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

BIBO stabilisation of continuous time takagi sugeno systems under persistent perturbations and input saturation

[EN] This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi¿Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.The authors wish to thank the Editor-in-Chief and the anonymous reviewers for their valuable comments and suggestions. This work has been funded by Ministerio de Economia y Competitividad (Spain) through the research project DPI2015-71443-R and by Generalitat Valenciana (Valencia, Spain) through the research project GV/2017/029.Salcedo-Romero-De-Ávila, J.; Martínez Iranzo, MA.; Garcia-Nieto, S.; Hilario Caballero, A. (2018). BIBO stabilisation of continuous time takagi sugeno systems under persistent perturbations and input saturation. International Journal of Applied Mathematics and Computer Science (Online). 28(3):457-472. https://doi.org/10.2478/amcs-2018-0035S45747228

Piecewise-Takagi-Sugeno asymptotically exact estimation of the domain of attraction of nonlinear systems

[EN] This report generalises recent results on stability analysis and estimation of the domain of attraction of nonlinear systems via exact piecewise affine Takagi Sugeno models. Algorithms in the form of linear matrix inequalities are proposed that produce progressively better estimates which are proved to asymptotically render the actual domain of attraction; regions already proven to belong to such domain of attraction can be removed and the estimate can contain significant portions of the modelling region boundary; in this way, level-set approaches in prior literature can be significantly improved. Illustrative examples and comparisons are provided. (C) 2016 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.The authors gratefully acknowledge the support of the following institutions: Project Ciencia Basica SEP-CONACYT CB-168406, the CONACyT/COECYT Sonora scholarship 383252, project DPI2016-81002-R (Spanish government, MINECO), and the scholarship GRISOLIA/2014/006 from Generalitat Valenciana (regional government).Gonzalez-German, IT.; Sala, A.; Bernal Reza, MÁ.; Robles-Ruiz, R. (2017). Piecewise-Takagi-Sugeno asymptotically exact estimation of the domain of attraction of nonlinear systems. Journal of the Franklin Institute. 354(3):1514-1541. https://doi.org/10.1016/j.jfranklin.2016.11.033S15141541354

A CENTER MANIFOLD THEORY-BASED APPROACH TO THE STABILITY ANALYSIS OF STATE FEEDBACK TAKAGI-SUGENO-KANG FUZZY CONTROL SYSTEMS

The aim of this paper is to propose a stability analysis approach based on the application of the center manifold theory and applied to state feedback Takagi-Sugeno-Kang fuzzy control systems. The approach is built upon a similar approach developed for Mamdani fuzzy controllers. It starts with a linearized mathematical model of the process that is accepted to belong to the family of single input second-order nonlinear systems which are linear with respect to the control signal. In addition, smooth right-hand terms of the state-space equations that model the processes are assumed. The paper includes the validation of the approach by application to stable state feedback Takagi-Sugeno-Kang fuzzy control system for the position control of an electro-hydraulic servo-system

New Optimal Approach for the Identification of Takagi-Sugeno Fuzzy Model

A novel optimal method is developed to improve the identification and estimation of Takagi-Sugeno (TS) fuzzy model. The idea comes from the fact that the main drawback of T-S model is that it can not be applied when the membership functions are overlapped by pairs. This limits the application of the T-S model because this type of membership function has been widely used in the stability and controller design of fuzzy systems. It is also very popular in industrial control applications. The method presented here can be considered as a generalized version of T-S fuzzy model with optimized performance in approximating nonlinear functions. Various examples are chosen to show the high function approximation accuracy and fast convergence obtained by applying the proposed method in approximating nonlinear systems locally and globally in comparison with the original T-S model

An Optimal T-S Model for the Estimation and Identification of Nonlinear Functions

A novel optimal method is developed to improve the identification and estimation of Takagi-Sugeno (TS) fuzzy model. The idea comes from the fact that the main drawback of T-S model is that it can not be applied when the membership functions are overlapped by pairs. This limits the application of the T-S model because this type of membership function has been widely used in the stability and controller design of fuzzy systems. It is also very popular in industrial control applications. The method presented here can be considered as a generalized version of T-S fuzzy model with optimized performance in approximating nonlinear functions. Various examples are chosen to show the high function approximation accuracy and fast convergence obtained by applying the proposed method in approximating nonlinear systems locally and globally in comparison with the original T-S model

Contributions to nonlinear system modelling and controller synthesis via convex structures

