Enforcing Local Properties in Online Learning First Order TS-fuzzy Systems by Incremental Regularization

Embedded systems deseminate more and more. Because their complexity increases and their design time has to be reduced, they have to be increasingly equipped with self-tuning properties. One form is self-adaption of the system behavior, which can potentially lead the system into safety critical states. In order to avoid this and to speed up the self-tuning process, we apply a specific form of regularization, incremental regularization. The SILKE approach has been developed as an incremental regularization scheme for a special class of online learning Takagi-Sugeno fuzzy systems. Its aim is to control the process of self-tuning by guiding the online learning process towards local meta-level characteristics such as a smooth system behavior without outliers. This ability has been investigated experimentally and formally for zero order systems before. This paper now analyzes the regularization ability of the SILKE approach to enforce local smoothness in first order TS-fuzzy systems in order to enlarge the methodological basis for more complex applications. Keywords— First order Takagi Sugeno fuzzy systems, incremental learning, self-optimization, incremental regularization, fuzzy con-