The Behavioral Approach to Open and Interconnected Systems

In this article we have presented an approach to the mathematical description of dynamical systems. The central notion is the behavior, which consists of the set of time trajectories that are declared possible by the model of a dynamical system. Often, the behavior is defined as the set of solutions of a system of differential equations. Models that specify a behavior usually involve latent variables in addition to the manifest variables the model aims at. We have also described a methodology for modeling interconnected systems, called tearing, zooming, and linking. The underlying mathematical language consists of terminals, modules, the interconnection graph, the module embedding, and the manifest variable assignment. The combination of module equations, interconnection constraints, and manifest variable assignment leads to a latent-variable representation for the behavior of the manifest variables the model aims. This methodology of tearing, zooming, and linking offers a systematic procedure for modeling interconnected systems that is much better adapted to the physics of interconnected systems than input/output-modeling procedures such as, for example, Simulink. The methodology of tearing, zooming, and linking has many things in common with bond graphs.