In this paper, an adaptive fuzzy-decentralized robust output-feedback-control approach is proposed for a class of large-scale strict-feedback nonlinear systems with the unmeasured states. The large-scale nonlinear systems in this paper are assumed to possess the unstructured uncertainties, unmodeled dynamics, and unknown high-frequency-gain sign. Fuzzy-logic systems are used to approximate the unstructured uncertainties, K-filters are designed to estimate the unmeasured states, and a dynamical signal and a special Nussbaum gain function are introduced into the control design to solve the problem of unknown high-frequency-gain sign and dominate unmodeled uncertainties, respectively. Based on the backstepping design and adaptive fuzzy-control methods, an adaptive fuzzy-decentralized robust output-feedback-control scheme is developed. It is proved that the proposed adaptive fuzzy-control approach can guarantee that all the signals in the closed-loop system are uniformly and ultimately bounded, and the tracking errors converge to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by using simulation results.
This paper investigates the problem of robust H-infinity output-feedback control for a class of nonlinear systems under unreliable communication links. The nonlinear plant is represented by a Takagi-Sugeno (T-S) uncertain fuzzy model, and the communication links between the plant and controller are assumed to be imperfect, i.e., data-packet dropouts occur intermittently, which is often the case in a network environment. Stochastic variables that satisfy the Bernoulli random-binary distribution are adopted to characterize the data-missing phenomenon, and the attention is focused on the design of a piecewise static-output-feedback (SOF) controller such that the closed-loop system is stochastically stable with a guaranteed H-infinity performance. Based on a piecewise Lyapunov function combined with some novel convexifying techniques, the solutions to the problem are formulated in the form of linear matrix inequalities (LMIs). Finally, simulation examples are also provided to illustrate the effectiveness of the proposed approaches.
Based on the adaptive-control technique, this paper deals with the problem of fault-tolerant tracking control for near-space-vehicle (NSV) attitude dynamics. First, Takagi-Sugeno (T-S) fuzzy models are used to describe the NSV attitude dynamics; then, an actuator-fault model is developed. Next, an adaptive fault-tolerant tracking-control scheme is proposed based on the online estimation of actuator faults, in which a compensation control term is introduced in order to reduce the effect of actuator faults. Compared with some existing results of fault-tolerant control (FTC) in nonlinear systems, the technique presented in this paper is not dependent on fault detection and isolation (FDI) mechanism and is easy to implement in aerospace-engineering applications. Finally, simulation results are given to illustrate the effectiveness and potential of the proposed FTC scheme.
Higher order fuzzy logic systems (FLSs), such as interval type-2 FLSs, have been shown to be very well suited to deal with the high levels of uncertainties present in the majority of real-world applications. General type-2 FLSs are expected to further extend this capability. However, the immense computational complexities associated with general type-2 FLSs have, until recently, prevented their application to real-world control problems. This paper aims to address this problem by the introduction of a complete representation framework, which is referred to as zSlices-based general type-2 fuzzy systems. The proposed approach will lead to a significant reduction in both the complexity and the computational requirements for general type-2 FLSs, while it offers the capability to represent complex general type-2 fuzzy sets. As a proof-of-concept application, we have implemented a zSlices-based general type-2 FLS for a two-wheeled mobile robot, which operates in a real-world outdoor environment. We have evaluated the computational performance of the zSlices-based general type-2 FLS, which is suitable for multiprocessor execution. Finally, we have compared the performance of the zSlices-based general type-2 FLS against type-1 and interval type-2 FLSs, and a series of results is presented which is related to the different levels of uncertainty handled by the different types of FLSs.
Robust adaptive-fuzzy-tracking control of a class of uncertain multi-input/multi-output nonlinear systems with coupled interconnections is considered in this paper. Takagi-Sugeno (T-S) fuzzy systems are used to approximate the unknown system functions. A novel adaptive-control scheme is developed on the basis of the so-called "dynamic-surface control" and "minimal-learning parameters" techniques. The proposed scheme has following two key features. First, the number of parameters updated online for each subsystem is reduced to one, and both problems of "curse of dimension" for high-dimensional systems and "explosion of complexity" inherent in the conventional backstepping methods are circumvented. Second, the potential controller-singularity problem in some of the existing adaptive-control schemes with feedback-linearization techniques is overcome. It is shown via Lyapunov theory that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded. Finally, simulation results via two examples are presented to demonstrate the effectiveness and advantages of the proposed scheme.
