Using fuzzy relational hybrid models to control mixed‐valued dynamic systems with discrete‐valued inputs

Abstract

This is the first attempt to bring the fuzzy relational hybrid models from modelling to control. The main challenge is to configure both the plant model and the controller appropriately so that the overall system has good analytical and numerical properties. However, to close the control loop effectively by connecting the fuzzy relational hybrid model blocks, it is needed for its core mathematical operator to be associative. Therefore, in this paper: (1) It has been shown that the core mathematical operator that relates the connected g-normal fuzzy relational hybrid model blocks, that is, the Yager-product fuzzy relational inner composition, unlike most fuzzy relational inner compositions, is associative; (2) An intelligent adaptive control scheme has been developed for a class of plants in which the states of the system can be mixed-valued and all inputs are of discrete-valued type (either quantitative or qualitative). Benefiting from the associative property, the proposed control scheme uses the g-normal fuzzy relational hybrid model building blocks in the role of the controller as well as the plant model with no prior knowledge of the elements of the fuzzy relational matrices. Being applied to control a synchronous buck converter in both regulation and tracking scenarios, and under parameters uncertainties, the proposed scheme has been evaluated by computer simulation.