Stability and control of fuzzy dynamic systems via cell-state transitions in fuzzy hypercubes

The objective of this paper is to provide fuzzy control designers with a generalized design tool for stable fuzzy logic controllers in an optimal sense. Given multiple sets of data disturbed by vagueness uncertainty, we generate the implicative rules that guarantee stability and robustness of closed-loop fuzzy dynamic systems. First, the mathematical basis of fuzzy hypercubes and fuzzy dynamic systems is rigorously studied by considering the membership conditions for perfect recall and the evidential combination for reliable reasoning. Second, the author suggests the cell-state transition method, which utilizes Hsu´s cell-to-cell mapping concept. As a result, a generic and implementable design methodology for obtaining a fuzzy feedback gain K, a fuzzy hypercube, is provided and illustrated with simple examples. The designed rules or membership functions in K form the cell-state transitions that lead an initial state to the goal state globally. The cell-state transition approach provides flexibility in choosing different controller rule bases depending on optimal strategies