Interval-valued intuitionistic fuzzy (IVIF) sets are useful to deal with fuzziness inherent in decision data and decision-making processes. The aim of this paper is to develop a nonlinear-programming methodology that is based on the technique for order preference by similarity to ideal solution to solve multiattribute decision-making (MADM) problems with both ratings of alternatives on attributes and weights of attributes expressed with IVIF sets. In this methodology, nonlinear-programming models are constructed on the basis of the concepts of the relative-closeness coefficient and the weighted-Euclidean distance. Simpler auxiliary nonlinear-programming models are further deduced to calculate relative-closeness of IF sets of alternatives to the IVIF-positive ideal solution, which can be used to generate the ranking order of alternatives. The proposed methodology is validated and compared with other similar methods. A real example is examined to demonstrate the applicability and validity of the methodology proposed in this paper.
This paper is devoted to design adaptive sliding-mode controllers for the Takagi-Sugeno (TS) fuzzy system with mismatched uncertainties and exogenous disturbances. The uncertainties in state matrices are mismatched and norm-bounded, while the exogenous disturbances are assumed to be bounded with an unknown bound, which is estimated by a simple and effective adaptive approach. Both state- and static-output-feedback sliding-mode-control problems are considered. In terms of linear-matrix inequalities (LMIs), both sliding surfaces and sliding-mode controllers can be easily obtained via a convex optimization technique. Finally, two simulation examples and a real experiment are utilized to illustrate the applicability and effectiveness of the design procedures proposed in this paper.
In this paper, the robust H ∞ -control problem is investigated for a class of uncertain discrete-time fuzzy systems with both multiple probabilistic delays and multiple missing measurements. A sequence of random variables, all of which are mutually independent but obey the Bernoulli distribution, is introduced to account for the probabilistic communication delays. The measurement-missing phenomenon occurs in a random way. The missing probability for each sensor satisfies a certain probabilistic distribution in the interval. Here, the attention is focused on the analysis and design of H ∞ fuzzy output-feedback controllers such that the closed-loop Takagi-Sugeno (T-S) fuzzy-control system is exponentially stable in the mean square. The disturbance-rejection attenuation is constrained to a given level by means of the H ∞ -performance index. Intensive analysis is carried out to obtain sufficient conditions for the existence of admissible output feedback controllers, which ensures the exponential stability as well as the prescribed H ∞ performance. The cone-complementarity-linearization procedure is employed to cast the controller-design problem into a sequential minimization one that is solved by the semi-definite program method. Simulation results are utilized to demonstrate the effectiveness of the proposed design technique in this paper.
In this paper, the robust H-infinity-control problem is investigated for a class of uncertain discrete-time fuzzy systems with both multiple probabilistic delays and multiple missing measurements. A sequence of random variables, all of which are mutually independent but obey the Bernoulli distribution, is introduced to account for the probabilistic communication delays. The measurement-missing phenomenon occurs in a random way. The missing probability for each sensor satisfies a certain probabilistic distribution in the interval [0 1]. Here, the attention is focused on the analysis and design of H-infinity fuzzy output-feedback controllers such that the closed-loop Takagi-Sugeno (T-S) fuzzy-control system is exponentially stable in the mean square. The disturbance-rejection attenuation is constrained to a given level by means of the H-infinity-performance index. Intensive analysis is carried out to obtain sufficient conditions for the existence of admissible output feedback controllers, which ensures the exponential stability as well as the prescribed H-infinity performance. The cone-complementarity-linearization procedure is employed to cast the controller-design problem into a sequential minimization one that is solved by the semi-definite program method. Simulation results are utilized to demonstrate the effectiveness of the proposed design technique in this paper.
The Choquet and the Sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required. However, their applicability is restricted because of the special operations used in the construction of these integrals. Therefore, we provide a concept of integrals generalizing both the Choquet and the Sugeno case. For functions with values in the nonnegative real numbers, universal integrals are introduced and investigated, which can be defined on arbitrary measurable spaces and for arbitrary monotone measures. For a fixed pseudo-multiplication on the nonnegative real numbers, the smallest and the greatest universal integrals are given. Finally, another construction method for obtaining universal integrals is introduced, and the restriction to the unit interval, i.e., to fuzzy integrals, is considered.
The power-average (PA) operator and the power-ordered-weighted-average (POWA) operator are the two nonlinear weighted-average aggregation tools whose weighting vectors depend on the input arguments. In this paper, we develop a power-geometric (PG) operator and its weighted form, which are on the basis of the PA operator and the geometric mean, and develop a power-ordered-geometric (POG) operator and a power-ordered-weighted-geometric (POWG) operator, which are on the basis of the POWA operator and the geometric mean, and study some of their properties. We also discuss the relationship between the PA and PG operators and the relationship between the POWA and POWG operators. Then, we extend the PG and POWG operators to uncertain environments, i.e., develop an uncertain PG (UPG) operator and its weighted form, and an uncertain power-ordered-weighted-geometric (UPOWG) operator to aggregate the input arguments taking the form of interval of numerical values. Furthermore, we utilize the weighted PG and POWG operators, respectively, to develop an approach to group decision making based on multiplicative preference relations and utilize the weighted UPG and UPOWG operators, respectively, to develop an approach to group decision making based on uncertain multiplicative preference relations. Finally, we apply both the developed approaches to broadband Internet-service selection.
