Basil M. Al-Hadithi

The fuzzy Kalman filter: State estimation using possibilistic techniques

A new method to implement fuzzy Kalman filters is introduced. The combination of possibilistic techniques and the extended Kalman filter has special application in fields where inaccurate information is involved. The novelty of this article comes from the fact that by using possibility distributions, instead of Gaussian distributions, a fuzzy description of the expected state and observation is sufficient to obtain a good estimation. Some characteristics of this approach are that uncertainty does not need to be symmetric, and that a wide region of possible values for the expectations is allowed. To implement the algorithm, this approach also contributes a method to propagate uncertainty through the process model and the observation model, based on trapezoidal possibility distributions. Finally, several examples of a real mobile robot moving through a localization process, while using qualitative landmarks, are shown.

A general methodology for online TS fuzzy modeling by the extended Kalman filter

HighlightsWe present an online fuzzy modeling methodology based on the extended Kalman filter.This methodology can work with noise, is very efficient and completely general.The model can be obtained in a recursive way only based on input-output data.There are no restrictions in the type of membership functions used.Membership functions can even be mixed in the antecedents of the rules. This paper presents an online TS fuzzy modeling general methodology based on the extended Kalman filter. The model can be obtained in a recursive way only based on input-output data. The methodology can work online with the system, properly in the presence of noise, is very efficient computationally and completely general. It is general in the sense theorically there are no restrictions neither in the number of inputs nor outputs, neither in the type nor distribution of membership functions used (which can even be mixed in the antecedents of the rules). Some examples and comparisons with other online fuzzy identification models from signals are provided to illustrate the skill of the online identification of the proposed methodology.

Variable Structure Control with chattering elimination and guaranteed stability for a generalized T-S model

In this paper, a fuzzy based Variable Structure Control (VSC) with guaranteed stability is presented. The main objective is to obtain an improved performance of highly non-linear unstable systems. The main contribution of this work is that, firstly, new functions for chattering reduction and error convergence without sacrificing invariant properties are proposed, which is considered the main drawback of the VSC control. Secondly, the global stability of the controlled system is guaranteed. The well known weighting parameters approach, is used in this paper to optimize local and global approximation and modeling capability of T-S fuzzy model. A one link robot is chosen as a nonlinear unstable system to evaluate the robustness, effectiveness and remarkable performance of optimization approach and the high accuracy obtained in approximating nonlinear systems in comparison with the original T-S model. Simulation results indicate the potential and generality of the algorithm. The application of the proposed FLC-VSC shows that both alleviation of chattering and robust performance are achieved with the proposed FLC-VSC controller. The effectiveness of the proposed controller is proven infront of disturbances and noise effects.

Generalization of stability criterion for Takagi--Sugeno continuous fuzzy model

The stability analysis of a generalized class of continuous fuzzy systems in terms of Lyapunov stability theory is presented. Firstly, the stability problem of fuzzy systems described by Takagi-Sugenos continuous model is stated. Secondly, new stability conditions which guarantee the stability of the fuzzy system are derived. The new stability conditions can be regarded as a general solution for Takagi-Sugeno fuzzy system, in which the offset term is not equal to zero. Finally, the suggested stability theorems are verified by some illustrative examples.

Análisis de Estabilidad de Sistemas Borrosos

En este trabajo se revisa el estado del arte sobre estabilidad de sistemas borrosos, poniendose de manifiesto las dificultades para su analisis, debido a la caracteristica falta de linealidad de los mismos. Se revisan los estudios basados en el criterio del circulo, las tecnicas para calcular indices de estabilidad, asi como tecnicas basadas en aplicacion del teorema de estabilidad de Lyapunov, que permite utilizar metodos numericos de busqueda de soluciones. Ademas, se revisan los trabajos de estabilidad mediante el uso del modelo borroso de Takagi-Sugeno (T-S), el enfoque de las Desigualdades Matriciales Lineales (LMI), que ha tenido un interes creciente en los ultimos anos, asi como otra linea de investigacion basada en estabilidad energetica.

New incremental Takagi-Sugeno state model for optimal control of multivariable nonlinear time delay systems

In this work, a novel approach based on incremental state models has been proposed for the modeling of multivariable nonlinear delayed systems expressed by a generalized version of Takagi-Sugeno (T-S) fuzzy model. One of the key features of the new approach is that the proposed incremental state model compared with the no incremental one, naturally solves the problem of computing the target state, since for a desired output vector, a zero incremental state can be taken as an objective. Moreover, the control action in an incremental form is equivalent to introduce an integral action, thereby cancelling the steady state errors. Among other advantages using incremental models are the disappearance of the affine terms. Then, a fuzzy based linear quadratic regulator (FLC-LQR) is designed. Furthermore, a new optimal observer for multivariable fuzzy systems is developed, because not all states of the nonlinear system are fully available or measured. A multivariable thermal mixing tank system is chosen to evaluate the robustness of the proposed controller. The results obtained show a robust, well damped response with zero steady state error in the presence of disturbances and modeling errors. Graphical abstractDisplay Omitted HighlightsNew incremental state model is proposed for MIMO nonlinear delayed systems.The control action in an incremental form guarantees zero steady state errors.New Optimal observer is proposed, because not all states are available or measured.

