Showing papers in "IEEE Transactions on Fuzzy Systems in 2016"
TL;DR: The definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature are reviewed and the relationships between them are analyzed.
Abstract: In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.
386 citations
TL;DR: This paper investigates an adaptive fuzzy tracking control design problem for single-input and single-output uncertain nonstrict feedback nonlinear systems and proposes both adaptive fuzzy state feedback and observer-based output feedback control designs.
Abstract: This paper investigates an adaptive fuzzy tracking control design problem for single-input and single-output uncertain nonstrict feedback nonlinear systems. For the cases of the states measurable and the states immeasurable, fuzzy logic systems are separately adopted to approximate the unknown nonlinear functions or model the uncertain nonlinear systems. In the unified framework of adaptive backstepping control design, both adaptive fuzzy state feedback and observer-based output feedback control design schemes are proposed. The stability of the closed-loop systems is proved by using Lyapunov function theory. The simulation examples are provided to confirm the effectiveness of the proposed control methods.
382 citations
TL;DR: In this paper, a hybrid fuzzy adaptive output feedback control design approach is proposed for a class of multiinput and multioutput strict-feedback nonlinear systems with unknown time-varying delays, unmeasured states, and input saturation.
Abstract: In this paper, a hybrid fuzzy adaptive output feedback control design approach is proposed for a class of multiinput and multioutput strict-feedback nonlinear systems with unknown time-varying delays, unmeasured states, and input saturation. First, fuzzy logic systems are employed to approximate unknown nonlinear functions in the system. Next, a smooth function is used to approximate the input saturation and an adaptive fuzzy state observer is constructed to solve the problem of unmeasured states. Based on the designed adaptive fuzzy state observer, a serial-parallel estimation model is established. By applying adaptive fuzzy dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial–parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws is developed based on Lyapunov–Krasovskii functional. It is proved that all variables of the closed-loop system are bounded and the system outputs can follow the given bounded reference signals as close as possible. A simulation example is provided to further show the effectiveness of this novel control scheme.
366 citations
TL;DR: An adaptive fuzzy optimal control design is addressed for a class of unknown nonlinear discrete-time systems that contain unknown functions and nonsymmetric dead-zone and can be proved based on the difference Lyapunov function method.
Abstract: In this paper, an adaptive fuzzy optimal control design is addressed for a class of unknown nonlinear discrete-time systems. The controlled systems are in a strict-feedback frame and contain unknown functions and nonsymmetric dead-zone. For this class of systems, the control objective is to design a controller, which not only guarantees the stability of the systems, but achieves the optimal control performance as well. This immediately brings about the difficulties in the controller design. To this end, the fuzzy logic systems are employed to approximate the unknown functions in the systems. Based on the utility functions and the critic designs, and by applying the backsteppping design technique, a reinforcement learning algorithm is used to develop an optimal control signal. The adaptation auxiliary signal for unknown dead-zone parameters is established to compensate for the effect of nonsymmetric dead-zone on the control performance, and the updating laws are obtained based on the gradient descent rule. The stability of the control systems can be proved based on the difference Lyapunov function method. The feasibility of the proposed control approach is further demonstrated via two simulation examples.
366 citations
TL;DR: Two approaches are developed for reliable fuzzy static output feedback controller design of the underlying fuzzy PDE systems and it is shown that the controller gains can be obtained by solving a set of finite linear matrix inequalities based on the finite-difference method in space.
Abstract: This paper investigates the problem of output feedback robust $\mathscr{H}_{\infty }$ control for a class of nonlinear spatially distributed systems described by first-order hyperbolic partial differential equations (PDEs) with Markovian jumping actuator faults. The nonlinear hyperbolic PDE systems are first expressed by Takagi–Sugeno fuzzy models with parameter uncertainties, and then, the objective is to design a reliable distributed fuzzy static output feedback controller guaranteeing the stochastic exponential stability of the resulting closed-loop system with certain $\mathscr{H}_{\infty }$ disturbance attenuation performance. Based on a Markovian Lyapunov functional combined with some matrix inequality convexification techniques, two approaches are developed for reliable fuzzy static output feedback controller design of the underlying fuzzy PDE systems. It is shown that the controller gains can be obtained by solving a set of finite linear matrix inequalities based on the finite-difference method in space. Finally, two examples are presented to demonstrate the effectiveness of the proposed methods.
