Fuzzy systems as nonlinear dynamic system identifiers. II. Stability analysis and simulations

The author develops two identifiers of nonlinear dynamic systems based on fuzzy system models. It is proved that all signals in the fuzzy identifiers are uniformly bounded. Conditions under which the identification errors converge to zero are provided. It is also proved that the fuzzy identifiers are capable of following the output of a very general nonlinear dynamic system to arbitrary accuracy in any finite time interval. The most important advantage of the fuzzy identifiers is that linguistic descriptions about the systems (in terms of fuzzy IF-THEN rules) can be directly incorporated into the fuzzy identifiers. Two fuzzy identifiers for the chaotic glycolytic oscillator are simulated. The results show that they can identify the chaotic system at a reasonable speed and accuracy without using any linguistic descriptions, and that, by incorporating some linguistic descriptions, the speed and accuracy of the fuzzy identifiers is greatly improved