The mathematical model and a new development of the systematic synthesis technique for a fuzzy dynamic system with a fuzzy controller will be presented. In a fuzzy dynamic system, a fuzzy relational matrix will be introduced as a counterpart of a differential equation in conventional control theory. Then, as an application of the concepts of fuzzy inverse problems, a new approach to the design of a fuzzy controller for a given dynamic system will also be discussed.
A mathematical description of a fuzzy dynamic system will be developed; a systematic method to derive a fuzzy controller strategy from an underlying fuzzy system model will also be established. The theoretical development presented here enables the suboptimal control of the fuzzy system. The analysis proposed here may not be exhaustive but it does provide some insight into the basic operations and properties of fuzzy dynamic systems.
As an illustrative example, a fuzzy controller problem with a unit delay will be discussed in detail and the simulation results will be presented.