Fuzzy Affine Research Articles

New Results on Nonsynchronous-Observer-Based Output-Feedback Control of Fuzzy-Affine-Model-Based Discrete-Time Nonlinear Systems

This work investigates the non-synchronous observer-based output feedback control of nonlinear systems by T-S fuzzy affine models. In order to estimate the unmeasurable system states and handle the non-synchronization issue of premise variables between the observer/controller and the original system, a new non-synchronous piecewise fuzzy affine observer is firstly synthesized to estimate the unmeasurable system state variables. Via utilizing some elegant matrix inequalities with convexification techniques, new observer-based piecewise output feedback controller design results are proposed within the framework of piecewise quadratic Lyapunov functions. Simulation studies are given to illustrate the validity of the developed approach.

A New Design of Fuzzy Affine Model-Based Output Feedback Control for Discrete-Time Nonlinear Systems

The observer-based output feedback control problem for nonlinear systems is studied through Takagi-Sugeno fuzzy affine models. A novel piecewise fuzzy affine observer is designed to estimate the unmeasurable state variables. To remove the assumptions in the existing works that the system input matrices and/or output matrices should be common, full rank and uncertainties-free, a new approach is developed for the observer-based piecewise output feedback controller synthesis by making sufficient use of Young's inequality with its variance. Through fuzzy piecewise quadratic Lyapunov functions, improved and less conservative results on the output feedback controller design are obtained in terms of linear matrix inequalities, and the restrictions imposed in the existing results can be relaxed. Simulation studies are provided to confirm the effectiveness and conservatism reduction of the developed method.

Fuzzy-Affine-Model-Based Filtering Design for Continuous-Time Roesser-Type 2-D Nonlinear Systems.

This article tackles the problem of filtering design for continuous-time Roesser-type 2-D nonlinear systems via Takagi-Sugeno (T-S) fuzzy affine models. The aim is to design an admissible piecewise affine (PWA) filter such that the filtering error system is asymptotically stable with a prescribed disturbance attenuation level. First, 2-D Roesser nonlinear systems are approximated by a kind of 2-D fuzzy affine models with norm-bounded uncertainties. Then, the premise variable space of the 2-D fuzzy affine systems is partitioned into two classes of subspaces, that is: 1) crisp regions and 2) fuzzy regions. For each region, boundary continuity matrices and characterizing matrices are constructed by utilizing the space partition information and 2-D structure. After that, novel piecewise Lyapunov functions are constructed, based on which together with S-procedure, the asymptotic stability with performance is guaranteed for the filtering error system. By the projection lemma and some elegant convexification techniques, the PWA filtering design conditions are obtained. Finally, the less conservativeness and effectiveness of the proposed approach over a common Lyapunov function-based one are illustrated by simulation studies.

Fuzzy-Affine-Model-Based Filtering Design With Memory-Based Dynamic Event-Triggered Protocol

In this article, a novel dynamic event-triggered protocol is constructed to deal with the filtering problem for affine systems presented by Takagi–Sugeno (T–S) fuzzy model. Unlike the traditional fuzzy systems, a unified framework of T–S fuzzy affine systems is formulated, which is more capable of approximation over different operating regions. For achieving desirable performance while saving communication resources, the memory-based dynamic event-triggered protocol is constructed by flexibly exploiting a series of historically triggered packets. The fading channel is time-varying and described as a novel nonhomogeneous Markov process, in which a higher level deterministic switching signal regulates the variation of transition probabilities. By adopting the region-dependent Lyapunov theory, the mean-square exponentially stable, and expected <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance for resulting systems is guaranteed. In the end, an inverted pendulum model is applied to verify the results of the theoretical analysis.

Frequency Information-Based Observer Design for Takagi–Sugeno Fuzzy Affine Systems

This brief studies the problem of observer design for discrete-time uncertain Takagi-Sugeno (T-S) fuzzy affine systems subject to external disturbances and measurement noises with known frequency ranges. A class of novel observers with more design parameters is proposed. Based on the premise variable space partition information, piecewise Lyapunov functions are constructed together with the frequency range information of disturbances and noises, less conservative asymptotic stability with finite frequency performance analysis results are obtained. Then, based on Projection lemma, a novel observer design approach is proposed to T-S fuzzy affine systems, which tends to be less conservative than the non-frequency information and/or common Lyapunov function based observer design ones. Finally, simulation results on a circuit system are given to demonstrate the effectiveness and advantages of the proposed method.

