Fuzzy systems as nonlinear dynamic system identifiers. I. Design

Fuzzy systems are used as identifiers for nonlinear dynamic systems. A theoretical justification for the fuzzy identifiers is provided by proving that they are capable of following the output of a very general nonlinear dynamic system to arbitrary accuracy in any finite time interval. The fuzzy identifiers are constructed from a set of adaptable fuzzy IF-THEN rules and can combine both numerical information and linguistic information into their designs in a uniform fashion. Two fuzzy identifiers are developed. The first is designed through the following four steps: (1) define some fuzzy sets which do not change in the state space of the system; (2) construct fuzzy rule bases of the fuzzy identifier; (3) design the fuzzy systems in the fuzzy identifier based on the fuzzy rule bases of (2); and (4) develop an adaptive law for the free parameters in the fuzzy identifier. The second fuzzy identifier is designed in a similar way except that the parameters characterizing the fuzzy sets in the state space change during the adaptation procedure and the fuzzy systems and the adaptive law are different. It is proved that both fuzzy identifiers are globally stable under certain conditions