Introducing the Fuzzy Relational Hybrid Model as a Building Block for Intelligent Modeling of Hybrid Dynamical Systems

In this paper, a novel intelligent modeling framework is introduced for modeling hybrid dynamical systems, which may contain both continuous-valued and discrete-valued dynamics and/or signals. The proposed modeling framework consists of a fuzzy relational hybrid model (FRHM) structure and an online identification algorithm. The FRHM structure has some useful properties, e.g., the ability of modeling both hard and soft switchings (even simultaneously), model transparency (in view of knowledge extraction and knowledge embedment), and possibility of connecting disjoint models through mathematical operations (to construct larger model structures). In addition, the proposed FRHM structure can be used to model a wide variety of hybrid dynamical systems, including nonlinear dynamical systems, dynamical systems with switchings or logical functions, dynamical systems with discrete-valued or qualitative inputs and/or outputs, etc. The fuzzy relational hybrid dynamical system is an important product of the proposed modeling structure, which, in this paper, has applied to modeling an asynchronous dc-dc buck converter as the case study.