测误差方程中由未知前件变量导致的相关项利用Lipschitz条件进行限制;然后,根据Lyapunov函数得到系统稳定性条件,同时提出一种基于特征值的矩阵缩放方法和一种基于模糊 Lyapunov 函数的高增益观测器方法计算观测器-控制器的增益矩阵;最后,针对动力定位船舶的控制问题对两种方法进行仿真验证和比较分析,以表明所提出方法的有效性.     

State feedback tracking control for indirect field-oriented induction motor using fuzzy approach

This paper deals with the synthesis of fuzzy controller applied to the induction motor with a guaranteed model reference tracking performance. First, the Takagi-Sugeno (T-S) fuzzy model is used to approximate the nonlinear system in the synchronous d-q frame rotating with field-oriented control strategy. Then, a fuzzy state feedback controller is designed to reduce the tracking error by minimizing the disturbance level. The proposed controller is based on a T-S reference model in which the desired trajectory has been specified. The inaccessible rotor flux is estimated by a T-S fuzzy observer. The developed approach for the controller design is based on the synthesis of an augmented fuzzy model which regroups the model of induction machine, fuzzy observer, and reference model. The gains of the observer and controller are obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation and experimental results are given to show the performance of the observer-based tracking controller.     

Output feedback LMI tracking control conditions with H∞ criterion for uncertain and disturbed T-S models

This work concerns the tracking problem of uncertain Takagi-Sugeno (T-S) continuous fuzzy model with external disturbances. The objective is to get a model reference based output feedback tracking control law. The control scheme is based on a PDC structure, a fuzzy observer and a H_∞ performance to attenuate the external disturbances. The stability of the whole closed-loop model is investigated using the well-known quadratic Lyapunov function. The key point of the proposed approaches is to achieve conditions under a LMI (linear matrix inequalities) formulation in the case of an uncertain and disturbed T-S fuzzy model. This formulation facilitates obtaining solutions through interior point optimization methods for some nonlinear output tracking control problems. Finally, a simulation is provided on the well-known inverted pendulum testbed to show the efficiency of the proposed approach.     

非线性模糊时滞系统鲁棒自适应控制

研究一类基于模糊T-S模型的非线性时滞系统鲁棒镇定问题．基于记忆型状态反馈策略，首先给出由T-S模糊模型描述的非线性时滞系统在时滞精确已知情况下的鲁棒镇定准则；然后给出非线性时滞系统在时滞未知情况下的鲁棒自适应控制策略．所设计的控制器可确保闭环系统渐近稳定，且具有良好的可操作性．最后通过仿真实例证明了该方法的正确性和有效性．     

An observer-based approach to controlling time-delay chaotic systems via Takagi-Sugeno fuzzy model

This study presents a fuzzy model-based control criterion for time-delay chaotic systems with uncertainty. The Takagi-Sugeno (T-S) fuzzy model is adopted for representing a chaotic system possessing a time delay. A unified approach for designing a fuzzy observer, which integrates parallel distributed compensation with an adaptive updating method, is first discussed. An observer-based fuzzy control scheme is then developed to deal with stabilization and tracking problems. Based on Lyapunov stability analysis, sufficient conditions that ensure robust control performance of time-delay chaotic systems are derived. These conditions are represented in terms of linear matrix inequalities and adaptive updating laws. Finally, the proposed approach is validated through numerical synchronization, stabilization, and model tracking control simulations.     

Stability and asynchronous stabilization for a class of discrete-time switched nonlinear systems with stable and unstable subsystems

The stability analysis and asynchronous stabilization problems for a class of discrete-time switched nonlinear systems with stable and unstable subsystems are investigated in this paper. The Takagi-Sugeno (T-S) fuzzy model is used to represent each nonlinear subsystem. Through using the T-S fuzzy model, the studied systems are modeled into the switched T-S fuzzy systems. By using the switching fuzzy-basis-dependent Lyapunov functions (FLFs) approach and mode-dependent average dwell time (MDADT) technique, the stability conditions for the open-loop switched T-S fuzzy systems with unstable subsystems and asynchronous stabilization conditions for the closed-loop switched T-S fuzzy systems with unstable subsystems are obtained. Both the stability results and asynchronous stabilization results are derived in terms of linear matrix inequalities (LMIs). Finally two numerical examples are provided to illustrate the effectiveness of the results obtained.     

