Multiobjective identification of Takagi-Sugeno fuzzy models

The problem of identifying the parameters of the constituent local linear models of Takagi-Sugeno fuzzy models is considered. In order to address the tradeoff between global model accuracy and interpretability of the local models as linearizations of a nonlinear system, two multiobjective identification algorithms are studied. Particular attention is paid to the analysis of conflicts between objectives, and we show that such information can be easily computed from the solution of the multiobjective optimization. This information is useful to diagnose the model and tune the weighting/priorities of the multiobjective optimization. Moreover, the result of the conflict analysis can be used as a constructive tool to modify the fuzzy model structure (including membership functions) in order to meet the multiple objectives. Simple illustrative examples as well as experimental results show the usefulness of the method.     

An approach to online identification of Takagi-Sugeno fuzzy models.

An approach to the online learning of Takagi-Sugeno (TS) type models is proposed in the paper. It is based on a novel learning algorithm that recursively updates TS model structure and parameters by combining supervised and unsupervised learning. The rule-base and parameters of the TS model continually evolve by adding new rules with more summarization power and by modifying existing rules and parameters. In this way, the rule-base structure is inherited and up-dated when new data become available. By applying this learning concept to the TS model we arrive at a new type adaptive model called the Evolving Takagi-Sugeno model (ETS). The adaptive nature of these evolving TS models in combination with the highly transparent and compact form of fuzzy rules makes them a promising candidate for online modeling and control of complex processes, competitive to neural networks. The approach has been tested on data from an air-conditioning installation serving a real building. The results illustrate the viability and efficiency of the approach. The proposed concept, however, has significantly wider implications in a number of fields, including adaptive nonlinear control, fault detection and diagnostics, performance analysis, forecasting, knowledge extraction, robotics, behavior modeling.     

Modified Gath-Geva fuzzy clustering for identification of Takagi-Sugeno fuzzy models

The construction of interpretable Takagi-Sugeno (TS) fuzzy models by means of clustering is addressed. First, it is shown how the antecedent fuzzy sets and the corresponding consequent parameters of the TS model can be derived from clusters obtained by the Gath-Geva (GG) algorithm. To preserve the partitioning of the antecedent space, linearly transformed input variables can be used in the model. This may, however, complicate the interpretation of the rules. To form an easily interpretable model that does not use the transformed input variables, a new clustering algorithm is proposed, based on the expectation-maximization (EM) identification of Gaussian mixture models. This new technique is applied to two well-known benchmark problems: the MPG (miles per gallon) prediction and a simulated second-order nonlinear process. The obtained results are compared with results from the literature.     

Robust fuzzy control for discrete perturbed time-delay affine Takagi-Sugeno fuzzy models

The purpose of this paper is to study the stability analysis and controller synthesis principles of Discrete Perturbed Time-Delay Affine (DPTDA) Takagi-Sugeno (T-S) fuzzy models. In general, the T-S fuzzy model is a weighted sum of some linear subsystems via fuzzy membership functions. This paper considers fuzzy rules include both linear nominal parts and uncertain parameters in the time-delay affine T-S fuzzy model. For DPTDA T-S fuzzy models, the T-S fuzzy control scheme is used to confront the H_∞ performance constraints. Some sufficient conditions are derived on robust H_∞ disturbance attenuation in which both robust stability and a prescribed performance are required to be achieved. In order to find suitable fuzzy controllers, the Iterative Linear Matrix Inequality (ILMI) algorithm is employed to solve these sufficient conditions. At last, a numerical simulation for the nonlinear truck-trailer system is given to show the applications of the present design approach.     

A robust design criterion for interpretable fuzzy models with uncertain data

We believe that nonlinear fuzzy filtering techniques may be turned out to give better robustness performance than the existing linear methods of estimation (H/sup 2/ and H/sup /spl infin// filtering techniques), because of the fact that not only linear parameters (consequents), but also the nonlinear parameters (membership functions) attempt to identify the uncertain behavior of the unknown system. However, the fuzzy identification methods must be robust to data uncertainties and modeling errors to ensure that the fuzzy approximation of unknown system's behavior is optimal in some sense. This study presents a deterministic approach to the robust design of fuzzy models in the presence of unknown but finite uncertainties in the identification data. We consider online identification of an interpretable fuzzy model, based on the robust solution of a regularized least-squares fuzzy parameters estimation problem. The aim is to resolve the difficulties associated with the robust fuzzy identification method due to lack of a priori knowledge about upper bounds on the data uncertainties. The study derives an optimal level of regularization that should be provided to ensure the robustness of fuzzy identification strategy by achieving an upper bound on the value of energy gain from data uncertainties and modeling errors to the estimation errors. A time-domain feedback analysis of the proposed identification approach is carried out with emphasis on stability, robustness, and steady-state issues. The simulation studies are provided to show the superiority of the proposed fuzzy estimation over the classical estimation methods.     

