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In this study, we propose an adaptive fuzzy event-triggered control scheme for an autonomous aerial refueling hose system involving uncertainty, an event-triggered mechanism, and actuator failures. The unknown nonlinear function is approximated using the designed fuzzy logic systems. Through introduction of the adaptive compensation scheme, the problem of an infinite number of actuator failures, including partial and complete failures, is solved. In addition, the event-triggered control strategy is designed to achieve vibration suppression while decreasing the communication burden between the controllers and actuators. The stability of the closed-loop system is demonstrated via the Lyapunov direct method. Finally, simulation examples are presented to confirm the validity of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Data-based spatio-temporal modeling has rapidly developed over the past ten years. However, traditional spatio-temporal modeling methods will encounter some uncertainty caused by model reduction. In addition, the established model is complicated and short of linguistic interpretability. In this study, a novel three-dimensional (3-D) fuzzy modeling framework without model reduction is proposed and a new 3-D fuzzy modeling method based on clustering and support vector regression is developed. This method is based on a 3-D fuzzy system that naturally fuses time/space separation and time/space synthesis into a unified framework. Utilizing the machine learning algorithms (clustering and support vector regression), a 3-D fuzzy system is constructed for modeling an unknown nonlinear distributed parameter system. The advantages of the proposed modeling method over the traditional spatio-temporal modeling method are linguistic interpretability and no reliance on model reduction. The proposed modeling method consists of three steps. First, the nearest neighborhood clustering algorithm is used to learn initial structure model of antecedent sets of 3-D fuzzy rules. Then, similarity measure is used to simplify the initial structure via combining similar fuzzy sets and similar fuzzy rules. Finally, a support vector regression algorithm is applied to calculate spatial functions in the consequent sets of 3-D fuzzy rules. The simulation results demonstrate the effectiveness of the proposed modeling method. [ABSTRACT FROM AUTHOR]

The classification problem in the real-world applications always involves uncertainties in both stochastic and fuzzy nature. This paper proposes a classification framework based on the unified probabilistic fuzzy configuration for data with uncertainties in both stochastic and fuzzy nature. The design and tuning procedures are also developed in terms of probability-based performance measure for working in the complex environment. A theoretical analysis is conducted to derive its quantificational model and disclose the interesting features. In addition to a superior performance than the traditional fuzzy method, the proposed method generates probabilistic fuzzy rules that can help users to better understand how the classifier works. This explainable characteristic is crucial for the decision making. Finally, the effectiveness of the proposed classifier will be demonstrated on its application to the Pima Indians Diabetes data and low back pain diagnosis. The satisfactory classification and the explainable characteristic disclose its potential in classification of data with uncertainties. [ABSTRACT FROM AUTHOR]

In practical applications, there are usually complex stochastic and vague uncertainties caused by inherent randomness and unknown dynamics. How to model uncertainty and interpret the modeling result is of significance for practical applications. To address these issues, a new probabilistic fuzzy logic system (PFLS) is proposed based on two-stage Bayesian learning. On the basis of the structure of traditional FLS, the proposed PFLS can be used as probabilistic fuzzy interpreter for complex uncertainty modeling. Specifically, in the training stage, expectation–maximization-based Gaussian mixture model is used to classify given data and learn the corresponding probability distributions, which are further used to generate samples to compensate for the limited given data. Based on Bayesian learning, fuzzy rules are learned by maximizing joint probability distributions of given data and rules. In the later inference stage, Bayesian learning-based probabilistic fuzzy inference is developed to make the activated fuzzy rules best match the input and output data pairs. Through integration with the two-stage Bayesian learning, PFLS can properly handle both vague and stochastic uncertainties, and interpret modeling results with fuzzy rules under maximum likelihood. Experiments based on temperature predictions in complex industrial processes demonstrate the effectiveness of the proposed method. • Propose probabilistic fuzzy logic system to handle stochastic and vague uncertainties. • Develop a method of learning rule base to make the rules best match given data. • Design probabilistic fuzzy inference to make activated rule best match input–output pairs. [ABSTRACT FROM AUTHOR]