It has been widely pointed out that classical ontology is not sufficient to deal with imprecise and vague knowledge for some real-world applications like personal diabetic-diet recommendation. On the other hand, fuzzy ontology can effectively help to handle and process uncertain data and knowledge. This paper proposes a novel ontology model, which is based on interval type-2 fuzzy sets ( T2FSs ), called type-2 fuzzy ontology ( T2FO ), with applications to knowledge representation in the field of personal diabetic-diet recommendation. The T2FO is composed of 1) a type-2 fuzzy personal profile ontology ( type-2 FPPO ); 2) a type-2 fuzzy food ontology ( type-2 FFO ); and 3) a type-2 fuzzy-personal food ontology ( type-2 FPFO ). In addition, the paper also presents a T2FS-based intelligent diet-recommendation agent ( IDRA ), including 1) T2FS construction; 2) a T2FS-based personal ontology filter ; 3) a T2FS-based fuzzy inference mechanism ; 4) a T2FS-based diet-planning mechanism ; 5) a T2FS-based menu-recommendation mechanism ; and 6) a T2FS-based semantic-description mechanism . In the proposed approach, first, the domain experts plan the diet goal for the involved diabetes and create the nutrition facts of common Taiwanese food. Second, the involved diabetics are requested to routinely input eaten items. Third, the ontology-creating mechanism constructs a T2FO , including a type-2 FPPO , a type-2 FFO , and a set of type-2 FPFOs . Finally, the T2FS-based IDRA retrieves the built T2FO to recommend a personal diabetic meal plan. The experimental results show that the proposed approach can work effectively and that the menu can be provided as a reference for the involved diabetes after diet validation by domain experts.
A novel-function approximator is constructed by combining a fuzzy-logic system with a Fourier series expansion in order to model unknown periodically disturbed system functions. Then, an adaptive backstepping tracking-control scheme is developed, where the dynamic-surface-control approach is used to solve the problem of "explosion of complexity" in the backstepping design procedure, and the time-varying parameter-dependent integral Lyapunov function is used to analyze the stability of the closed-loop system. The semiglobal uniform ultimate boundedness of all closed-loop signals is guaranteed, and the tracking error is proved to converge to a small residual set around the origin. Two simulation examples are provided to illustrate the effectiveness of the control scheme designed in this paper.
Support vector machines (SVMs) is a popular machine learning technique, which works effectively with balanced datasets. However, when it comes to imbalanced datasets, SVMs produce suboptimal classification models. On the other hand, the SVM algorithm is sensitive to outliers and noise present in the datasets. Therefore, although the existing class imbalance learning (CIL) methods can make SVMs less sensitive to class imbalance, they can still suffer from the problem of outliers and noise. Fuzzy SVMs (FSVMs) is a variant of the SVM algorithm, which has been proposed to handle the problem of outliers and noise. In FSVMs, training examples are assigned different fuzzy-membership values based on their importance, and these membership values are incorporated into the SVM learning algorithm to make it less sensitive to outliers and noise. However, like the normal SVM algorithm, FSVMs can also suffer from the problem of class imbalance. In this paper, we present a method to improve FSVMs for CIL (called FSVM-CIL), which can be used to handle the class imbalance problem in the presence of outliers and noise. We thoroughly evaluated the proposed FSVM-CIL method on ten real-world imbalanced datasets and compared its performance with five existing CIL methods, which are available for normal SVM training. Based on the overall results, we can conclude that the proposed FSVM-CIL method is a very effective method for CIL, especially in the presence of outliers and noise in datasets.
This paper addresses the problem of robust fault estimation and fault tolerant control (FTC) for Takagi-Sugeno (T-S) fuzzy systems. A fuzzy-augmented fault estimation observer (AFEO) design is proposed to achieve fault estimation of T-S models with actuator faults. Furthermore, based on the information of online fault estimation, an observer-based dynamic output feedback-fault tolerant controller (DOFFTC) is designed to compensate for the effect of faults by stabilizing the closed-loop system. Sufficient conditions for the existence of both AFEO and DOFFTC are given in terms of linear matrix inequalities. Simulation results of an inverted pendulum system are presented to illustrate the effectiveness of the proposed method.
This paper is concerned with H-infinity-design for a class of networked control systems (NCSs) with multiple state-delays via the Takagi-Sugeno (T-S) fuzzy model. The transfer delays and packet loss that are induced by the limited bandwidth of communication networks are considered. The focus of this paper is on the analysis and design of a full-order H-infinity filter, such that the filtering-error dynamics are stochastically stable, and a prescribed H-infinity attenuation level is guaranteed. Sufficient conditions are established for the existence of the desired filter in terms of linear-matrix inequalities (LMIs). An example is given to illustrate the effectiveness and applicability of the proposed design method.