336 citations
TL;DR: The problem of fuzzy observer-based controller design is investigated for nonlinear networked control systems subject to imperfect communication links and parameter uncertainties and the proposed method can ensure that the resulting closed-loop system is stochastically stable with the predefined disturbance attenuation performance.
Abstract: The problem of fuzzy observer-based controller design is investigated for nonlinear networked control systems subject to imperfect communication links and parameter uncertainties. The nonlinear networked control systems with parameter uncertainties are modeled through an interval type-2 (IT2) Takagi–Sugeno (T-S) model, in which the uncertainties are handled via lower and upper membership functions. The measurement loss occurs randomly, both in the sensor-to-observer and the controller-to-actuator communication links. Specially, a novel data compensation strategy is adopted in the controller-to-actuator channel. The observer is designed under the unmeasurable premise variables case, and then, the controller is designed with the estimated states. Moreover, the conditions for the existence of the controller can ensure that the resulting closed-loop system is stochastically stable with the predefined disturbance attenuation performance. Two examples are provided to illustrate the effectiveness of the proposed method.
248 citations
TL;DR: F fuzzy logic system is introduced to approximate the unknown nonlinear dynamics, and adaptive high-gain observer is designed to estimate the unmeasured states and it is proved that all the signals in the multiagent systems are semiglobally uniformly ultimately bounded.
Abstract: In this paper, the consensus tracking control problem of second-order multiagent systems with unknown nonlinear dynamics, immeasurable states, and disturbances is investigated. The nonlinear dynamics in multiagent systems do not satisfy the matched condition. In this paper, fuzzy logic system is introduced to approximate the unknown nonlinear dynamics, and adaptive high-gain observer is designed to estimate the unmeasured states. Based on backstepping approach and Lyapunov theory, a new adaptive fuzzy distributed controller is proposed for each agent only using the information of itself and its neighbors. Then the consensus tracking is achieved under the designed distributed controller. Moreover, it is proved that all the signals in the multiagent systems are semiglobally uniformly ultimately bounded, and the consensus tracking error converges to a small neighborhood of the origin that can be designed as small as possible. Finally, the simulation result illustrates the effectiveness of the designed controller.
240 citations
TL;DR: A new adaptive sliding mode controller based on system output is presented to guarantee that the closed-loop system is uniformly ultimately bounded.
Abstract: In this paper, a novel adaptive sliding mode controller is designed for Takagi–Sugeno (T–S) fuzzy systems with actuator saturation and system uncertainty. By the delta operator approach, the discrete-time nonlinear system is described by a T–S fuzzy model with unmeasurable state. By singular value decomposition of system input matrix, a reduced-order system is obtained for the design of sliding mode surface. A new adaptive sliding mode controller based on system output is presented to guarantee that the closed-loop system is uniformly ultimately bounded. Four examples are provided to illustrate the effectiveness and applicability of the proposed control scheme.
231 citations
TL;DR: It is proved that all the signals of the closed-loop system are the semiglobal uniformly ultimately bounded, and the tracking error is made within a small neighborhood around zero.
