Fuzzy Programming Problem in the Weakly Structurable Dynamic System and Choice of Decisions GIA SIRBILADZE

Abstract: This work deals with the problems of the Weakly Structurable Continuous Dynamic System (WSCDS) optimal control and briefly discuss the results developed by G. Sirbiladze [17]. Sufficient and necessary conditions are presented for the existence of an extremal fuzzy optimal control processes, for which we use R. Bellman’s optimality principle and take into consideration the gain-loss fuzzy process. A separate consideration is given to the case where an extremal fuzzy control process acting on the WSCDS (1) depends and (2) does not depend on an WSCDS state. Applying Bellman’s optimality principle and assuming that the gain-loss process exists for the WSCDS, a variant of the fuzzy integral representation of an optimal control is given for the WSCDS. This variant employs the instrument of extended extremal fuzzy composition measures constructed in [16]. The questions of defining a fuzzy gain relation for the WSCDS are considered, taking into account the avail-able expert knowledge on the WSCDS subject-matter. An example of constructing of the WSCDS optimal control is presented