Modeling of Hybrid Systems

Abstract

AbstractHybrid dynamical systems contain both time-driven continuous dynamics and event-driven discrete dynamics that interact with each other, and their interactions determine the behavior of the system over time. To fully understand the tight interactions between discrete and continuous dynamics, we need a unified modeling framework. Various models have been developed for hybrid systems; they can be broadly classified into two groups according to their origins. On the one hand, computer scientists look at hybrid systems primarily as discrete (computer) programs interacting with the continuous environment. They extend their computational models, such as finite state machines, automata, and Petri nets, from discrete systems to hybrid systems by embedding the continuous-variable dynamics into these discrete models. On the other hand, researchers from the areas of dynamical systems and control regard hybrid systems as a collection of differential/difference equations with discontinuous or multi-valued variables. They extend the models and methodologies for traditional continuous-variable systems, such as those described by ordinary differential/difference equations, by including discrete variables to describe the jumping or switching phenomena. Both approaches have their own strengths. For instance, the first group of approaches has traditionally been able to deal with complex discrete dynamics emphasizing analysis results (verification) and simulation methodologies, while the second group typically deals with complex continuous-variable dynamics and mainly concerns itself with stability, robustness, optimality, and synthesis issues.