Abstract: In this paper, an adaptive fuzzy controller is constructed for a class of nonlinear discrete-time systems with unknown functions and bounded disturbances. The main characteristics of the systems are that they take into account the effect of discrete-time dead zone and the system states are not required to be measurable. The stability problem of this class of systems is for the first time to be addressed in this paper. Due to the unavailability of the states and the presence of the discrete-time dead zone, the controller design becomes more difficult. To stabilize the uncertain nonlinear discrete-time systems, the fuzzy logic systems are used to approximate the unknown functions, a fuzzy state observer is designed to estimate the immeasurable states, and the effect caused by discrete-time dead zone can be solved via establishing an adaptation auxiliary signal. Based on the Lyapunov approach, it is proved that all the signals of the closed-loop system are the semiglobal uniformly ultimately bounded, and the tracking error is made within a small neighborhood around zero. The feasibility of the developed control scheme is verified via two simulation examples.
182 citations
TL;DR: It is shown that the stability and tracking performances of the closed-loop system can be achieved even in the presence of unknown non linear faults, and the FTC scheme can handle the nonaffine nonlinear faults effectively.
Abstract: This paper studies the fuzzy adaptive output feedback fault-tolerant control (FTC) problem for a class of single-input and single-output uncertain nonlinear systems with time-varying nonaffine nonlinear faults in strict-feedback form. In the design procedure, filtered signals are adopted to circumvent algebraic loop problems on implementing the usual controllers. By using fuzzy logic systems to approximate the unknown nonlinearity effects and changes in model dynamics due to faults, a fuzzy state observer is first presented to estimate the unmeasured states. Based on the online estimating information from the adaptive mechanism, an observer-based dynamic output feedback fault-tolerant controller is designed via the backstepping technique. It is shown that the stability and tracking performances of the closed-loop system can be achieved even in the presence of unknown nonlinear faults. In comparison with the existing approaches, the FTC scheme can handle the nonaffine nonlinear faults effectively. Finally, a simulation example is included to validate the advantages of the proposed approaches.
160 citations
TL;DR: The event-based sliding-mode control (ESMC) is designed for each linear subsystem of the global fuzzy model first, and the conditions for “fuzzily” amalgamated ESMC are discussed to stabilize theglobal fuzzy model.
Abstract: This paper studies the aperiodic sampled-data control for the sliding-mode control (SMC) scheme of fuzzy systems with communication-induced delays via the event-triggered method. In practice, it is impossible to update control in continuous manner; thus, an event-based control technique has become popular with the advantage that the control task is executed only if it is triggered by an event. In this paper, the event-based sliding-mode control (ESMC) is designed for each linear subsystem of the global fuzzy model first. Then, the conditions for “fuzzily” amalgamated ESMC are discussed to stabilize the global fuzzy model. This ensures that the SMC is executed only when necessary. Furthermore, the results are extended to the fuzzy systems with communication-induced delays. Finally, case studies are carried out to demonstrate the effectiveness of the derived results.
TL;DR: A novel adaptive fuzzy control scheme is presented via the backstepping technique that guarantees that all the signals of the closed-loop system are semiglobally uniformly bounded in probability, and the tracking error converges to a neighborhood of the origin in the sense of mean quantic value.
Abstract: This paper addresses the problem of adaptive fuzzy control for a class of stochastic pure-feedback nonlinear systems with unknown direction hysteresis. Compared with the existing researches on hysteresis problem, the stochastic disturbances and the unknown hysteresis are simultaneously considered in the pure-feedback systems. In addition, the hysteresis parameters as well as the direction of hysteresis are unknown. By introducing an auxiliary virtual controller and employing the new properties of Nussbaum function, the major technique difficulty arising from the unknown direction hysteresis is overcome. Based on the fuzzy logic system's online approximation capability, a novel adaptive fuzzy control scheme is presented via the backstepping technique. It is shown that the proposed control scheme guarantees that all the signals of the closed-loop system are semiglobally uniformly bounded in probability, and the tracking error converges to a neighborhood of the origin in the sense of mean quantic value. Finally, simulation results further demonstrate the effectiveness of the proposed control scheme.
TL;DR: This paper proposes three different methods to build preaggregation functions and experimentally shows that in fuzzy rule-based classification systems, the results obtained when applying the fuzzy reasoning methods obtained using two classical averaging operators such as the maximum and the Choquet integral are improved.
