The efficient and accurate management of time in simulations of hybrid models is an outstanding engineering problem. General a priori knowledge about the dynamic behavior of the hybrid system (i.e. essentially continuous, essentially discrete, or ‘truly hybrid’) facilitates this task. Indeed, for essentially discrete and essentially continuous systems, existing software packages can be conveniently used to perform quite sophisticated and satisfactory simulations. The situation is different for ‘truly hybrid’ systems, for which direct application of existing software packages results in a lengthy design process, cumbersome software assemblies, inaccurate results, or some combination of these independent of the designer’s a priori knowledge about the system’s structure and behavior. The main goal of this paper is to provide a methodology whereby simulation designers can use a priori knowledge about the hybrid model’s structure to build a straightforward, efficient, and accurate simulator with existing software packages. The proposed methodology is based on a formal decomposition and re-articulation of the hybrid system; this is the main theoretical result of the paper. To set the result in the right perspective, we briefly review the essentially continuous and essentially discrete approaches, which are illustrated with typical examples. Then we present our new, split system approach, first in a general formal context, then in three more specific guises that reflect the viewpoints of three main communities of hybrid system researchers and practitioners. For each of these variants we indicate an implementation path. Our approach is illustrated with an archetypal problem of power grid control.
Stability analysis and controller synthesis for hybrid dynamical systems