Space-decomposition based 3D fuzzy control design for nonlinear spatially distributed systems with multiple control sources using multiple single-output SVR learning

Abstract

Three-dimensional fuzzy logic controller (3D FLC) is a recently developed FLC integrating space information expression and processing for nonlinear spatially distributed dynamical systems (SDDSs). Like a traditional FLC, expert knowledge can help design a 3D FLC. Nevertheless, there are some situations where expert knowledge cannot be formulated into precise words; what's worse, it might not be explicitly expressed in words. In contrast, spatio-temporal data sets containing control laws are usually available. In this study, a data-driven based 3D FLC design method using multiple single-output support vector regressions (SVRs) is proposed for SDDSs with multiple control sources. Firstly, in terms of the locally spatial influence feature of control sources on the space domain, a complex SDDS is decomposed into multiple SDDSs with one control source and a space-decomposition based 3D fuzzy control scheme is proposed. Secondly, multiple single-output SVRs with ε-insensitive cost function are used to learn and design multiple 3D FLCs from spatio-temporal data sets. Thirdly, a five-step design scheme is proposed, including space decomposition, data collection, spatial support-vector learning, 3D fuzzy rule construction, and 3D fuzzy controller integration. Finally, the proposed method is applied to a packed-bed reactor and simulation results were used to verify its effectiveness.