Abstract: In this paper, we introduce the notion of preaggregation function. Such a function satisfies the same boundary conditions as an aggregation function, but, instead of requiring monotonicity, only monotonicity along some fixed direction (directional monotonicity) is required. We present some examples of such functions. We propose three different methods to build preaggregation functions. We experimentally show that in fuzzy rule-based classification systems, when we use one of these methods, namely, the one based on the use of the Choquet integral replacing the product by other aggregation functions, if we consider the minimum or the Hamacher product t-norms for such construction, we improve the results obtained when applying the fuzzy reasoning methods obtained using two classical averaging operators such as the maximum and the Choquet integral.
TL;DR: A novel adaptive fuzzy output feedback tracking control design method with the parameters adaptation laws is developed and the stability of the closed-loop system and the convergence of the tracking error are proved based on Lyapunov function and the average dwell-time methods.
Abstract: This paper studies adaptive fuzzy output feedback tracking control problem for nonstrict-feedback switched nonlinear systems. The switched systems under consideration contain unknown nonlinearities, unmeasured states, and unknown deadzones. Fuzzy logic systems are utilized to approximate the unknown nonlinearities, and a switched fuzzy state observer is designed, and thus, the immeasurable states are estimated via it. In the framework of observer-based output feedback control, and by using the certainty equivalence deadzone inverse, a novel adaptive fuzzy output feedback control design method with the parameters adaptation laws is developed. The stability of the closed-loop system and the convergence of the tracking error are proved based on Lyapunov function and the average dwell-time methods. Two simulation examples are provided to check the effectiveness of the proposed approach.
TL;DR: This paper identifies two new complete, distributive lattices over the unit disc of the complex plane and explores interpretations of them based on fuzzy antonyms and negations in Pythagorean fuzzy sets.
Abstract: Complex fuzzy logic is a new multivalued logic system that has emerged in the last decade. At this time, there are a limited number of known instances of complex fuzzy logic, and only a partial exploration of their properties. There has also been relatively little progress in developing interpretations of complex-valued membership grades. In this paper, we address both problems by examining the recently developed Pythagorean fuzzy sets (a generalization of intuitionistic fuzzy sets). We first characterize two lattices that have been suggested for Pythagorean fuzzy sets and then extend these results to the unit disc of the complex plane. We thereby identify two new complete, distributive lattices over the unit disc, and explore interpretations of them based on fuzzy antonyms and negations.
TL;DR: A Max-Min theorem is provided in order to guarantee the saddle-point Nash equilibrium, and when the system dynamics is described by a linear uncertain differential equation and the performance index function is quadratic, the existence of saddle- point Nash equilibrium is obtained via the solvability of a corresponding Riccati equation.
Abstract: Uncertain differential game investigates interactive decision making of players over time, and the system dynamics is described by an uncertain differential equation. This paper goes further to study the two-player zero-sum uncertain differential game. In order to guarantee the saddle-point Nash equilibrium, a Max–Min theorem is provided. Furthermore, when the system dynamics is described by a linear uncertain differential equation and the performance index function is quadratic, the existence of saddle-point Nash equilibrium is obtained via the solvability of a corresponding Riccati equation. Finally, a resource extraction problem is analyzed by using the theory proposed in this paper.
TL;DR: A new mode-dependent average dwell time (MDADT) switching property is proposed, which is different from the existing one in the literature, and the stabilization condition under such MDADT switching signals is established for the switched nonlinear systems with possibly all unstable subsystems.
Abstract: This paper is concerned with the control problem for a class of switched nonlinear systems possibly composed of all unstable modes by using time-controlled switching signals. To tackle the problem, a new mode-dependent average dwell time (MDADT) switching property is proposed, which is different from the existing one in the literature. Then, the stabilization condition under such MDADT switching signals is established for the switched nonlinear systems with possibly all unstable subsystems. By proposing a class of time-scheduled multiple quadratic Lyapunov function and applying T–S fuzzy models to represent the underlying nonlinear subsystems, numerically easily verified stabilization conditions are further derived in the form of linear matrix inequalities. A numerical example is finally provided to illustrate the effectiveness of the obtained theoretical results.
