Fuzzy Estimation Research Articles

Robust control of electrically driven robots by adaptive fuzzy estimation of uncertainty

This paper presents a novel robust decentralized control of electrically driven robot manipulators by adaptive fuzzy estimation and compensation of uncertainty. The proposed control employs voltage control strategy, which is simpler and more efficient than the conventional strategy, the so-called torque control strategy, due to being free from manipulator dynamics. It is verified that the proposed adaptive fuzzy system can model the uncertainty as a nonlinear function of the joint position error and its time derivative. The adaptive fuzzy system has an advantage that does not employ all system states to estimate the uncertainty. The stability analysis, performance evaluation, and simulation results are presented to verify the effectiveness of the method. A comparison between the proposed Nonlinear Adaptive Fuzzy Control (NAFC) and a Robust Nonlinear Control (RNC) is presented. Both control approaches are robust with a very good tracking performance. The NAFC is superior to the RNC in the face of smooth uncertainty. In contrast, the RNC is superior to the NAFC in the face of sudden changes in uncertainty. The case study is an articulated manipulator driven by permanent magnet dc motors.

ESTIMATORS BASED ON FUZZY RANDOM VARIABLES AND THEIR MATHEMATICAL PROPERTIES

In statistical inference, the point estimation problem is very cru- cial and has a wide range of applications. When, we deal with some concepts such as random variables, the parameters of interest and estimates may be reported/observed as imprecise. Therefore, the theory of fuzzy sets plays an important role in formulating such situations. In this paper, we rst recall the crisp uniformly minimum variance unbiased (UMVU) and Bayesian estimators and then develop the concept of fuzzy estimators for fuzzy parameters based on fuzzy random variables.

Smith Predictor Based Fuzzy Estimator for Uncertain Time-Delayed Systems

In this paper, a novel robust control method is proposed for uncertain time-delayed systems. The objective is to guarantee system stability and robustness against modeling errors. A fuzzy estimator is developed to predict the uncertain plant time-delay. Smith predictor is exploited. An adaptive tuning law is developed to further improve the control system performance. The proposed robust control method is successfully applied to a heat exchanger control system. Simulation results show that the approach is indeed effective. System robustness as well as stability is achieved.

Fuzzy Synthetic Estimation of Multi-Process Planning Schemes in CAPP

Aiming at the evalution and selection of multi-process plans in CAPP, a general kind of fuzzy comprehensive evalution is proposed according to the principle of fuzzy consistent relation and fuzzy consistent matrix and the correlation of gray system theory, and detailed evalution step is given. Three kind of the process plans are evaluated with the method of fuzzy comprehensive evaluation. The fuzzy synthetic estimation module is founded based on the product quality , manufacturing cost and production cycle. It has been adopted to cases in production and has realized the optimization of process schemes in CAPP.

A Criterion for the Fuzzy Set Estimation of the Regression Function

We propose a criterion to estimate the regression function by means of a nonparametric and fuzzy set estimator of the Nadaraya-Watson type, for independent pairs of data, obtaining a reduction of the integrated mean square error of the fuzzy set estimator regarding the integrated mean square error of the classic kernel estimators. This reduction shows that the fuzzy set estimator has better performance than the kernel estimations. Also, the convergence rate of the optimal scaling factor is computed, which coincides with the convergence rate in classic kernel estimation. Finally, these theoretical findings are illustrated using a numerical example.

Identification Filtering with fuzzy estimations

A digital identification filter interacts with an output reference model signal known as a black-box output system. The identification technique commonly needs the transition and gain matrixes. Both estimation cases are based on mean square criterion obtaining of the minimum output error as the best estimation filtering. The evolution system represents adaptive properties that the identification mechanism includes considering the fuzzy logic strategies affecting in probability sense the evolution identification filter. The fuzzy estimation filter allows in two forms describing the transition and the gain matrixes applying actions that affect the identification structure. Basically, the adaptive criterion conforming the inference mechanisms set, the Knowledge and Rule bases, selecting the optimal coefficients in distribution form. This paper describes the fuzzy strategies applied to the Kalman filter transition function, and gain matrixes. The simulation results were developed using Matlab©.

Radial Basis Function Controller of a Class of Nonlinear Systems Using Mamdani Type as a Fuzzy Estimator

In this work we consider the application of an adaptive neural network control for a class of single input single output non linear systems. The method uses a neural network system of Radial Basis Function (RBF) type to approximate the feedback linearization law and a fuzzy inference system of Mamdani type to estimate the control signal error between the ideal unknown control signal and the actual control signal. The rule base of the Mamdani fuzzy system is constructed using simple expert reasoning. The parameters of the (RBF) controller are adapted and changed using the gradient descent law based on the estimated control error. The simulation is carried out on a three tanks system with the objective of controlling the level of one tank. The simulation results show that the proposed RBF-Mamdani scheme performs successful and robust control in comparison to the results obtained using a PI controller.