An affine fuzzy model with local and global interpretations

Abstract: Universal approximation properties of Mamdani fuzzy model are well known. On the other hand, Takagi-Sugeno fuzzy model with affine consequent was thought to be a local approximator of the dynamics. However, it can also be tuned to be an universal approximator, but loosing its local interpretation. In this paper, an innovative affine global model with universal approximation capabilities which maintains local interpretation is introduced. This novel model can be considered a generalization of Takagi-Sugeno affine fuzzy model, and is based on decoupling the dynamic parameters of the system at the fuzzification step. We demonstrate how this new model can exactly match non-linear functions expressed either as product form or additive form. Finally, we apply all the above to model a multivariable tank, analyzing the modelling errors obtained, depending on the model used: Mamdani, Takagi-Sugeno or the affine one with decoupled dynamics.

A friendly online C compiler to improve programming skills based on student self-assessment

This paper presents an online C compiler designed so that students can program their practical assignments in Programming courses. What is really innovative is the self‐assessment of the exercises based on black‐box tests and train students’ skill to test software. Moreover, this tool lets instructors, not only proposing and classifying practical exercises, but also evaluating automatically the efforts dedicated and the results obtained by the students. The system has been applied to the 1st‐year students at the Industrial Engineering specialization at the Universidad Politecnica de Madrid. Results show that the students obtained better academic performance, reducing the failure rate in the practical exam considerably with respect to previous years, in addition that an anonymous survey proved that students are satisfied with the system because they get instant feedback about their programs.

Chattering-free fuzzy variable structure control for multivariable nonlinear systems

Graphical abstractFLC-VSC for multivariable nonlinear systems is presented. The main contribution of this work is the development of new functions for chattering elimination without sacrificing invariant properties (Figs. 1 and 2 represent the temporal evolution of s1 and s2 before applying the proposed algorithm and Figs. 3 and 4 after applying the proposed algorithm respectively). Fig. 5 shows fuzzy sets of the switching surface. Fig. 6 shows the transient response of a two-link robot model. Display Omitted HighlightsA fuzzy based variable structure control for multivariable nonlinear systems is presented.A generic matrix formulation of the FLC-VSC algorithm for nonlinear multivariable systems, is proposed.The weighting parameters approach is used to optimize local and global modelling capability of T-S fuzzy model.The global stability of the controlled system is guaranteed.A fuzzy switching function is added as an additional fuzzy variable. In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) with guaranteed stability for multivariable systems is presented. It is aimed at obtaining an improved performance of nonlinear multivariable systems. The main contribution of this work is firstly developing a generic matrix formulation of the FLC-VSC algorithm for nonlinear multivariable systems, with a special attention to non-zero final state. Secondly, ensuring the global stability of the controlled system. The multivariable nonlinear system is represented by T-S fuzzy model. The identification of the T-S model parameters has been improved using the well known weighting parameters approach to optimize local and global approximation and modeling capability of T-S fuzzy model. The main problem encountered is that T-S identification method cannot be applied when the membership functions (MFs) are overlapped by pairs. This in turn restricts the application of the T-S method because this type of membership function has been widely used in control applications. In order to overcome the chattering problem a switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules together with the state variables. A two-link robot system and a mixing thermal system are chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of proposed FLC-VSC method.

Fuzzy optimal control using generalized Takagi-Sugeno model for multivariable nonlinear systems

Graphical abstractDisplay Omitted HighlightsSeveral algorithms of FLC-LQR are developed to obtain enhanced performance of nonlinear unstable multivariable systems.The multivariable nonlinear system is represented by a generalized (T-S) model.Good response and zero steady state error in front of disturbances and modeling errors.A comparison is carried out with other algorithms to show the superiority of the proposed ones.A two-link robot is chosen to evaluate the validity of the proposed algorithms. In this work, the main objective is to obtain enhanced performance of nonlinear multivariable systems. Several algorithms of Fuzzy Logic Controller based Linear Quadratic Regulator (FLC-LQR) are presented. The multivariable nonlinear system is represented by a generalized Takagi-Sugeno (T-S) model developed by the authors in previous works. This model has been improved using the well known weighting parameters approach to optimize local and global approximation. In comparison with existent works, the proposed controller is based on the calculation of the control action in each point of the state space according to the dynamic properties of the nonlinear system at that point. This control methodology offers a robust, well damped dynamic response and zero steady state error when the system is subjected to disturbances and modeling errors. A two-link robot system is chosen to evaluate the robustness of the proposed controller algorithms.