Detection of Impending Vehicle Rollover with Road Bank Angle Consideration Using a Robust Fuzzy Observer

 This article describes a method of vehicle dynamics estimation for impending rollover detection. We estimate vehicle dynamic states in presence of the road bank angle as a disturbance in the vehicle model using a robust observer. The estimated roll angle and roll rate are used to compute the rollover index which is based on the prediction of the lateral load transfer. In order to anticipate rollover detection, a new method is proposed to compute the time to rollover (TTR) using the load transfer ratio (LTR). The nonlinear model, deduced from the vehicle lateral and roll dynamics, is represented by a Takagi-Sugeno (T-S) fuzzy model. This representation is used to account for the nonlinearities of lateral cornering forces. The proposed T-S observer is designed with unmeasurable premise variables to cater for non-availability of the slip angles measurement. The proposed approach is evaluated using CarSim simulator under different driving scenarios. Simulation results show good efficiency of the proposed T-S observer and the rollover detection method.     

Fuzzy fault tolerant predictive control for a diesel engine air path

This paper proposes a Fuzzy Fault Tolerant Predictive Control (FFTPC) with integral action method for a class of nonlinear systems. The Takagi-Sugeno (T-S) fuzzy approach is introduced as a modelling technique in order to consider the active control methods adapted to linear models. The proposed control strategy is based on a combination between Parallel Distributed Compensation (PDC) control law and Model Predictive Control (MPC) where the T-S fuzzy aspect uses the Unmeasurable Premise Variables (UPV). A T-S fuzzy observer provides an L2 norm estimation of system state vector and faults. The controller and observer gains are obtained by solving Linear Matrix Inequalities (LMIs) derived from the Lyapunov theory. The validity of the proposed Fault Tolerant Control (FTC) strategy is illustrated through an application to a Diesel Engine Air Path (DEAP) system.     

混合攻击下直流微电网的FDI估计与模糊控制联合设计

研究基于T-S模糊模型的直流微电网(DC-MG)系统在拒绝服务(DoS)和虚假数据注入(FDI)混合攻击下的协同估计控制框架.考虑网络化T-S模糊模型和并行分布补偿(PDC)模糊控制规则中的非均匀时间尺度,建立DC-MG系统的T-S模型.为了放宽现有的DoS攻击模型通常假定攻击的频率和持续时间均有限的要求,在攻击信号的休眠和活跃期的已知范围内提出一种新的DoS攻击模型.同时,构造一个切换脉冲观测器来估计由外部动态系统产生的未知FDI攻击信号.然后,利用依赖于攻击参数的时变Lyapunov函数方法,导出系统在混合攻击下的指数稳定性判据.此外,基于线性矩阵不等式给出了模糊控制器和FDI攻击观测器的联合设计方法.最后,通过案例研究验证了所提出理论结果的有效性.     

Fuzzy observer design using linear matrix inequalities for fuzzy closed-loop control systems

Linear observers play an important role in modern control theory and practice. A systematic design method of fuzzy observers would be important for fuzzy control as well. The fuzzy observer is designed by solving linear matrix inequalities (LMI) that represent control performance such as disturbance rejection and robust stability. Our approach in designing the fuzzy observer is based on the LMI formulation of the stability conditions for closed-loop Takagi-Sugeno (T-S) fuzzy systems, when states are not available for measurement of feedback. We present a new approach, which is to design an observer based on fuzzy implications, with fuzzy sets in the antecedents, and an asymptotic observer in the consequents. Each fuzzy rule is responsible for observing the states of a locally linear subsystem. An example illustrates the design procedure.     