The Separate Parameter Estimation in Univariate Fuzzy Linear Regression Model

Abstract Kim et al. [1] proposed a new fuzzy linear regression model and studied the asymptotic normality and strong consistency of the fuzzy least squares estimation. In this paper, we proposed a new estimation method to estimate the parameters in univariate fuzzy linear regression. Compared with the traditional least squares, our method is robust.

State Estimation over Customized Wireless Network

In this paper the state estimation techniques are investigated over customized wireless network for a continuous-time plant. It is assumed that the plant is connected to the controller over the proposed network. The feedback control over wireless networks includes limited bandwidth, time-varying and unknown delays with a high probability of data loss. Reasonably, some of these issues are deduced from the wireless networks structures. In order to deal with these problems the customized wireless network architecture is proposed for this Wireless Networked Control System (WNCS) and the problem of transmission delays and packet losses which induced by this scheme is studied. The time-varying delays of the TCP based shared network is estimated by fuzzy state estimation technique. Thereafter the kalman filtering is applied to address the problem of optimal filtering for this continuous-time plant with time-varying delays. The re-organized innovation analysis approach is applied to tackle the network induced time-varying delays. The simulation results show the applicability of the proposed approach.

Fuzzy rules-based approach to estimate the availability of transportation system

The productivity of manufacturing process significantly depends on an availability of material handling systems, which in turn depends on reliability and maintainability of transportation devices. For this reason the scheduling of maintenance operations is very important to keep the high availability of transportation system. The attention in the paper is focused on a crane control problem and availability of automated material handling device, which refers to capability of a device to realise transportation operations with expected quality. An anti-sway crane control problem was solved in the paper by using indirect adaptive pole placement system with fuzzy estimator of parameters of a crane dynamic model. The paper presents the fuzzy model used to heuristic estimation of the system availability coefficient, and genetic fuzzy system that forecasts prognoses of operating time between failures. The models were implemented in the monitoring and diagnostic system tested on the laboratory stand, the overhead travelling crane.

НЕЧІТКЕ МОДЕЛЮВАННЯ РЕЙТИНГУ НАУКОВИХ ПУБЛІКАЦІЙ

Розглядається проблема прийняття рішень в умовах невизначеності на основі застосування нечітких множин і нечіткої логіки. Побудовано нечітку експертну систему, що дозволяє провести оцінку якості публікацій, журналів, науковців і наукових організацій, формалізація якої складна й неможлива в умовах неповної або неточної інформації. У процесі дослідження показано, що нечіткі системи Сугено, налаштовані за допомогою алгоритмів навчання, мають найвищу точність завдяки відносно простим програмам навчання і практичній реалізації. Описано структуру і функції нечіткої експертної системи для оцінки якості наукових публікацій. Проведено тестування контролера на тестовій вибірці, що наведена у вихідних даних.

Estimation of the Randomized Complete Block Design Parameters with Fuzzy Goal Programming

Since goal programming was introduced by Charnes, Cooper and Ferguson (1955), goal programming has been widely studied and applied in various areas. Parameter estimation is quite important in many areas. Recently, many researches have been studied in fuzzy estimation. In this study, fuzzy goal programming was proposed by Hannan (1981) adapted to estimation of randomized complete block design parameters. Suggested fuzzy goal programming is used for estimation of randomized complete block design parameters. Two numerical examples are used to illustrate the applicability of the suggested method. Then, the results obtained from classical method and suggested methods have been compared.

Measurement of Power Supplier's Market Power Using a Proposed Fuzzy Estimator

Measuring the exercise of market power has always been a fundamental problem in electricity markets. According to a well-known economic definition, a seller's market power is defined as “the ability to maintain prices profitably above competitive levels for a significant period of time”. This standard definition implies that market power has a fuzzy nature, which leads to the development of a fuzzy system for estimating the exercised market power. As understood from the definition, both duration and magnitude of market power play key roles in the measurement of the exercised market power. The fuzzy estimator gathers these two relevant aspects in a unified framework and uses them to assign a unique measure to the exercised market power. The fuzzy estimator is applied to measure each power supplier's market power in an agent-based computational framework of the considered electricity market. In this agent-based simulation, the power suppliers use Q-learning to learn how to respond to competitors' behavior and market conditions. The experimental results confirm the capability of the proposed fuzzy estimator to monitor and diagnose the exercise of market power.

A new approach to fuzzy estimation of Takagi–Sugeno model and its applications to optimal control for nonlinear systems

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi–Sugeno (T–S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T–S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T–S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T–S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters’ weighting method is suggested for tuning T–S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T–S model. Simulation results indicate the potential, simplicity and generality of the algorithm.

