Fuzzy Model Identification and Self Learning with Smooth Compositions

Abstract

This paper develops a smooth model identifica-10 tion and self-learning strategy for dynamic systems taking 11 into account possible parameter variations and uncertain-12 ties. We have tried to solve the problem such that the 13 model follows the changes and variations in the system on 14 a continuous and smooth surface. Running the model to 15 adaptively gain the optimum values of the parameters on a 16 smooth surface would facilitate further improvements in 17 the application of other derivative based optimization 18 control algorithms such as MPC or robust control algo-19 rithms to achieve a combined modeling-control scheme. 20 Compared to the earlier works on the smooth fuzzy mod-21 eling structures, we could reach a desired trade-off between 22 the model optimality and the computational load. The 23 proposed method has been evaluated on a test problem as 24 well as the non-linear dynamic of a chemical process. 25 26 Keywords Fuzzy control Á Fuzzy IF-THEN systems 27 (TSK) Á Smooth compositions 28 1 Introduction 29 Soft computing methods are being used for identification of 30 non-linear and complex systems based on the input-output 31 data collected from the original system [1]. There are many

How Effective are Smooth Compositions in Predictive Control of TS Fuzzy Models?

“…Several interesting properties of smooth fuzzy compositions have been cited and proved in [1], and robustness advantage of smooth fuzzy models has been reported in almost all the contributions in the field [2,18,20,23]. However, they cannot be employed for the practical cases and industrial systems until an easy and industrial implementable algorithm appears.…”

“…Recently, some new smooth compositions have been presented and have been employed for modeling static input-output mapping of the dynamical systems in [2,18,19]. All the contributions in application of smooth compositions for advanced control of dynamic systems have employed the relational modeling framework [20].…”

“…Soft computing methods are being used for identification and control of nonlinear and complex systems based on the input-output data collected from the original system [1,2]. There are many applications of artificial neural network and fuzzy modeling framework for the identification and model-based control purpose in the industry and academia [3,4].…”

Application of Smooth Fuzzy Model in Image Denoising and Edge Detection

“…The fuzzy rules we have just constructed are supposed to have two IF and THEN parts, which can be interpreted to make a mathematical inference based on the fuzzy values employing the compositions of t-norms and s-norms. Different types of t-norms and s-norms have been introduced in the literature [18][19][20], where the min-max composition and product-sum composition are the mostly used compositions and are shown as follows:…”

Monotonic Fuzzy Systems With Goniometric Membership Functions

“…Those facts lead to increasing interest in smooth membership functions with compact support if the smooth monotone output is required [35]. Advantages of smooth fuzzy models have been shown in [45,46].…”