基于T-S模型的网络控制系统故障诊断

针对一类参数不确定并具有时延和丢包情况的非线性网络控制系统,为达到快速准确的进行故障诊断的目的,提出了一种基于T-S模糊模型的故障诊断方法.通过建立此系统的T-S模糊模型,利用平行分布补偿时延的思想设计了满足系统稳定性条件的状态反馈控制器,以及通过引入随机切换系统表示数据有无丢失情况下的基于模糊观测器的鲁棒故障诊断方法,然后基于 Lyapunov函数和线性矩阵不等式方法给出了该闭环网络控制系统渐近稳定的充分条件,最后通过仿真例子验证了该方法能够使闭环控制系统渐进稳定以及能够准确的进行故障诊断,验证了所设计方法的有效性.     

基于区间观测器的动态系统故障诊断技术综述

介绍一种基于区间观测器的故障诊断技术.为突出区间观测器在故障诊断方面的优势,总结归纳针对不同类型系统构造的可以达到故障诊断目的的区间观测器,并讨论观测器的设计条件.例如,事件触发机制下的故障检测区间观测器,针对线性参数变化系统设计的基于区间观测器的故障检测机制,在区间观测器的框架下实现带有未知互联项的T-S模糊大系统的故障隔离,以及利用区间观测器对多智能体系统实现故障隔离.最后探讨该领域亟待解决的问题.     

时滞依赖型中立系统的观测器设计与镇定

研究了一类时滞依赖型线性中立系统的观测器的设计与镇定问题,首先建立了一个时滞依赖型稳定性准则,基于LMI正定解的存在性,给出确保误差动力系统渐近稳定的充分条件及经状态反馈而达到镇定的设计方案.最后通过数值仿真来说明本文所得结论的正确性和有效性.     

一类复杂非线性系统的模糊控制

针对一类复杂非线性系统,把模糊T-S模型和自适应模糊逻辑系统结合起来,提出了一种跟踪控制方案.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:其次,应用基于权值、中心和宽度3个参数可调节的自适应时延模糊逻辑系统补偿器来消除建模误差和小确定性.文中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.     

T-S模糊系统的基于观测器的H∞控制设计

研究了T-S(Takagi-Sugeno)模糊系统H∞控制设计问题.放宽了Kim E等的T-S模糊 系统可二次稳定的条件.给出了T-S模糊系统新的观测器设计方法.然后给出了T-S模糊系统 基于观测器的H∞控制存在的两个新的充分条件.新方法不但简单,而且充分考虑了模糊子系统 间的相互作用.最后通过例子,应用LMI技术,说明了本文给出的T-S模糊系统的基于观测器 的H∞控制器的设计方法简便易行.     

Imperfect premise matching controller design for T-S fuzzy systems under network environments

This paper focuses on an imperfect premise matching controller design for T-S fuzzy systems under network environments. Different with the traditional parallel distribution compensation (PDC) method, the same premises between the PDC controller and the T-S fuzzy systems are no longer needed again in the proposed method. Under consideration of the unmatched grades of membership in the networked T-S fuzzy systems, a unified T-S fuzzy model is firstly proposed, in which a networked state-feedback fuzzy controller with communication delays is used to reconstruct the system. Then, based on the constructed model and by use of the Wirtinger-based inequality technique to deal with the cross items, two less conservative stability and stabilization criteria are derived to enhance the design flexibility. Finally, two numerical examples are used to show the effectiveness of proposed method.     

Observer-Based Stabilization of T–S Fuzzy Systems With Input Delay

This paper discusses the stabilization of Takagi-Sugeno (T-S) fuzzy systems with bounded and time-varying input delay. The robust stabilization via state feedback is first addressed, and delay-dependent stabilization conditions are proposed in terms of LMIs. Observer-based feedback stabilization is also discussed for T-S fuzzy input delay systems without uncertainties. A separate design principle is developed. Some illustrative examples are given to show the effectiveness and the feasibility of the proposed methods.