Many industrial processes belong to nonlinear distributed parameter systems (DPS) with significant spatio-temporal dynamics. They often work at multiple operating points due to different production and working conditions. To obtain a global model, the direct modeling and experiments in a large operating range are often very difficult. Motivated by the multi-modeling, a fuzzy-based spatio-temporal multi-modeling approach is proposed for nonlinear DPS. To obtain a reasonable operating space division, a priori information and the fuzzy clustering are used to decompose the operating space from coarse scale to fine scale gradually. To reduce the dimension in the local spatio-temporal modeling, the Karhunen–Loève method is used for the space/time separation. Both multi-modeling and space/time separation can reduce the modeling complexity. Finally, to get a smooth global model, a three-domain (3D) fuzzy integration method is proposed. Using the proposed method, the model accuracy will be improved and the experiments become easier. The effectiveness is verified by simulations. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of fuzzy control design for a class of nonlinear distributed parameter systems represented by a cascaded model consisting of a Takagi–Sugeno (T–S) fuzzy ordinary differential equation and a linear first-order hyperbolic partial differential equation (PDE), where the control input affects the entire system through a boundary condition of the PDE. This characteristic makes the PDE subject to an inhomogeneous boundary condition. A state transformation is introduced to make the inhomogeneous boundary condition homogeneous, and a composite Lyapunov function that involves a fuzzy Lyapunov function and an entropy-like Lyapunov function is constructed for the transformed system. Based on this composite Lyapunov function, a sufficient condition for the closed-loop exponential stability of the cascaded system is presented in terms of a set of algebraic linear matrix inequalities in space. Using the sector bound approach and the finite spatial domain, a linear matrix inequality-based fuzzy control design procedure is developed from the obtained stability analysis result. Finally, simulation results on two numerical examples are provided to illustrate the effectiveness and merit of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations (PDEs). Both distributed measurement form and collocated boundary measurement form are considered. A Takagi–Sugeno (T–S) fuzzy PDE model is first applied to accurately represent the semilinear parabolic PDE system. Based on the T–S fuzzy PDE model, two types of fuzzy boundary controllers, which are easily implemented since only boundary actuators are used, are proposed to ensure the exponential stability of the resulting closed-loop system. Sufficient conditions of exponential stabilization are established by employing the Lyapunov direct method and the vector-valued Wirtinger's inequality and presented in terms of standard linear matrix inequalities. Finally, the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of two examples. [ABSTRACT FROM PUBLISHER]

Traditional wavelet system is a two-domain (time and frequency domains) wavelet system (2DWS), which works only in time and frequency domains. The 2DWS is not able to treat time-frequency information and fuzziness simultaneously. For this reason, a three-domain (fuzzy, time, and frequency domains) fuzzy wavelet system (3DFWS) is proposed, where the three-domain mechanism provides a solution to handle fuzzy uncertainties and time-frequency information together. The major advantage of 3DFWS is able to use the prior knowledge via the novel fuzzy domain to analyze uncertain data and signals, which will enhance the potentials of 2DWS. Experimental and simulation studies show that the performance of the proposed 3DFWS is superior to the traditional one for simultaneous processing of time-frequency and fuzziness. [ABSTRACT FROM AUTHOR]

Generation of wind is a very complicated process and influenced by large numbers of unknown factors. A probabilistic fuzzy system based prediction model is designed for the short-term wind speed prediction. By introducing the third probability dimension, the proposed prediction model can capture both stochastic and the deterministic uncertainties, and guarantee a better prediction in complex stochastic environment. The effectiveness of this intelligent wind speed prediction model is demonstrated by the simulations on a group of wind speed data. The robust modeling performance further discloses its potential in the practical prediction of wind speed under complex circumstance. [ABSTRACT FROM PUBLISHER]

A type-2 hierarchical fuzzy system (T2HFS) is presented for the high-dimensional data-based modeling with uncertainties. Type-2 fuzzy logic system (T2FLS) is a powerful tool to handle uncertainties in complex processes. However, the operation of type-reduction has greatly increased the computational burden of T2FLSs. By integrating the T2FLS with hierarchical structure, a systematic design methodology of T2HFS is proposed to avoid the rule explosion and to simplify the computation complexity. The design methodology has included several procedures to establish the T2HFS. Firstly, the PCA-based method is developed to capture the prominent component from training data, and to determine the hierarchical structure of T2HFS. Furthermore, a novel clustering method is proposed to design the basic type-2 fuzzy logic unit (T2FLU) in uncertain environments. Finally, a hybrid-learning method is presented to fine-tune the parameters for the global optimization where the statistical and deterministic optimization methods are developed for the nominal and auxiliary performance, respectively. Simulation results have shown that the proposed T2HFS is very effective for the high-dimensional data-based modeling and control in uncertain environment. [ABSTRACT FROM AUTHOR]

A novel inference configuration is proposed to improve the computational efficiency and information loss in the probabilistic fuzzy inference process. The probabilistic inference and the fuzzy inference are unified in one operation based on the continuous form of the probabilistic fuzzy set. Besides the faster inference operation, it is able to produce fuzzy outputs in a complete probabilistic distribution that in turn will provide information about the approximation bound. The computational analyses of six different fuzzy systems demonstrate the inference efficiency of the proposed method. Its effectiveness can be further demonstrated on the application to modeling of an industrial curing process. The robust modeling performance discloses its potential in process modeling under complex environment. [ABSTRACT FROM AUTHOR]