TL;DR: A weighted piecewise-fuzzy observer-based residual generator is proposed, aiming at achieving an optimal integration of residual evaluation and threshold computation into FD systems.
Abstract: The main focus of this paper is on the analysis and integrated design of $\mathcal {L}_2$ observer-based fault detection (FD) systems for discrete-time nonlinear industrial processes. To gain a deeper insight into this FD framework, the existence condition is introduced first. Then, an integrated design of $\mathcal {L}_2$ observer-based FD approach is realized by solving the proposed existence condition with the aid of Takagi–Sugeno fuzzy dynamic modeling technique and piecewise-fuzzy Lyapunov functions. Most importantly, a weighted piecewise-fuzzy observer-based residual generator is proposed, aiming at achieving an optimal integration of residual evaluation and threshold computation into FD systems. The core of this approach is to make use of the knowledge provided by fuzzy models of each local region and then to weight the local residual signal by means of different weighting factors. In comparison with the standard norm-based fuzzy observer-based FD methods, the proposed scheme may lead to a significant improvement of the FD performance. In the end, the effectiveness of the proposed method is verified by a numerical example and a case study on the laboratory setup of continuous stirred tank heater plant.
TL;DR: A novel IT2 switched output feedback controller is designed to ensure that the closed-loop system is asymptotically stable with an H∞ performance and a mass-spring-damping system is proposed to show the feasibility and the merit of the proposed scheme over the other existing ones.
Abstract: This paper investigates the dynamic output feedback control problem for interval type-2 (IT2) fuzzy systems. A switched output feedback controller, which depends on the values of membership functions, is constructed. The membership functions of IT2 fuzzy systems contain parameter uncertainties and are different from the type-1 Takagi–Sugeno fuzzy systems. Based on the IT2 fuzzy set theory, the parameter uncertainties can be effectively obtained by upper and lower membership functions. A novel IT2 switched output feedback controller is designed to ensure that the closed-loop system is asymptotically stable with an $H_{\infty }$ performance. Finally, a mass–spring–damping system is proposed to show the feasibility and the merit of the proposed scheme over the other existing ones.
TL;DR: It is shown that the new stability and stabilization criteria can provide a larger upper bound of the sampling interval than some existing ones in the literature.
Abstract: In this paper, we investigate the problem of stability and stabilization for sampled-data fuzzy systems with state quantization. By using an input delay approach, the sampled-data fuzzy systems with state quantization are transformed into a continuous-time system with a delay in the state. The transformed system contains nondifferentiable time-varying state delay. Based on some integral techniques, some new stability and stabilization criteria are first proposed by a modified Lyapunov functional. Furthermore, in the case of no quantization, some new stability and stabilization criteria are also obtained. It is shown that the new stability and stabilization criteria can provide a larger upper bound of the sampling interval than some existing ones in the literature. Two simulation examples are given to show the effectiveness of the proposed design method.
TL;DR: Numerical results demonstrate that the eT2Class produces more reliable classification rates, while retaining more compact and parsimonious rule base than state-of-the-art EFCs recently published in the literature.
Abstract: Evolving fuzzy classifiers (EFCs) have achieved immense success in dealing with nonstationary data streams because of their flexible characteristics. Nonetheless, most real-world data streams feature highly uncertain characteristics, which cannot be handled by the type-1 EFC. A novel interval type-2 fuzzy classifier, namely evolving type-2 classifier (eT2Class), is proposed in this paper, which constructs an evolving working principle in the framework of interval type-2 fuzzy system. The eT2Class commences its learning process from scratch with an empty or initially trained rule base, and its fuzzy rules can be automatically grown, pruned, recalled, and merged on the fly referring to summarization power and generalization power of data streams. In addition, the eT2Class is driven by a generalized interval type-2 fuzzy rule, where the premise part is composed of the multivariate Gaussian function with an uncertain nondiagonal covariance matrix, while employing a subset of the nonlinear Chebyshev polynomial as the rule consequents. The efficacy of the eT2Class has been rigorously assessed by numerous real-world and artificial study cases, benchmarked against state-of-the-art classifiers, and validated through various statistical tests. Our numerical results demonstrate that the eT2Class produces more reliable classification rates, while retaining more compact and parsimonious rule base than state-of-the-art EFCs recently published in the literature.