Pricing of European call option under fuzzy interest rate

&lt;p style='text-indent:20px;'&gt;Option pricing under fuzzy environment is a hot research topic nowadays. Traditionally, option pricing were made in the case of fixed interest rate, while the fluctuate of interest rate may result in profit loss or bring unexpected risk. Thus, based on credibility theory, a new option pricing model under fuzzy interest rate are constructed in this paper. In fact, almost all fuzzy option pricing uses expected value method. In this paper, a new pricing method, fuzzy term structure and fuzzy affine term structure method, is adopted, and two European call option pricing formulas are obtained, one is that the fuzzy interest rate coefficients are constants, the other is that the fuzzy interest rate drift coefficient is a fuzzy process.&lt;/p&gt;

Asynchronous fault detection filtering design for continuous-time T-S fuzzy affine dynamic systems in finite-frequency domain

This paper investigates the problem of asynchronous fault detection filtering design for continuous-time Takagi-Sugeno (T-S) fuzzy affine dynamic systems in finite-frequency domain. The objective is to design an admissible piecewise affine filter such that the asymptotic stability of the filtering error system with the prescribed finite-frequency H−/H∞ performance can be guaranteed. It is assumed that the premise variables of the plant are unmeasurable so that the filter state transition and the plant state transition may be asynchronous. By applying the celebrated S-procedure, the generalized Kalman-Yakubovič-Popov lemma is extended such that the finite-frequency H−/H∞ performance of the fuzzy affine filtering error system is ensured. Furthermore, by utilizing piecewise quadratic Lyapunov functions, Projection lemma, and some matrix inequality linearization techniques, the finite-frequency fault detection filtering design approach is developed for the concerned T-S fuzzy affine dynamic system. It is shown that sufficient conditions for the existence of the fault detection filter are formulated as feasibility of a set of linear matrix inequalities. Finally, the effectiveness and advantages of the proposed design approach are illustrated by simulation studies.

Finite-Frequency $\mathcal {H}_{-}/\mathcal {H}_{\infty }$ Memory Fault Detection Filtering Design for Uncertain Takagi–Sugeno Fuzzy Affine Systems

This article is concerned with the finite-frequency <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_{-}/\mathcal {H}_{\infty }$</tex-math></inline-formula> memory fault detection filtering problem for discrete-time Takagi&#x2013;Sugeno fuzzy affine systems with norm-bounded uncertainties. The objective is to design a piecewise affine memory filter by using system historical information such that the resulting closed-loop filtering error system is asymptotically stable with the prescribed finite-frequency <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_{-}/\mathcal {H}_{\infty }$</tex-math></inline-formula> performance. Based on the generalized Kalman&#x2013;Yakubovi&#x010D;&#x2013;Popov lemma combined with the celebrated <inline-formula><tex-math notation="LaTeX">$\mathcal {S}$</tex-math></inline-formula>-procedure, new sufficient conditions for the fuzzy affine filtering error system to have the finite-frequency <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_{-}/\mathcal {H}_{\infty }$</tex-math></inline-formula> performance are given at first. By further using piecewise fuzzy quadratic Lyapunov functions and Projection lemma, the filtering analysis results for the filtering error system to be asymptotically stable with the prescribed finite-frequency <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_{-}/\mathcal {H}_{\infty }$</tex-math></inline-formula> performance are obtained. Then, the filtering synthesis is carried out with the aid of matrix inequality convexification techniques, and the synthesis results are described in terms of linear matrix inequalities. It is further shown that a better filtering performance can be achieved by using more system historical information. Finally, simulation is provided to verify the effectiveness of the proposed approach.

Research on Reconstruction of Basketball Training Action Trajectory Based on Improved K-Means Clustering Algorithm

The automatic capture and analysis of basketball game movements can guide basketball training and provide an effective method for improving the efficiency of basketball training. This paper introduces the research status of clustering methods in the field of trajectory data mining and reconstruction in detail. By analyzing the trajectory data under the constraints of the road network, the spatiotemporal characteristics of the existing trajectory clustering methods, and the deficiencies of the existing trajectory clustering methods, a new trajectory clustering method based on trajectory segmentation and spatiotemporal similarity measurement is implemented. A motion capture and reconstruction method for basketball training based on visual image K-means clustering algorithm is proposed. Multiresolution frame scanning technology is used to collect machine images of basketball training movements, and edge contour processing is performed on the collected high-resolution basketball training movement images. Feature detection uses the three-dimensional model reconstruction method to segment the basketball training action area and combines the irregular triangle network model to realize the machine vision block template matching processing of basketball training actions and capture the basketball training action in the Gaussian fuzzy affine space. In time and feature extraction, wavelet lifting technology is used to identify the ambiguity of basketball training movements, image enhancement technology is used to improve the resolution and adaptability of basketball training movement capture, and machine vision image processing methods are used to achieve basketball training movement capture optimization. The simulation results show that the method has better adaptability and higher feature recognition ability for basketball training motion capture and improves the feature extraction and adaptive capture reconstruction ability of basketball training motion.

