A new method for identification of fuzzy models with controllability constraints

Takagi-Sugeno fuzzy models are cataloged as universal approximators and have been proven to be a powerful tool for the prediction of systems. However, in certain cases they may fail to inherit the main properties of a system which may cause problems for control design. In particular, a non-suitable model can generate a loss of closed-loop performance or stability, especially if that model is not controllable. Therefore, ensuring the controllability of a model to enable the computation of appropriate control laws to bring the system to the desired operating conditions. Therefore, a new method for identification of fuzzy models with controllability constraints is proposed in this paper. The method is based on the inclusion of a penalty component in the objective function used for consequence parameter estimation, which allows one to impose controllability constraints on the linearized models at each point of the training data. The benefits of the proposed scheme are shown by a simulation-based study of a benchmark system and a continuous stirred tank: the stability and the closed-loop performances of predictive controllers using the models obtained with the proposed method are better than those using models found by classical and local fuzzy identification schemes.