On the interpretation and identification of dynamic Takagi-Sugenofuzzy models

Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. It is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples

Membership-set estimation using random scanning and principal component analysis

A set-theoretic approach to parameter estimation based on the bounded-error concept is an appropriate choice when incomplete knowledge of observation error statistics and unavoidable structural model error invalidate the presuppositions of stochastic methods. Within this class the estimation of non-linear-in-the-parameters models is examined. This situation frequently occurs in modelling natural systems. The output error method proposed is based on overall random scanning with iterative reduction of the size of the scanned region. In order to overcome the problem of computational inefficiency, which is particularly serious when there is interaction between the parameter estimates, two modifications to the basic method are introduced. The first involves the use of principal component transformations to provide a rotated parameter space in the random scanning because large areas of the initial parameter space are thus excluded from further examination. The second improvement involves the standardization of the parameters so as to obtain an initial space with equal size extension in all directions. This proves to largely increase the computational robustness of the method. The modified algorithm is demonstrated by application to a simple three-parameter model of diurnal dissolved oxygen patterns in a lake

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use

Forecasting Long-Term Government Bond Yields: An Application of Statistical and AI Models

This paper evaluates several artificial intelligence and classical algorithms on their ability of forecasting the monthly yield of the US 10-year Treasury bonds from a set of four economic indicators. Due to the complexity of the prediction problem, the task represents a challenging test for the algorithms under evaluation. At the same time, the study is of particular significance for the important and paradigmatic role played by the US market in the world economy. Four data-driven artificial intelligence approaches are considered, namely, a manually built fuzzy logic model, a machine learned fuzzy logic model, a self-organising map model and a multi-layer perceptron model. Their performance is compared with the performance of two classical approaches, namely, a statistical ARIMA model and an econometric error correction model. The algorithms are evaluated on a complete series of end-month US 10-year Treasury bonds yields and economic indicators from 1986:1 to 2004:12. In terms of prediction accuracy and reliability of the modelling procedure, the best results are obtained by the three parametric regression algorithms, namely the econometric, the statistical and the multi-layer perceptron model. Due to the sparseness of the learning data samples, the manual and the automatic fuzzy logic approaches fail to follow with adequate precision the range of variations of the US 10-year Treasury bonds. For similar reasons, the self-organising map model gives an unsatisfactory performance. Analysis of the results indicates that the econometric model has a slight edge over the statistical and the multi-layer perceptron models. This suggests that pure data-driven induction may not fully capture the complicated mechanisms ruling the changes in interest rates. Overall, the prediction accuracy of the best models is only marginally better than the prediction accuracy of a basic one-step lag predictor. This result highlights the difficulty of the modelling task and, in general, the difficulty of building reliable predictors for financial markets.interest rates; forecasting; neural networks; fuzzy logic.

Speed control of induction motor using fuzzy recursive least squares technique

Este artículo presenta el diseño de un controlador adaptativo, el sistema de control emplea lógica difusa adaptativa, modos deslizantes y es entrenado con la técnica de mínimos cuadrados recursivos. El problema de la variación de parámetros es resuelto con el controlador adaptativo; se utiliza un regulador interno PI con el cual se produce que el control de velocidad del motor de inducción sea realizado por medio de las corrientes de estator en vez de los voltajes. Se usa el modelo del motor en el sistema de coordenadas de flujo orientado del rotor para el desarrollo y prueba del sistema de control.A simple adaptive controller design is presented in this paper, the control system uses the adaptive fuzzy logic, sliding modes and is trained with the recursive least squares technique. The problem of parameter variation is solved with the adaptive controller; the use of an internal PI regulator produces that the speed control of the induction motor be achieved by the stator currents instead the input voltage. The rotor-flux oriented coordinated system model is used to develop and test the control system

An adaptive extended fuzzy function state-observer based control with unknown control direction

In this paper, a novel adaptive extended fuzzy function state observer based controller is proposed to control a class of unknown or uncertain nonlinear systems. The controller uses Nussbaum-gain technique from literature to prevent controller singularity with unknown control direction and the controller degree of freedom is increased. A state observer which employs the adaptive extended fuzzy function system to approximate a nonlinear system dynamics and estimates the unmeasurable state. The stability of closed-loop control system are shown using Lyapunov stability criterion and Nussbaum function property. The proposed and conventional fuzzy system based controllers are designed to control an inverted pendulum in simulation and a flexible-joint manipulator in real-time experiment. The integral of absoulte error (IAE) of tracking, integral of squared error (ISE) of tracking and integral of required absolute control signal (IA U) performances are compared in applications. The aim of the paper is not only to improve the tracking performances, but also to implement the adaptive extended fuzzy function based controller to a real-time system and conduct the tracking with unknown control direction