Observer-Based Output Feedback Control of Nonlinear 2-D Systems via Fuzzy-Affine Models

Through Takagi-Sugeno fuzzy affine models, the observer-based output feedback control of discrete-time nonlinear two-dimensional systems is investigated, where the two-dimensional system information evolves dynamically along two independent directions. A piecewise fuzzy affine observer is designed to estimate the unmeasurable system states, and two enhanced observer-based piecewise output feedback control approaches are then developed. By making sufficient use of Young&#x2019;s matrix inequality with its variant, novel and less conservative observer-based piecewise output feedback controller design results are proposed via piecewise quadratic Lyapunov functions. Simulation studies on a doubly-indexed nonlinear process are provided to illustrate the effectiveness of the developed approaches.

Fuzzy-Affine-Model-Based Sampled-Data Filtering Design for Stochastic Nonlinear Systems

This article addresses the sampled-data piecewise affine (PWA) filter design problem for It&#x00F4; stochastic nonlinear systems represented by Takagi&#x2013;Sugeno fuzzy affine models. An input delay method is used to describe the sample-and-hold behavior of the measurement output. Based on a novel piecewise quadratic Lyapunov&#x2013;Krasovskii functional, some new results on the robust sampled-data PWA filtering design are proposed through a linearization procedure by using some convexification techniques. Simulation studies on a tunnel diode circuit system, and an inverted pendulum system are given to illustrate the effectiveness of the proposed method.

Nonsynchronized State Estimation for Fuzzy Markov Jump Affine Systems With Switching Region Partitions.

This article investigates the state estimation issue of discrete-time Takagi-Sugeno fuzzy Markov jump affine systems that cover both traditional fuzzy Markov jump systems and fuzzy affine systems as two special cases. The original system is transformed into a Markov jump piecewise-affine system that varies with different operating regions. The fuzzy rules are dependent on the system mode, and accordingly, the partition of the state space is mode dependent. To analyze the stochastic stability of the estimation error system, a novel mode-dependent piecewise Lyapunov function is constructed, in which the region indices of both the plant state and the estimator state are mode dependent. Then, the existence for a simultaneously mode-dependent and region-dependent fuzzy affine estimator is investigated by virtue of the S -procedure and ellipsoidal outer approximation such that the estimation error system is stochastically stable with a prescribed H∞ performance. In the end, an illustrative example of a tunnel diode circuit is adopted to showcase the effectiveness and practicability of the developed state estimation strategy.

A Novel Fuzzy Output Feedback Dynamic Sliding Mode Controller Design for Two-Dimensional Nonlinear Systems

The system information of 2-D systems is usually in propagation along two independent directions. This article focuses on the issue of output feedback sliding mode control (SMC) for 2-D nonlinear systems through T-S fuzzy affine models. Associated with the sliding surface function, a singular system is established to describe the sliding mode dynamics. Based on piecewise quadratic Lyapunov functions, some new stability analysis results on the sliding mode dynamical system are attained, and the analysis conservatism can be further reduced. A robust output feedback dynamic SMC synthesis scheme is developed to guarantee the finite-time reachability of the sliding surface. It is also worthy of mentioning that the proposed dynamic SMC synthesis method can handle the mismatched disturbances, and the control input channels are permitted to have parameter uncertainties. Simulation studies are given to illustrate the validity of the developed scheme.

A new design of output feedback sliding mode controller for T‐S fuzzy‐affine systems

AbstractThis work focuses on output feedback sliding mode control (SMC) for nonlinear systems via T‐S fuzzy affine models. Associated with the sliding surface, a singular system is firstly proposed to describe the dynamical features of the sliding motion. Adopting some convexification techniques and based on piecewise quadratic Lyapunov functions (PQLFs) and a common quadratic Lyapunov function (CQLF), sufficient criteria for the asymptotic stability analysis of the sliding mode dynamical system are attained. Two output feedback SMC synthesis schemes are developed to drive the closed‐loop system states to the sliding surface in finite time. A simulation example is presented to show the validity of the proposed methods.

A New Sampled-Data Output-Feedback Controller Design of Nonlinear Systems via Fuzzy Affine Models.

