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

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Asymptotically exact stabilisation for constrained discrete Takagi-Sugeno systems via set-invariance

[EN] Given a Takagi-Sugeno (TS) system, this paper proposes a novel methodology to obtain the state feedback controller guaranteeing, asymptotically as a Polya-related complexity parameter grows, the largest (membership-shape independent) possible domain-of-attraction with contraction-rate performance lambda, based on polyhedral lambda-contractive sets from constrained linear systems literature. The resulting controller is valid for any realisation of the memberships, as usual in most TS literature. For a finite complexity parameter, an inner estimate of such largest set is obtained; the frontier of such approximation can be understood as the level set of a polyhedral control-Lyapunov function. Convergence of a proposed iterative algorithm is asymptotically necessary and sufficient for TS system stabilisation: for a high-enough value of the complexity parameter, any conceivable shape-independent Lyapunov controller design procedure will yield a proven domain of attraction smaller or equal to the algorithm's output. (C) 2016 Elsevier B.V. All rights reserved.This work has been supported by grants DPI2015-70433- P and DPI2016-81002-R, from Spanish Government (MINECO) and grant PROMETEOII/2013/004 from Generalitat Valenciana.Ariño-Latorre, CV.; Sala, A.; Pérez Soler, E.; Bedate Boluda, F.; Querol-Ferrer, A. (2017). Asymptotically exact stabilisation for constrained discrete Takagi-Sugeno systems via set-invariance. Fuzzy Sets and Systems. 316:117-138. https://doi.org/10.1016/j.fss.2016.10.004S11713831

Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients

Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the $L_\infty$ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an $L_q$ norm with $q<\infty$ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis.Comment: 24 page

Workshop on the Integration of Finite Element Modeling with Geometric Modeling

The workshop on the Integration of Finite Element Modeling with Geometric Modeling was held on 12 May 1987. It was held to discuss the geometric modeling requirements of the finite element modeling process and to better understand the technical aspects of the integration of these two areas. The 11 papers are presented except for one for which only the abstract is given

Computer Vision Problems in 3D Plant Phenotyping

In recent years, there has been significant progress in Computer Vision based plant phenotyping (quantitative analysis of biological properties of plants) technologies. Traditional methods of plant phenotyping are destructive, manual and error prone. Due to non-invasiveness and non-contact properties as well as increased accuracy, imaging techniques are becoming state-of-the-art in plant phenotyping. Among several parameters of plant phenotyping, growth analysis is very important for biological inference. Automating the growth analysis can result in accelerating the throughput in crop production. This thesis contributes to the automation of plant growth analysis. First, we present a novel system for automated and non-invasive/non-contact plant growth measurement. We exploit the recent advancements of sophisticated robotic technologies and near infrared laser scanners to build a 3D imaging system and use state-of-the-art Computer Vision algorithms to fully automate growth measurement. We have set up a gantry robot system having 7 degrees of freedom hanging from the roof of a growth chamber. The payload is a range scanner, which can measure dense depth maps (raw 3D coordinate points in mm) on the surface of an object (the plant). The scanner can be moved around the plant to scan from different viewpoints by programming the robot with a specific trajectory. The sequence of overlapping images can be aligned to obtain a full 3D structure of the plant in raw point cloud format, which can be triangulated to obtain a smooth surface (triangular mesh), enclosing the original plant. We show the capability of the system to capture the well known diurnal pattern of plant growth computed from the surface area and volume of the plant meshes for a number of plant species. Second, we propose a technique to detect branch junctions in plant point cloud data. We demonstrate that using these junctions as feature points, the correspondence estimation can be formulated as a subgraph matching problem, and better matching results than state-of-the-art can be achieved. Also, this idea removes the requirement of a priori knowledge about rotational angles between adjacent scanning viewpoints imposed by the original registration algorithm for complex plant data. Before, this angle information had to be approximately known. Third, we present an algorithm to classify partially occluded leaves by their contours. In general, partial contour matching is a NP-hard problem. We propose a suboptimal matching solution and show that our method outperforms state-of-the-art on 3 public leaf datasets. We anticipate using this algorithm to track growing segmented leaves in our plant range data, even when a leaf becomes partially occluded by other plant matter over time. Finally, we perform some experiments to demonstrate the capability and limitations of the system and highlight the future research directions for Computer Vision based plant phenotyping

Nouveaux schémas de commande et d'observation basés sur les modèles de Takagi-Sugeno

