Takagi-Sugeno Fuzzy Modelling of Multivariable Nonlinear System via Genetic Algorithms

Abstract

In this paper, the Takagi-8ugeno (T-8) fuzzy model of a multivariable nonlinear system in state space form is obtained using the developed fuzzy modelling algorithm. In this fuzzy model, the system sate space equation is expressed as the fuzzy summation of the state variables, disturbance and control input. To obtain this model with high accuracy, the genetic algorithm (GA) with a new encoding method is applied to search for the optimal model parameters. The proposed hybrid intelligence technique can evolve the fuzzy rule structure (number of rules and selection of rules, number of premise inputs and selection of premise inputs) so that the obtained fuzzy model has the simplest structures without decreasing the modelling accuracy. To validate the proposed approach, the algorithm is applied to model a building structure with a magneto-rheological (MR) damper, which is a multivariable nonlinear system. The modelling errors between the system outputs and the corresponding fuzzy model outputs are compared with the automatically selected rules. It is confirmed by the validation results that the proposed hybrid intelligence technique can find the optimal T-8 fuzzy model for the nonlinear system.