This article focuses on the sampled-data output-feedback control problem for nonlinear systems represented by Takagi-Sugeno fuzzy affine models. An input delay approach is adopted to describe the sample-and-hold behavior of the measurement output. Via augmenting the system states with the control input, the resulting closed-loop system is converted into a singular system first. Based on the piecewise quadratic Lyapunov-Krasovskii functionals, some novel results on the sampled-data piecewise affine output-feedback controller design are attained by employing some convexification techniques. The simulation studies are presented to illustrate the effectiveness of the proposed scheme.

Fuzzy affine model-based output feedback controller design for nonlinear impulsive systems

This paper studies the robust output feedback control problem for a class of nonlinear systems with impulsive effects via T-S fuzzy affine models. By employing a state-input augmentation scheme, some new results on the piecewise affine (PWA) output feedback controller synthesis for T-S fuzzy affine impulsive systems are obtained through piecewise quadratic Lyapunov functions. Sufficient criteria for exponential stability analysis of the resulting closed-loop system are given within a convex optimization setup. A simulation example is shown to verify the effectiveness of the proposed approach.

Event-triggered state estimation for T-S fuzzy affine systems based on piecewise Lyapunov-Krasovskii functionals

This paper investigates the problem of event-triggered H∞ state estimation for Takagi-Sugeno (T-S) fuzzy affine systems. The objective is to design an event-triggered scheme and an observer such that the resulting estimation error system is asymptotically stable with a prescribed H∞ performance and at the same time unnecessary output measurement transmission can be reduced. First, an event-triggered scheme is proposed to determine whether the sampled measurements should be transmitted or not. The output measurements, which trigger the condition, are supposed to suffer a network-induced time-varying and bounded delay before arriving at the observer. Then, by adopting the input delay method, the estimation error system can be reformulated as a piecewise delay system. Based on the piecewise Lyapunov-Krasovskii functional and the Finsler’s lemma, the event-triggered H∞ observer design method is developed. Moreover, an algorithm is proposed to co-design the observer gains and the eventtriggering parameters to guarantee that the estimation error system is asymptotically stable with a given disturbance attenuation level and the signal transmission rate is reduced as much as possible. Simulation studies are given to show the effectiveness of the proposed method.

Fuzzy-Affine-Model-Based Output Feedback Dynamic Sliding Mode Controller Design of Nonlinear Systems

This paper investigates the problem of output feedback sliding mode control (SMC) for a class of uncertain nonlinear systems through Takagi–Sugeno fuzzy affine models. By adopting a state-input augmentation method, a descriptor system is first constructed to characterize the dynamical properties of the sliding motion. Based on a common quadratic Lyapunov function and piecewise quadratic Lyapunov functions, sufficient conditions for asymptotic stability analysis of the sliding motion are obtained with some convexification techniques. An output feedback dynamic SMC design scheme is proposed to force the states of the resulting closed-loop system onto the sliding surface locally in finite time. Two simulation examples are finally shown to illustrate the effectiveness of the proposed approaches.

A Novel Piecewise Affine Filtering Design for T-S Fuzzy Affine Systems Using Past Output Measurements.

This paper tackles the problem of piecewise affine memory filtering design for the discrete-time norm-bounded uncertain Takagi-Sugeno fuzzy affine systems. The objective is to design an admissible filter using past output measurements of the system, guaranteeing the asymptotic stability of the filtering error system with a given [Formula: see text] performance index. Based on the piecewise fuzzy Lyapunov functions and the projection lemma, a new sufficient condition for [Formula: see text] filtering performance analysis is first derived, and then the filter synthesis is carried out. It is shown that the filter gains can be obtained by solving a set of linear matrix inequalities. In addition, it is also shown that the filtering performance can be improved with the increasing number of past output measurements used in the filtering design. Finally, two examples are presented to show the advantages and effectiveness of the proposed approach.

Finite Frequency Memory Output Feedback Controller Design for T–S Fuzzy Dynamical Systems

In this paper, we will investigate the problem of finite frequency memory fixed-order output feedback controller design for Takagi–Sugeno (T–S) fuzzy affine systems. It is assumed that the disturbances reside in a finite frequency range, i.e., the low, middle, or high frequency range. The objective is to design a memory piecewise affine (PWA) controller by using past output measurements to guarantee the asymptotic stability of the resulting closed-loop system with a prescribed finite frequency $\mathscr H_{\infty }$ performance. Via the system state-input augmentation, a novel descriptor system approach is proposed to facilitate the controller design. All the design conditions are formulated in the form of linear matrix inequalities. It is also proven that the $\mathscr H_{\infty }$ performance can be improved with the memory control strategy. Finally, simulation studies are presented to show the effectiveness of the proposed design method.