This paper provides generalized nonquadratic stability conditions for continuous-time nonlinear models in the Takagi-Sugeno (TS) form obtained by sector-nonlinearity approach. Should global quadratic stability fail for a given nonlinear model, the proposed approach allows the obtaining of progressively better estimations of the stability domain via local asymptotic conditions in the form of linear-matrix inequalities (LMIs), which are efficiently solved by convex optimization techniques. Illustrative examples are presented to emphasize the broadening capabilities of the new stability analysis.
In this paper, we propose an index that helps preserve the semantic interpretability of linguistic fuzzy models while a tuning of the membership functions (MFs) is performed. The proposed index is the aggregation of three metrics that preserve the original meanings of the MFs as much as possible while a tuning of their definition parameters is performed. Additionally, rule-selection mechanisms can be used to reduce the model complexity, which involves another important interpretability aspect. To this end, we propose a postprocessing multiobjective evolutionary algorithm that performs rule selection and tuning of fuzzy-rule-based systems with three objectives: accuracy, semantic interpretability maximization, and complexity minimization. We tested our approach on nine real-world regression datasets. In order to analyze the interaction between the fuzzy-rule-selection approach and the tuning approach, these are also individually proved in a multiobjective framework and compared with their respective single-objective counterparts. We compared the different approaches by applying nonparametric statistical tests for pairwise and multiple comparisons, taking into consideration three representative points from the obtained Pareto fronts in the case of the multiobjective-based approaches. Results confirm the effectiveness of our approach, and a wide range of solutions is obtained, which are not only more interpretable but are also more accurate.
We point out some relevant issues that are related to the computing-with-words (CWW) paradigm and argue for an urgent need for a new, nontraditional look at the area, since the traditional approach has resulted in very valuable theoretical research results. However, there is no proper exposure and recognition in other areas to which CWW belongs and can really contribute, notably natural-language processing (NLP), in general, and natural-language understanding (NLU) and natural-language generation (NLG), in particular. First, we present crucial elements of CWW, in particular Zadeh's protoforms, and indicate their power and stress a need to develop new tools to handle more modalities. We argue that CWW also has a high implementation potential and present our approach to linguistic data(base) summaries, which is a very intuitive and human-consistent natural-language-based knowledge-discovery tool. Special emphasis is on the use of Zadeh's protoform (prototypical form) as a general form of a linguistic data summary. We present an extension of our interactive approach, which is based on fuzzy logic and fuzzy database queries, to implement such linguistic summaries. In the main part of the paper, we discuss a close relation between linguistic summarization in the sense considered and some basic ideas and solutions in NLG, thus analyzing possible common elements and an opportunity to use developed tools, as well as some inherent differences and difficulties. Notably, we indicate a close relation of linguistic summaries that are considered to be some type of an extended template-based, and even a simple phrase-based, NLG system and emphasize a possibility to use software that is available in these areas. An important conclusion is also an urgent need to develop new protoforms, thus going beyond the classical ones of Zadeh. For illustration, we present an implementation for a sales database in a computer retailer, thereby showing the power of linguistic summaries, as well as an urgent need for new types of protoforms. Although we use linguistic summaries throughout, our discussion is also valid for CWW in general. We hope that this paper-which presents our personal view and perspective that result from our long-time involvement in both theoretical work in broadly perceived CWW and real-world implementations-will trigger a discussion and research efforts to help find a way out of a strange situation in which, on one hand, one can clearly see that CWW is related to words (language) and computing and, hence, should be part of broadly perceived mainstream computational linguistics, which lack tools to handle imprecision. These tools can be provided by CWW. Yet, CWW is practically unknown to these communities and is not mentioned or cited, and-reciprocally-even the top people in CWW do not refer to the results that are obtained in these areas. We hope that our paper, for the benefit of both the areas, will help bridge this gap that results from a wrong and dangerous fragmentation of break science.
A novel growing-and-pruning (GP) approach is proposed, which optimizes the structure of a fuzzy neural network (FNN). This GP-FNN is based on radial basis function neurons, which have center and width vectors. The structure-learning phase and the parameter-training phase are performed concurrently. The structure-learning approach relies on the sensitivity analysis of the output. A set of fuzzy rules can be inserted or reduced during the learning process. The parameter-training algorithm is implemented using a supervised gradient decent method. The convergence of the GP-FNN-learning process is also discussed in this paper. The proposed method effectively generates a fuzzy neural model with a highly accurate and compact structure. Simulation results demonstrate that the proposed GP-FNN has a self-organizing ability, which can determine the structure and parameters of the FNN automatically. The algorithm performs better than some other existing self-organizing FNN algorithms.