A behavioral framework for compositionality: linear systems, discrete event systems and hybrid systems

In this paper we formulate a general framework based on the behavioral approach to dynamical systems, in which various issues regarding interconnection of systems can be addressed. The main part of the framework is that interconnections or compositions of systems can be modelled with interconnection of behaviors and generalized projection operations. Control problems such as supervisory control problem or feedback control problem can be expressed in terms of behavioral interconnection, and therefore can be put into this framework. In the paper we discuss some variants of control problems and provide solutions to them

Bisimulation as congruence in the behavioral setting

We cast the notion of bisimulation in the Willems' behavioral setting. We show that in this setting, bisimulation is also a congruence, as it is known in the field of concurrent processes. Bisimulation is a congruence means if A and A' are bisimilar systems, then A || B and A' || B are also bisimilar. Here, the operator || denotes systems composition, and B is any other system that is composed with A or A'