Sliding mode control theory‐based algorithm for online learning in type‐2 fuzzy neural networks: application to velocity control of an electro hydraulic servo system

Abstract

SUMMARYIn this paper, a novel sliding mode control theory‐based learning algorithm is proposed to train an interval type‐2 fuzzy neural network using type‐2 fuzzy triangular membership functions. The structure considered is a type‐2 Takagi–Sugeno–Kang fuzzy logic system in which the antecedents are type‐2 fuzzy sets, and consequents are crisp numbers (A2‐C0). In the proposed learning algorithm, instead of trying to minimize an error function as is generally performed, the weights of the fuzzy neural network are tuned by the proposed algorithm in a way that the error is enforced to satisfy a stable equation. The parameter update rules to achieve this are derived, and the convergence of the parameters is proved by the use of Lyapunov stability method. To illustrate the applicability and the efficacy of the proposed method, we tested it on the velocity control of an electro hydraulic servo system in the presence of flow nonlinearities and internal friction. The motivation behind testing the proposed learning algorithm on this system is that it contains several nonlinearities that limit the ability of conventional controllers in achieving a satisfactory performance. The simulation studies indicate that the type‐2 fuzzy neuro structure with the proposed learning algorithm results in a better performance than its type‐1 fuzzy counterpart. Moreover, the proposed learning algorithm is easy to implement because of its simple structure, which makes it less complicated than the other learning algorithms seen in literature. Copyright © 2012 John Wiley & Sons, Ltd.