This paper deals with the exponential stabilization problem for a class of nonlinear spatially distributed processes that are modeled by semilinear parabolic partial differential equations (PDEs), for which a finite number of actuators are used. A fuzzy control design methodology is developed for these systems by combining the PDE theory and the Takagi–Sugeno (T–S) fuzzy-model-based control technique. Initially, a T–S fuzzy parabolic PDE model is proposed to accurately represent a semilinear parabolic PDE system. Then, based on the T–S fuzzy model, a Lyapunov technique is used to design a continuous fuzzy state feedback controller such that the closed-loop PDE system is exponentially stable with a given decay rate. The stabilization condition is presented in terms of a set of spatial differential linear matrix inequalities (SDLMIs). Furthermore, a recursive algorithm is presented to solve the SDLMIs via the existing linear matrix inequality optimization techniques. Finally, numerical simulations on the temperature profile control of a catalytic rod are given to verify the effectiveness of the proposed design method. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, an inherent saturation of the fuzzy proportional–integral–derivative (PID) controller is revealed due to the finite fuzzy rules used. An equivalent structure and model of the fuzzy rule base is derived to show a saturation property. The bandwidth of the fuzzy PID control system can be adjusted by changing saturation parameter. Parameters of the fuzzy PID controller can be designed based on the inherent saturation. Compared with the conventional PID controller, the fuzzy PID controller has two advantages because of the inherent saturation: (1) without the additional filter, it can prevent impulse signal effectively; (2) without the additional anti-windup structure, a robust performance can be maintained when the input saturation occurs. The fuzzy PID controller is applied to an integrated circuit curing process. The simulation and experiment results demonstrate these effects of the inherent saturation, and its influence to the robustness of fuzzy PID controller. [Copyright &y& Elsevier]

Abstract: In this paper, a PSO-based intelligent integration of design and control is proposed for one kind of nonlinear curing process. This method combines the merits of both fuzzy modeling/control and PSO method, where fuzzy modeling/control is proposed to approximate/control the nonlinear process in a large operating region and the PSO-based intelligent optimization method is developed to solve non-convex and non-differential integration problem with design and control optimized simultaneously. Finally, the proposed method is compared with the traditional sequential method on controlling the temperature profile of a nonlinear curing process. [ABSTRACT FROM AUTHOR]

An interval-valued fuzzy logic controller (I-V FLC) is presented to control a class of nonlinear distributed parameter systems. The proposed FLC is inspired by human operators' knowledge or expert experience to control a distributed parameter process from the point of view of overall space domain. Based on spatial fuzzy set, the I-V FLC employs a centralized rule base over the space domain. Using spatial membership degree fusion operation, the I-V FLC can compress spatial input information into interval-valued fuzzy sets and then execute an interval-valued rule inference mechanism; thereby the I-V FLC has the capability to process spatial information over the space domain. Compared with traditional FLCs, the I-V FLC can improve its control performance due to its increased ability to express and process spatial information. The I-V FLC is successfully applied to a catalytic packed-bed reactor and compared with the traditional FLCs. The results demonstrate its effectiveness to control the unknown nonlinear distributed parameter process. [ABSTRACT FROM AUTHOR]

The observer-based indirect and direct adaptive fuzzy controllers are developed for a class of SISO uncertain nonlinear systems. The proposed approaches do not need the availability of the state variables. By designing the state observer, the adaptive fuzzy systems, which are used to model the unknown functions, can be constructed using the state estimations. Thus, a new hybrid adaptive fuzzy control method is proposed by combining the above adaptive fuzzy system with the H∞ control technique. Based on Lyapunov stability theorem, the proposed adaptive fuzzy control system can guarantee the stability of the whole closed-loop systems and obtain good tracking performance as well. The proposed methods are applied to an inverted pendulum system and a chaotic system and achieve satisfactory simulation results. [Copyright &y& Elsevier]

Presents information on a study which focused on a classical model reference adaptive control model used for designing nominal scaling gain of fuzzy logic control (FLC) systems. Mathematical model of FLC: Model reference adaptive mechanism for nominal scaling gain design; Feedforward type of model reference adaptive fuzzy control (MRAFC); Conclusions.

Presents more systematic analysis and design that are given for the conventional fuzzy control. Fuzzy two-term control; Fuzzy three-term control (FZ-PID); Simulation and performance analysis of fuzzy control; Conclusions.

This paper presents a~stable neuro-fuzzy (NF) adaptive control approach for the trajectory tracking of the robotic manipulator with poorly known dynamics. Firstly, the fuzzy dynamic model of the manipulator is established using the Takagi–Sugeno (T–S) fuzzy framework with both structure and parameters identified through input/output data from the robot control process. Secondly, based on the derived fuzzy dynamics of the robotic manipulator, the dynamic NF adaptive controller is developed to improve the system performance by adaptively modifying the fuzzy model parameters on-line. The dynamic NF system aims to approximate the whole robot dynamics rather than its nonlinear components as is done by static neural networks. The dynamic inversion introduced for the controller design is constructed by the dynamic NF system and will help the NF controller design because it does not require the assumption that the robot states should be within a~compact set. It is generally known that the compact set cannot be specified before the control loop is closed. Thirdly, the system stability and the convergence of tracking errors are guaranteed by Lyapunov stability theory, and the learning algorithm for the dynamic NF system is obtained thereby. Finally, simulation studies are carried out to show the viability and effectiveness of the proposed control approach. [Copyright &y& Elsevier]