On the stability issues of linear Takagi-Sugeno fuzzy models

Stability issues of linear Takagi-Sugeno (TS) fuzzy models (1985, 1992) are investigated. We first propose a systematic way of searching for a common matrix, which, in turn, is related to stability for N subsystems that are under a pairwise commutative assumption. The robustness issue under uncertainty in each subsystem is then considered. We then show that the pairwise commutative assumption can, in fact, be relaxed by a similar approach as that for uncertainty. The result is applicable to a rather broad class of TS models, which are nonHurwitz and/or nonpairwise commutative     

Passive fuzzy controller design via observer feedback for stochastic Takagi-Sugeno fuzzy models with multiplicative noises

This paper investigates the fuzzy control problem of a class of nonlinear continuous-time stochastic systems with achieving the passivity performance. A model-based observer feedback fuzzy control utilizing the concept of so-called parallel distributed compensation (PDC) is employed to stabilize the class of nonlinear stochastic systems that are represented by the Takagi-Sugeno (T-S) fuzzy models. Based on the Lyapunov criteria, the Linear Matrix Inequality (LMI) technique is used to synthesize the observer feedback fuzzy controller design such that the closed-loop system satisfies stability and passivity constraints, simultaneously. Finally, a numerical example is given to demonstrate the applicability and effectiveness of the proposed design method.     

Learning interpretable fuzzy inference systems with FisPro

Fuzzy inference systems (FIS) are likely to play a significant part in system modeling, provided that they remain interpretable following learning from data. The aim of this paper is to set up some guidelines for interpretable FIS learning, based on practical experience with fuzzy modeling in various fields. An open source software system called FisPro has been specifically designed to provide generic tools for interpretable FIS design and learning. It can then be extended with the addition of new contributions. This work presents a global approach to design data-driven FIS that satisfy certain interpretability and accuracy criteria. It includes fuzzy partition generation, rule learning, input space reduction and rule base simplification. The FisPro implementation is discussed and illustrated through several detailed case studies.     

基于Takagi-Sugeno模糊双线性模型的连续搅拌反应釜H∞控制

本文研究了一类连续搅拌反应釜(CSTR)系统的H1控制问题. 系统中的非线性动态特性可采用Takagi-Sugeno(T-S)模糊双线性模型进行描述. 通过引入两个自由矩阵, 给出一个新的保证闭环模糊双线性系统在H1性能指标下全局渐近稳定的充分条件和控制器设计方法, 并且该条件最终可归结为求解一组线性矩阵不等式的可行性问题. CSTR系统的仿真结果表明设计方法的有效性.     

Stability analysis of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays.

This correspondence investigates the global exponential stability problem of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays (TSFDCNNs). Based on the Lyapunov-Krasovskii functional theory and linear matrix inequality technique, a less conservative delay-dependent stability criterion is derived to guarantee the exponential stability of TSFDCNNs. By constructing a Lyapunov-Krasovskii functional, the supplementary requirement that the time derivative of time-varying delays must be smaller than one is released in the proposed delay-dependent stability criterion. Two illustrative examples are provided to verify the effectiveness of the proposed results.     

Stable nonlinear controller design for a Takagi-Sugeno fuzzy model

This paper proposes another adaptive control scheme for nonlinear systems using a Takagi-Sugeno fuzzy model. Takagi-Sugeno fuzzy models have been widely used to identify the structures and parameters of unknown or partially known plants, and to control nonlinear systems. This scheme shows a good approximation capability by the fuzzy blending of local dynamics. Since a Takagi-Sugeno fuzzy model is a nonlinear system in nature, and its parameters are not linearly parameterized, it is difficult to design an adaptive controller using conventional design methods for adaptive controllers which are derived from linearly parameterized systems. In this paper, the functional form of the local dynamics are assumed to be known, but the corresponding parameters are unknown. This additional information about system nonlinearity makes it possible to design an adaptive controller for a nonlinearly parameterized system. The control law is similar to that of a conventional adaptive control technique, while its parameter-update rule is based on the local search method. A parameter-update law is derived so that the time-derivative of the Lyapunov function is negative in the region of interest. Simulation results have shown that this adaptive controller is capable of a good performance. This work was presented in part at the Fifth International Symposium on Artificial Life and Robotics, Oita, Japan, January 26–28, 2000     

Type-1 and Type-2 effective Takagi-Sugeno fuzzy models for decentralized control of multi-input-multi-output processes

