Simulation of hybrid systems in Omola/Omsim

Abstract. Hybrid systems|those composed of the interaction of discrete and continuous inputs, outputs, states, and dynamic equations|are an important class of models of complex, real-world phenomena. However, the simulation tools currently available seem to be (1) ad hoc retro- tting of existing packages, (2) hastily-built new languages, or (3) specialized software for particular subclasses (e.g., piecewise-constant dynamics). Our goal is to produce fast, high delity simulations of (networks of) a very broad class of hybrid systems in a user-friendly environment. In this paper, we rst review expertise in the mathematical modeling of hybrid systems, viz. the hybrid dynamical systems of Branicky (HDS). Also, we discuss the object-oriented modeling and simulation of combined discrete/continuous systems using the Omola modeling language and Omsim simulation environment developed over the last eight years at Lund. Leveraging these, we are led to our main contribution: a general set of hybrid systems model classes which encompass HDS and hence several other models popularized in the literature that combine nite automata and discrete event systems with ordinary di erential (ODEs) and di erential algebraic equations (DAEs). These Omola model classes may beviewed as \templates " or \macros " for quick and easy entering of hybrid systems for subsequent analysis and numerically-sophisticated simulation using Omsim