Trade-off between approximation accuracy and complexity: TS controller design via HOSVD based complexity minimization

Higher order singular value decomposition (HOSVD) based complexity reduction method is proposed in this paper to tensor product based model approximation methods, especially, to Takagi-Sugeno (TS) fuzzy or polytopic models. The main motivation is that the TS model has exponentially growing computational complexity with the improvement of its approximation property through, as usually practiced, increasing the density of fuzzy partitions. The reduction technique proposed here is capable of pinpointing the contribution of each local linear model consequents of the fuzzy rules, which serves to remove the weakly contributing ones according to a given threshold. Reducing the number of local models leads directly to complexity reduction. The explicit form in this paper for the proposed reduction can also be applied on polytopic model approximation methods. A detailed illustrative example of a non-linear dynamic model is also given.