TL;DR: An overview of freely available and open-source fuzzy systems software is presented in order to provide a well-established framework that helps researchers to find existing proposals easily and to develop well-founded future work.
Abstract: Fuzzy systems have been used widely thanks to their ability to successfully solve a wide range of problems in different application fields. However, their replication and application require a high level of knowledge and experience. Furthermore, few researchers publish the software and/or source code associated with their proposals, which is a major obstacle to scientific progress in other disciplines and in industry. In recent years, most fuzzy system software has been developed in order to facilitate the use of fuzzy systems. Some software is commercially distributed, but most software is available as free and open-source software, reducing such obstacles and providing many advantages: quicker detection of errors, innovative applications, faster adoption of fuzzy systems, etc. In this paper, we present an overview of freely available and open-source fuzzy systems software in order to provide a well-established framework that helps researchers to find existing proposals easily and to develop well-founded future work. To accomplish this, we propose a two-level taxonomy, and we describe the main contributions related to each field. Moreover, we provide a snapshot of the status of the publications in this field according to the ISI Web of Knowledge. Finally, some considerations regarding recent trends and potential research directions are presented.
TL;DR: The concept of transfer learning is applied to prototype-based fuzzy clustering (PFC) and the idea of leveraging knowledge from the source domain is exploited to develop a set of transfer PFC algorithms that demonstrate effectiveness in comparison with both the original P FC algorithms and the related clustering algorithms like multitask clustering and coclustering.
Abstract: Traditional prototype-based clustering methods, such as the well-known fuzzy c-means (FCM) algorithm, usually need sufficient data to find a good clustering partition. If available data are limited or scarce, most of them are no longer effective. While the data for the current clustering task may be scarce, there is usually some useful knowledge available in the related scenes/domains. In this study, the concept of transfer learning is applied to prototype-based fuzzy clustering (PFC). Specifically, the idea of leveraging knowledge from the source domain is exploited to develop a set of transfer PFC algorithms. First, two representative PFC algorithms, namely, FCM and fuzzy subspace clustering, have been chosen to incorporate with knowledge leveraging mechanisms to develop the corresponding transfer clustering algorithms based on an assumption that there are the same number of clusters between the target domain (current scene) and the source domain (related scene). Furthermore, two extended versions are also proposed to implement the transfer learning for the situation that there are different numbers of clusters between two domains. The novel objective functions are proposed to integrate the knowledge from the source domain with the data in the target domain for the clustering in the target domain. The proposed algorithms have been validated on different synthetic and real-world datasets. Experimental results demonstrate their effectiveness in comparison with both the original PFC algorithms and the related clustering algorithms like multitask clustering and coclustering.
TL;DR: Through stochastic analysis and Lyapunov functional approach, sufficient conditions are established under which the filtering error dynamics is exponentially mean-square stable with a prespecified H∞ performance.
Abstract: This paper is concerned with the nonfragile $H_\infty$ filtering problem for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with both randomly occurring gain variations (ROGVs) and channel fadings. the phenomenon of the ROGVs is introduced into the system model so as to account for the parameter fluctuations occurring during the filter implementation. Two sequences of random variables obeying the Bernoulli distribution are employed to describe the phenomenon of the ROGVs bounded by prescribed norms. In addition, the Rice fading model is utilized to describe the phenomena of channel fadings, where the occurrence probabilities of the random channel coefficients are allowed to time varying. Through stochastic analysis and Lyapunov functional approach, sufficient conditions are established under which the filtering error dynamics is exponentially mean-square stable with a prespecified $H_\infty$ performance. The set of the desired nonfragile $H_\infty$ filters is characterized by solving a convex optimization problem via the semidefinite programming method. An illustrative example is given to show the usefulness and effectiveness of the proposed design method in this paper.