Esta tesis discute diferentes metodologías de modelado para extraer mejores prestaciones o resultados de estabilidad que aquéllas que el modelado convencional basado en sector no-lineal de sistemas Takagi-Sugeno (también denominados cuasi-LPV) es capaz de producir. En efecto, incluso si las LMIs pueden probar distintas cotas de prestaciones o márgenes de estabilidad (tasa de decaimiento, $\mathcal H_\infty$, etc.) para sistemas politópicos, es bien conocido que las prestaciones probadas dependen del modelo elegido y, dado un sistema no-lineal, dicho modelo politópico no es único. Por tanto, se presentan exploraciones hacia cómo obtener el modelo que es menos perjudicial para la medida de prestaciones elegida. Como una última contribución, mejores resultados son obtenidos mediante la extensión del modelado politópico Takagi-Sugeno a un marco de inclusiones en diferencias cuasi-convexas con planificación de ganancia. En efecto, una versión sin planificación de ganancia fue propuesta por un equipo de investigadores de la Universidad de Sevilla (Fiaccini, Álamo, Camacho) para generalizar el modelado politópico, y esta tesis propone una version aún más general de algunos de dichos resultados que incorpora planificación de ganancia.This thesis discusses different modelling methodologies to eke out best performance/stability results than conventional sector-nonlinearity Takagi-Sugeno (also known as quasi-LPV) systems modelling techniques are able to yield. Indeed, even if LMIs can prove various performance and stability bounds (decay rate, $\mathcal H_\infty$, etc.) for polytopic systems, it is well known that the proven performance depends on the chosen model and, given a nonlinear dynamic systems, the polytopic embeddings available for it are not unique. Thus, explorations on how to obtain the model which is less deletereous for performance are presented. As a last contribution, extending the polytopic Takagi-Sugeno setup to a gain-scheduled quasi-convex difference inclusion framework allows to improve the results over the polytopic models. Indeed, the non-scheduled convex difference inclusion framework was proposed by a research team in University of Seville (Fiacchini, Alamo, Camacho) as a generalised modelling methodology which included the polytopic one; this thesis poses a further generalised gain-scheduled version of some of these results.Aquesta tesi discuteix diferents metodologies de modelatge per extreure millors prestacions o resultats d'estabilitat que aquelles que el modelatge convencional basat en sector no-lineal de sistemes Takagi-Sugeno (també anomenats quasi-LPV) és capaç de produir. En efecte, fins i tot si les LMIs poden provar diferents cotes de prestacions o marges d'estabilitat (taxa de decaïment, $\mathcal H_\infty$, etc.) per a sistemes politòpics, és ben conegut que les prestacions provades depenen del model triat i, donat un sistema no-lineal, el dit model politòpic no és únic. Per tant, es presenten exploracions cap a com obtenir el model que és menys perjudicial per a la mesura de prestacions triada. Com una darrera contribució, millors resultats són obtinguts mitjançant l'extensió del modelatge politòpic Takagi-Sugeno a un marc d'inclusions en diferències quasi-convexes amb planificació de guany. En efecte, una versió sense planificació de guany va ser proposada per un equip d'investigadors de la Universitat de Sevilla (Fiaccini, Álamo, Camacho) per a generalitzar el modelatge politòpic, i aquesta tesi proposa una versió més general d'alguns d'aquests resultats que incorpora planificació de guany.Robles Ruiz, R. (2018). Contributions to nonlinear system modelling and controller synthesis via convex structures [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/100848TESI

Fuzzy Modelling and Control of the Air System of a Diesel Engine

This paper proposes a fuzzy modelling approach oriented to the design of a fuzzy controller for regulating the fresh airflow of a real diesel engine. This strategy has been suggested for enhancing the regulator design that could represent an alternative to the standard embedded BOSCH controller, already implemented in the Engine Control Unit (ECU), without any change to the engine instrumentation. The air system controller project requires the knowledge of a dynamic model of the diesel engine, which is achieved by means of the suggested fuzzy modelling and identification scheme. On the other hand, the proposed fuzzy PI controller structure is straightforward and easy to implement with respect to different strategies proposed in literature. The results obtained with the designed fuzzy controller are compared to those of the traditional embedded BOSCH controller

Fuzzy control turns 50: 10 years later

In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.Guerra, T.; Sala, A.; Tanaka, K. (2015). Fuzzy control turns 50: 10 years later. Fuzzy Sets and Systems. 281:162-182. doi:10.1016/j.fss.2015.05.005S16218228