SVR Learning-Based Spatiotemporal Fuzzy Logic Controller for Nonlinear Spatially Distributed Dynamic Systems

A data-driven 3-D fuzzy-logic controller (3-D FLC) design methodology based on support vector regression (SVR) learning is developed for nonlinear spatially distributed dynamic systems. Initially, the spatial information expression and processing as well as the fuzzy linguistic expression and rule inference of a 3-D FLC are integrated into spatial fuzzy basis functions (SFBFs), and then the 3-D FLC can be depicted by a three-layer network structure. By relating SFBFs of the 3-D FLC directly to spatial kernel functions of an SVR, an equivalence relationship of the 3-D FLC and the SVR is established, which means that the 3-D FLC can be designed with the help of the SVR learning. Subsequently, for an easy implementation, a systematic SVR learning-based 3-D FLC design scheme is formulated. In addition, the universal approximation capability of the proposed 3-D FLC is presented. Finally, the control of a nonlinear catalytic packed-bed reactor is considered as an application to demonstrate the effectiveness of the proposed 3-D FLC.

I. Introduction

IN THE real world, many physical processes and systems, such as industrial chemical reactor, semiconductor manufacturing, solar power plant, and thermal processing, have the characteristics of spatial distribution. They are usually called spatially distributed dynamic systems, or distributed parameter systems (DPS) [1], [2]. The states, controls, and outputs of the processes depend on the space position as well as on the time [3]. The spatially distributed dynamic systems usually give rise to control problems that involve the regulation of highly distributed control variables using spatially distributed control actuators and measurement sensors.