Extended fuzzy function model with stable learning methods for online system identification

The aim of the online nonlinear system identification is the accurate modeling of the current local input‐output behavior of the plant without using any prior knowledge and offline modeling phase. It is a challenging task for many intelligent systems when used for real‐time control applications. In this paper, we propose a novel computationally efficient extended fuzzy functions (EFF) model for system identification of unknown nonlinear discrete‐time systems. The main contributions are to introduce an effective quasi‐nonlinear model (EFF) and propose adaptive learning rates (ALR) for recursive least squares (RLS) and gradient‐descent (GD) methods. The asymptotic convergence of the modeling errors and boundedness of the parameters are proved by using the input‐to‐state stability (ISS) approach. Numerical simulations are performed for Box–Jenkins gas furnace system and a nonlinear dynamic system. The benefits of its accuracy, stability and simple implementation in practice indicate that EFF model is a promising technique for online identification of nonlinear systems. Copyright © 2010 John Wiley & Sons, Ltd.