On the Interpretation and Identiication of Dynamic Takagi-sugeno Fuzzy Models

Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identiied from experimental data. Ideally, it is desirable that a dynamic Takagi-Sugeno fuzzy model should give accurate global nonlinear prediction, and at the same time that its local models are close approximations to the local linearizations of the nonlinear dynamic system. The latter is important in many applications where the constituent local models are used individually, and aids considerable validation and interpretation of the model. This deenes a multi-objective identiication problem; namely, the construction of a dynamic model that is a good approximation of both local and global dynamics of the underlying system. While these objectives are often connicting, it is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using aane local model structures, which suggests that a solution to the multi-objective identiication problem exists. However, it is also shown that the aane local model structure is a highly sensitive parameterization when applied in transient operating regimes, i.e. far away from equilibrium. The reason is essentially that the constant term in the aane local model tend to dominate over the linear term during transients. In addition, it is inherently more diicult to design informative experiments in transient regions compared to near-equilibrium regions. Due to the multi-objective nature of the identiication problem studied here, special considerations must be made during model structure selection, experiment design and identiication in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear 1 identifcation algorithms are studied. These include constrained and regularized identiication and locally weighted identiication. Their usefulness in the present context is illustrated by examples.