TL;DR: A recurrent fuzzy neural cerebellar model articulation network (RFNCMAN) fault-tolerant control of a six-phase permanent magnet synchronous motor (PMSM) position servo drive is proposed and implemented in a 32-bit floating-point DSP.
Abstract: A recurrent fuzzy neural cerebellar model articulation network (RFNCMAN) fault-tolerant control of a six-phase permanent magnet synchronous motor (PMSM) position servo drive is proposed in this study. First, the fault detection and operating decision method of the six-phase PMSM position servo drive is developed. Then, an ideal computed torque controller is designed for the tracking of the rotor position reference command. In general, it is impossible to design an ideal computed control law owing to the uncertainties of the six-phase PMSM position servo drive, which are difficult to know in advance for practical applications. Therefore, the RFNCMAN, which combined the merits of a recurrent fuzzy cerebellar model articulation network and a recurrent fuzzy neural network, is proposed to estimate a nonlinear equation included in the ideal computed control law with a robust compensator designed to compensate the minimum reconstructed error. Furthermore, the adaptive learning algorithm for the online training of the RFNCMAN is derived using the Lyapunov stability to guarantee the closed-loop stability. Finally, the proposed RFNCMAN fault-tolerant control system is implemented in a 32-bit floating-point DSP. The effectiveness of the six-phase PMSM position servo drive using the proposed intelligent fault-tolerant control system is verified by some experimental results.
TL;DR: It will be theoretically shown that the FOU gives the opportunity to the SIT2-FLC to generate commonly employed nonlinear control curves while also providing a certain degree of robustness which cannot be accomplished by its T1 counterpart.
Abstract: Recent results on fuzzy control have shown that interval type-2 (IT2) fuzzy logic controllers (FLCs) might achieve better control performance due to the additional degree of freedom provided by the footprint of uncertainty (FOU) in their IT2 fuzzy sets. However, the design and robust stability analysis of the IT2-FLCs are still challenging problems due to their relatively more complex internal structure. In this paper, we will derive the explicitly fuzzy mapping (FM) of a single-input IT2-FLC (SIT2-FLC) to present design methods and investigate its robustness. The analytical information of the IT2-FM will give the opportunity to provide explanations on the roles of the FOU parameters by taking advantage of the well-developed framework of nonlinear control theory. Comparative theoretical explorations will be presented on the differences between the type-1 (T1) FM and IT2-FM to clearly show the role of the FOU on the robust control system performance. It will be proven that the robust stability of the IT2 fuzzy system is guaranteed with the aids of the well-known Popov–Lyapunov method. Moreover, analytical design methods are presented for SIT2-FLCs to generate commonly employed control curves by only tuning the size of the FOUs without a need of an optimization procedure. It will be theoretically shown that the FOU gives the opportunity to the SIT2-FLC to generate commonly employed nonlinear control curves while also providing a certain degree of robustness which cannot be accomplished by its T1 counterpart. The presented results provide theoretical explanations on the role of the FOU on the performance and robustness of the SIT2-FLC.
TL;DR: The proposed scheme has overcome some application limitations existing in the literature and it is shown that the position tracking errors and the parameter estimation errors can remain bounded under the proposed control laws, which are validated by simulation studies.
