Comparison approaches for identification of all-data cloud-based evolving systems

In this paper we deal with identification of nonlinear systems which are modelled by fuzzy rule-based models that do not assume fixed partitioning of the space of antecedent variables. We first present an alternative way of describing local density in the cloud-based evolving systems. The Mahalanobis distance among the data samples is used which leads to the density that is more suitable when the data are scattered around the input-output surface. All the algorithms for the identification of the cloud parameters are given in a recursive form which is necessary for the implementation of an evolving system. It is also shown that a simple linearised model can be obtained without identification of the consequent parameters. All the proposed algorithms are illustrated on a simple simulation model of a static system

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

A simple fuzzy rule-based system through vector membership and kernel-based granulation.

It is widely recognized that the human reasoning can be approximated by fuzzy rule-based (FRB) systems which can be seen as one of the basic frameworks for representation of intelligent systems. During the last quarter of a century two particular types of FRB systems, namely Zadeh-Mamdani (ZM) and Takagi-Sugeno (TS) dominated the field. In this paper we propose an alternative type which is simpler and more intuitive while preserving the advantages of its predecessors, such as flexibility, modularity, human-intelligibility. The newly proposed concept of vector membership (VM) and kernel-based granulation (KG) of complex systems (respectively their mathematical descriptions) we see as the next, more efficient form of system modelling that is widely applicable to a plethora of applications ranging from time-series prediction, clustering, classification, control, decision support systems to other problems where conventional fuzzy rule-based systems are used. The proposed simple FRB based on VM and KG are non-parametric and fully represent the real data. Contrast this to the mere approximation of the real data distributions that is provided by Gaussian (scalar), triangular, trapezoidal etc. parametric types of membership functions that are used in currently existing types of FRB (ZM and TS). Note that even probabilistic models that are usually based on Gaussian distributions or a mixture of Gaussians or other parametric representations provide only an approximation of the real data distribution (it should be noted that particle filters are perhaps the only form of non-parametric representation that is similar in this sense to the newly proposed simple FRB with VM and KG, but they are computationally cumbersome with exponentially growing complexity). The main contribution of the proposed simple FRB with VM and KG is that while preserving all the advantages of ‘traditional’ FRB systems they avoid the well known problems related to (multiple scalar) membership functions definition, identification and update. They fully take into account and exactly represent the spatial distribution and similarity of all the real data by proposing an innovative and much simplified form of the antecedent part. At the same time, transformations to the ‘traditional’ (ZM and TS) fuzzy sets expressed by parametric membership functions per variable are also possible. In papers that will follow we will demonstrate on practical examples (including classification, prediction, decision support and other classes of problems) the benefits of this scheme. (c) IEEE Pres