SVD-based complexity reduction to TS fuzzy models

Abstract

Abstract-One of the typical important criteria to be considered in real-time control applications is the computational complexity of the controllers, observers, and models applied. In this paper, a singular value decomposition (SVD)-based complexity reduction technique is proposed for Takagi Sugeno (TS) fuzzy models. The main motivation is that the TS fuzzy model has exponentially growing computational complexity with the improvement of its approximation property through, as usually practiced, increasing the density of antecedent terms. The reduction technique proposed here is capable of defining the contribution of each local linear model included in the TS fuzzy model, which serves to remove the weakly contributing ones as according to a given threshold. Reducing the number of models leads directly to the computational complexity reduction. This work also includes a number of numerical and application examples.

SVD-based reduction to MISO TS models

“…For further detailed investigation of TS fuzzy models and closely related concepts see [1]- [10] and [30]. A TS model consists of a number of local linear models assigned to fuzzy regions, which are designed to approximate the dynamic features at the corresponding operating fuzzy points in vector space .…”

“…Presumably, the SVD technique in this paper and in [12] and [13] can be replaced by other orthogonal techniques investigated by Yen and Wang in [11]. An extension of [11] to multidimensional cases may also be conducted in a similar fashion as the higher order SVD reduction technique proposed in [10], [12], and [13] and in this paper. Further developments of SVD-based fuzzy reduction [12], [13] are proposed in [10], [17], [18], and [38].…”

“…An extension of [11] to multidimensional cases may also be conducted in a similar fashion as the higher order SVD reduction technique proposed in [10], [12], and [13] and in this paper. Further developments of SVD-based fuzzy reduction [12], [13] are proposed in [10], [17], [18], and [38]. Examples of applying SVD reduction can be found in [35]- [37].…”

“…The present work constitutes a detailed investigation of the preliminary approaches outlined in [10] and gives a possible solution to the problem analyzed above. The algorithms proposed here are mostly developed in [12] and [13], but are restructured in terms of tensor description in order to facilitate further developments for TS fuzzy models.…”

“…Section V briefly summarizes those properties of HOSVD, which are significant in complexity reduction. Section VI presents the HOSVD based reduction of multiple-input-single-output (MISO) TS fuzzy models expounding the approaches defined in the preliminary work [10]. Section VII gives a detailed example of a dynamic system through numerical and analytical considerations to show the effectiveness of the proposed method.…”