Fuzzy estimation for temperature distribution of furnace inner surface

A fuzzy inference method (FIM) for predicting the temperature distribution of the furnace inner surface is proposed in this work. The deviations between the computed and measured temperature at measurement points of furnace wall are taken as input parameters of fuzzy inference units (FIUs), and the corresponding fuzzy inference components of measured information are obtained by the FIUs. According to the importance of the various measured information, the fuzzy inference components then are weighted and synthesized to gain the compensations of the guessed temperature distribution. Finally, the temperature distribution estimation of the furnace inner surface is accomplished. Numerical experiments are performed to study the effects of measurement points number, measurement errors and other factors on the predicted results. Comparisons with the conjugate gradient method (CGM) and the genetic algorithm (GA) are also conducted, and they all show the validity and superiority of the proposed method in the current paper.

Direct adaptive neural network controller for a class of nonlinear systems based on fuzzy estimator of the control error

A new approach of direct adaptive control of single input single output nonlinear systems in affine form using single-hidden layer neural network (NN) is introduced. In contrast to the algorithms in the literature, the weights adaptation laws are based on the control error and not on the tracking error or its filtered version. Since the control error is being expressed in terms of the NN controller, hence its weights updating laws are obtained via back-propagation concept. A fuzzy inference system (FIS) with heuristically defined rules is introduced to provide an estimate of this error based on the past history of the system behaviour. The stability of the closed loop is studied using Lyapunov theory. A fixed structure is then proposed for the FIS and the design parameters reduce to the parameters of the NN. The method is reproducible and does not require any pre-training of the network weights.

State Estimate-based Friction Fuzzy Modeling and Robust Adaptive Control

This paper develops a fuzzy state estimate-based robust adaptive control scheme for a class of mechanical systems with multiple degrees of freedom. The unmeasurable state variables used in both modeling friction force and adaptive controller design are estimated by a fuzzy estimator. By strictly positive real lemma and Lyapunov stability theory, the ultimately uniform boundedness of the state estimation errors is ensured. This paper also proposes a multivariable robust control algorithm using the estimated states and adaptive fuzzy friction mode, where the updating rule for parameter adjustment in the fuzzy friction model is derived by Lyapunov theory. It is shown that the tracking error of the closed-loop system is ultimately uniformly bounded (UUB). A mass-spring-damping system with multiple degrees of freedom is employed in the simulation studies. Simulation results demonstrate the effectiveness of our proposed state-estimate based fuzzy friction modeling and adaptive control strategy.

Pricing European Call Currency option based on Adaptive Fuzzy Numbers with Possibilistic Mean

In this paper we use the fuzzy estimators based on confidence intervals in order to estimate the volatility of currency exchange rate having sample data. We model the uncertainty of the characteristics such as interest rates and volatility using adaptive fuzzy numbers and replace the fuzzy currency option price and the fuzzy volatility by the possibilistic mean value. Furthermore, a numerical example is presented, and we get the expected prices which depend on given degree of confidence. Key words: Currency Option; Option Pricing; Possibilistic Mean Value; Fuzzy Volatility; G-K Model

CMAC-based previous step supervisory control schemes for relaxing bound in adaptive fuzzy control

In this paper, a novel scheme of incorporating a learning mechanism into previous step supervisory controllers for adaptive fuzzy control is proposed to relax bounds required in the control process. In traditional supervisory adaptive fuzzy control approaches, the use of fuzzy estimators for approximating system functions and a robust supervisory control law are necessary to deal with any possible uncertainties caused in the system. This kind of supervisory controller depends on the robust bounds of system functions so that it can ensure the Lyapunov stability of controlled systems. However, in those approaches, the output may not be able to follow the reference trajectory well if the robust bounds are predicted improperly. In our implementation, CMAC (Cerebellar Model Articulation Controllers) is used as the learning mechanism because of its quick learning capability. Under the Lyapunov stable criterion, the proposed CMAC learning mechanism can improve the output performance and can relax the robust bound limitation so that practical systems can easily be realized. In summary, the proposed approach not only can relax bounds for previous step supervisory controllers in adaptive fuzzy control, but also can significantly improve the control performance of the system.

Parameter estimation from small biased samples: Fuzzy sets vs statistics

We consider a problem of estimating an unknown location parameter from several small biased samples. The biases and scale parameters of the samples are not known as well. For the case of two samples a fuzzy estimator based on a triangular membership function is introduced and studied. In particular, it is shown that its asymptotic bias is less than that of the weighted mean for the majority of key parameters in the problem. For small samples the fuzzy estimator is compared with the weighted mean and weighted median for a bunch of distributions. The main conclusion is that the fuzzy estimator performs better in most of the scenarii, however its advantage is subtle except for a few cases. Similar conclusions are obtained for the case of three information sources. The theoretical and simulation results for two samples might serve as a guidance for choosing a particular estimation method from the discussed ones based on preliminary information on relations between unknown parameters.