Effective model is a novel tool for decentralized controller design to handle the interconnected interactions in a multi-input-multi-output (MIMO) process. In this paper, Type-1 and Type-2 effective Takagi-Sugeno fuzzy models (ETSM) are investigated. By means of the loop pairing criterion, simple calculations are given to build Type-1/Type-2 ETSMs which are used to describe a group of non-interacting equivalent single-input-single-output (SISO) systems to represent an MIMO process, consequently the decentralized controller design can be converted to multiple independent single-loop controller designs, and enjoy the well-developed linear control algorithms. The main contributions of this paper are: i) Compared to the existing T-S fuzzy model based decentralized control methods using extra terms to characterize interactions, ETSM is a simple feasible alternative; ii) Compared to the existing effective model methods using linear transfer functions, ETSM can be carried out without requiring exact mathematical process functions, and lays a basis to develop robust controllers since fuzzy system is powerful to handle uncertainties; iii) Type-1 and Type-2 ETSMs are presented under a unified framework to provide objective comparisons. A nonlinear MIMO process is used to demonstrate the ETSMs’ superiority over the effective transfer function (ETF) counterparts as well as the evident advantage of Type-2 ETSMs in terms of robustness. A multi-evaporator refrigeration system is employed to validate the practicability of the proposed methods.     

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.     

Stability analysis and design of Takagi-Sugeno fuzzy systems

This work presents stable composite control criteria for multivariable Takagi-Sugeno (T-S) fuzzy systems. On the basis of the linear matrix inequality (LMI) control strategy and parametric optimization, the composite fuzzy control algorithms are derived. Unlike earlier studies of fuzzy control systems on an LMI framework, this investigation develops a supervisory control approach, such that a fuzzy controller can be synthesized more efficiently. Moreover, a robust control scheme is applied to the T-S fuzzy model with parametric uncertainties. The sufficient conditions are deduced in the form of reduced LMIs and adaptive tuning rules. Finally, numeric simulations are given to validate the proposed approach.     

执行器饱和T-S模糊系统的鲁棒耗散容错控制

研究了一类执行器饱和状态变时滞T-S模糊系统的鲁棒容错控制问题. 通过时滞相关Lyapunov函数和对状态的椭球域约束, 基于线性矩阵不等式技术, 提出了非线性系统稳定的不变集条件和模糊鲁棒耗散容错控制器存在的充分条件. 控制方案的设计结果不仅为执行器饱和状态变时滞T-S模糊系统的无源控制和H1鲁棒控制建立了统一框架, 而且保证了闭环控制系统对执行器故障的稳定性和容错性. 最后以时滞倒车系统的控制仿真验证了方法 的有效性.     

一种新的XML编码方案

提出了配比查询的概念,分析了现有XML编码方案在应用于配比查询时的不足,提出了一种新的XML编码方案,并给出了相应的查询算法。     

Robust stability of impulsive Takagi-Sugeno fuzzy systems with parametric uncertainties

This paper presents a kind of time-varying impulsive Takagi-Sugeno (T-S) fuzzy model with parametric uncertainties in which each subsystem of the model is time-varying. Several robust stabilities of time-varying systems with parametric uncertainties, such as general robust stability, robustly asymptotical stability and exponential stability, are studied using uniformly positive definite matrix functions and the Lyapunov method. Specifically, robust stability conditions of time-invariant impulsive T-S fuzzy systems are also derived in the formulation of quasi-linear matrix inequalities (QLMIs) and an iterative LMIs algorithm is designed for solving QLMIs. Finally, a unified chaotic system with continuous periodic switch and a unified time-invariant chaotic system are used for demonstrating the effectiveness of our respective results.     

Local and global bifurcations in simple Takagi-Sugeno fuzzy systems

The relevance of bifurcation analysis in Takagi-Sugeno (T-S) fuzzy systems is emphasized mainly through examples. It is demonstrated that even the most simple cases can show a great variety of behaviors. To understand the richness of asymptotic dynamics one can find in T-S systems, a methodology is proposed by invoking bifurcation theory. Several local and global bifurcations (some of them, degenerate) are detected and summarized in the corresponding bifurcation diagrams. It is claimed,that this kind of careful analysis could help to cope with some criticism raised regarding the blind use of fuzzy systems     

一类T-S模糊控制系统的稳定性分析及设计

研究了一类输入采用双交叠模糊分划的T-S模糊控制系统稳定性分析及控制器设计问题.基于分段模糊Lyapunov函数,提出了一个新的判定开环T-S模糊系统稳定性的充分条件,该方法只需在各个模糊区间里满足模糊Lyapunov方法中的条件,其保守性比公共Lyapunov函数法和分段Lyapunov函数法的保守性更低.运用并行分布补偿法(PDC)进一步探讨了闭环T-S模糊控制系统的稳定性分析问题并设计了模糊控制器.最后,一个仿真示例说明了本文方法的有效性.