This thesis addresses the estimation and controller design for continuous-time nonlinear systems. The methodologies developed are based on the Takagi-Sugeno (TS) representation of the nonlinear model via the sector nonlinearity approach. All strategies intend to get more relaxed conditions.The results presented for controller design are split in two parts. The first part is about standard TS models under control schemes based on: 1) a quadratic Lyapunov function (QLF); 2) a fuzzy Lyapunov function (FLF); 3) a line-integral Lyapunov functions (LILF); 4) a novel non-quadratic Lyapunov functional (NQLF). The second part concerns to TS descriptor models. Two strategies are proposed: 1) within the quadratic framework, conditions based on a general control law and some matrix transformations; 2) an extension to the nonquadratic approach based on a line-integral Lyapunov function (LILF) using non-PDC control law schemes and the Finsler’s Lemma; this strategy offers parameter-dependent linear matrix inequality (LMI) conditions instead of bilinear matrix inequality (BMI) constraints for second-order systems. On the other hand, the problem of the state estimation for nonlinear systems via TS models is also addressed considering: a) the particular case where premise vectors are based on measured variables and b) the general case where premise vectors can be based on unmeasured variables. Several examples have been included to illustrate the applicability of the obtained results.Cette thèse aborde l'estimation et la conception de commande de systèmes non linéaires à temps continu. Les méthodologies développées sont basées sur la représentation Takagi-Sugeno (TS) du modèle non linéaire par l'approche du secteur non-linéarité. Toutes les stratégies ont l'intention d'obtenir des conditions plus détendu. Les résultats présentés pour la conception de commande sont divisés en deux parties. La première partie est environ sur les modèles TS standard au titre des schémas de commande basés sur: 1) une fonction de Lyapunov quadratique (QLF); 2) une fonction de Lyapunov floue (FLF); 3) une fonction de Lyapunov intégrale de ligne (LILF); 4) un nouveau fonctionnelle de Lyapunov non-quadratique (NQLF). La deuxième partie concerne des modèles TS descripteurs. Deux stratégies sont proposées: 1) dans le cadre quadratique, des conditions basées sur une loi de commande général et quelques transformations de matrices; 2) une extension de l'approche non quadratique basée sur LILF utilisant un schéma de commande non-PDC et le lemme du Finsler; cette stratégie offre conditions sur la forme d’inégalité matricielles linéaires (LMI) dépendant des paramètres au lieu des contraintes sur la forme d’inégalité matricielles bilinéaires (BMI) pour les systèmes de second ordre. D'autre part, le problème de l'estimation de l'état pour les systèmes non linéaires via modèles TS est également abordé considérant: a) le cas particulier où les vecteurs prémisses sont basées sur les variables mesurées et b) le cas général où les vecteurs prémisse peuvent être basés sur des variables non mesurées. Plusieurs exemples ont été inclus pour illustrer l'applicabilité des résultats obtenus

Modeling of objects using planar facets in noisy range images

Products designed and manufactured before the advent of Computer Aided Design (CAD) and Computer Aided Manufacturing (CAM) technology have not been documented electronically. To avoid the laborious procedure of redesigning the parts, a reverse engineering approach can be adopted. This approach involves, taking a picture of the object and constructing a solid model from the image data. Range image is a three dimensional image of an object or a scene. This image can be obtained from special cameras, called range image cameras, or can be constructed from the Coordinate Measuring Machine\u27s (CMM) output data. Adaptive Fuzzy c-Elliptotype (AFC) clustering algorithm is used to identify the planar facets in a range image. A modified version of AFC algorithm can handle noisy range images. Unknown number of planar facets can be identified using the Agglomerative clustering approach. The object is reconstructed using segmented image data. The equations of the edge are obtained from the plane intersections. An edge validity criterion is developed to validate the existence of an edge. Vertices are the two extreme points on the edge. A Boundary representation of the object is developed. The information about this object is then passed to a CAD software using Initial Graphics Exchange Specification (IGES)

Design and analysis of real intelligent mapping systems with applications to systems and control.

by Yeung Wai Leung.Thesis (M.Phil.)--Chinese University of Hong Kong, 1995.Includes bibliographical references (leaves 92-[96]).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Fuzzy Inference and Real Intelligent Mapping --- p.1Chapter 1.2 --- Organization of the thesis --- p.5Chapter 2 --- Fuzzy Logic inference --- p.7Chapter 2.1 --- Fuzzy logic --- p.7Chapter 2.1.1 --- Fuzzy sets --- p.7Chapter 2.1.2 --- Operations on fuzzy sets --- p.10Chapter 2.2 --- Fuzzy Inference --- p.11Chapter 3 --- Weaknesses of fuzzy inference --- p.17Chapter 3.1 --- Is the use of linguistic fuzzy if-then rules and membership func- tions a good means of representing human expert knowledge? --- p.17Chapter 3.2 --- Role of conventional fuzzy inference doubtful if the expert knowl- edge is in the form of sampled input-output data --- p.21Chapter 3.3 --- Computational requirements --- p.23Chapter 3.4 --- Low transparency --- p.24Chapter 3.5 --- Analytical difficulties --- p.25Chapter 4 --- Real Intelligent Mapping --- p.27Chapter 5 --- Design of Real Intelligent Mapping Systems Using Dirichlet Tessellation --- p.33Chapter 5.1 --- Dirichlet tessellation for function approximation --- p.34Chapter 5.2 --- Identification of a DT based RIM system by least-squares --- p.42Chapter 5.3 --- Examples --- p.48Chapter 5.3.1 --- Defining the problem --- p.48Chapter 5.3.2 --- Balancing an inverted pendulum --- p.49Chapter 5.3.3 --- Balancing an inverted pendulum with cart --- p.53Chapter 5.3.4 --- Truck backing-up --- p.56Chapter 5.3.5 --- Chaotic time series prediction --- p.60Chapter 5.4 --- Interactive CAD platform for RIM systems design --- p.63Chapter 6 --- Analysis of Dirichlet tessellation based Real Intelligent Mapping Systems --- p.67Chapter 6.1 --- Local Stability Analysis of DT Based RIM Systems --- p.69Chapter 6.1.1 --- Balancing an inverted pendulum --- p.71Chapter 6.1.2 --- Truck backing-up --- p.73Chapter 6.2 --- Global stability analysis of DT based RIM systems --- p.74Chapter 6.3 --- Design of a stable DT based RIM system --- p.79Chapter 6.4 --- A method for analyzing Second order DT based RIM systems --- p.82Chapter 6.5 --- Piecewise-polynomial real domain representation of a class of fuzzy controller and its stability --- p.85Chapter 7 --- Conclusion --- p.90Bibliography --- p.9