Abstract: This paper addresses adaptive fuzzy control for multimaster–multislave teleoperation for multiple mobile manipulators carrying a common object in a cooperative manner that subjected to asymmetric time-varying delays and model parameter uncertainties. In the proposed control framework, a novel switched error filtering is designed. By introducing the filtering output in the control torque design, the complete closed-loop master/slave systems are modeled as a special class of switched system that are composed of two subsystems, i.e., the local master (slave) dynamics with well-defined auxiliary variable and the switched error filter subsystem, which is fairly different from the existing subsystem decomposition method. Utilizing the Lyapunov–Krasovskii method, the complete closed-loop master (slave) system is proved to be state-independent input-to-output stable. The proposed scheme has overcome some application limitations existing in the literature. It is shown that the position tracking errors and the parameter estimation errors can remain bounded under the proposed control laws, which are validated by simulation studies.
TL;DR: The modified AHP improves the classification performance not only of the IT2FLS but of all other classifiers as well, and can be implemented as a real clinical decision support system that is useful for medical practitioners.
Abstract: This paper proposes a modification to the analytic hierarchy process (AHP) to select the most informative genes that serve as inputs to an interval type-2 fuzzy logic system (IT2FLS) for cancer classification. Unlike the conventional AHP, the modified AHP allows us to process quantitative factors that are ranking outcomes of individual gene selection methods including t-test, entropy, receiver operating characteristic curve, Wilcoxon test, and signal-to-noise ratio. The IT2FLS is introduced for the classification task due to its great ability for handling nonlinear, noisy, and outlier data, which are common problems in cancer microarray gene expression profiles. An unsupervised learning strategy using the fuzzy c-means clustering is employed to initialize parameters of the IT2FLS. Other classifiers such as multilayer perceptron network, support vector machine, and fuzzy ARTMAP are also implemented for comparisons. Experiments are carried out on three well-known microarray datasets: diffuse large B-cell lymphoma, leukemia cancer, and prostate. Rather than the traditional cross validation, leave-one-out cross-validation strategy is applied for the experiments. Results demonstrate the performance dominance of the IT2FLS against the competing classifiers. More noticeably, the modified AHP improves the classification performance not only of the IT2FLS but of all other classifiers as well. Accordingly, the proposed combination between the modified AHP and IT2FLS is a powerful tool for cancer classification and can be implemented as a real clinical decision support system that is useful for medical practitioners.
TL;DR: By utilizing the backstepping technique and employing the stochastic small-gain theorem, a direct adaptive fuzzy output feedback control scheme is developed that can guarantee that the closed-loop system is input-to-state practically stable in probability.
Abstract: This paper addresses an output feedback stabilization problem for a class of stochastic nonlinear systems with unmodeled dynamics preceded by hysteretic quantized input. To deal with unmeasurable states, a novel state observer that contains the quantized control is introduced. By presenting a new nonlinear decomposition for the hysteretic quantized input, the major technique difficulty coming from the discrete quantized input is overcome. By utilizing the backstepping technique and employing the stochastic small-gain theorem, a direct adaptive fuzzy output feedback control scheme is developed. The proposed design approach can guarantee that the closed-loop system is input-to-state practically stable in probability. Finally, a simulation example verifies the proposed control scheme.
TL;DR: The notion of intuitionistic fuzzy time series to handle the nondeterminism in time series forecasting is given and an intuitionistic-fuzzy-set-based fuzzy timeseries forecasting model is also proposed.
Abstract: Atanassov introduced the notion of intuitionistic fuzzy set as generalization of the fuzzy set, which has been proved to be very useful tool in handling nondeterminacy (hesitation) in the system. In the implementation of fuzzy time series forecasting, nondeterminacy is always neglected without any reason. In this paper, we give the notion of intuitionistic fuzzy time series to handle the nondeterminism in time series forecasting. An intuitionistic fuzzy time series forecasting model is also proposed. The proposed intuitionistic fuzzy time series forecasting method uses intuitionistic fuzzy logical relations on time series data. Performance of the proposed method is verified by applying it on two time series data. The effectiveness of the proposed intuitionistic fuzzy time series forecasting method is verified by comparing the forecasted output with other intuitionistic-fuzzy-set-based fuzzy time series forecasting methods using root-mean-square error and average forecasting error.