Bisimulation of Dynamical Systems

Bisimulation relations for dynamical, control, and hybrid systems

The fundamental notion of bisimulation equivalence for concurrent processes, has escaped the world of continuous, and subsequently, hybrid systems. Inspired by the categorical framework of Joyal, Nielsen and Winskel, we develop novel notions of bisimulation equivalence for dynamical systems as well as control systems. We prove that this notion can be captured by the abstract notion of bisimulat...

Bisimulation Relations for Dynamical and Control Systems

In this paper we propose a new equivalence relation for dynamical and control systems called bisimulation. As the name implies this definition is inspired by the fundamental notion of bisimulation introduced by R. Milner for labeled transition systems. It is however, more subtle than its namesake in concurrency theory, mainly due to the fact that here, one deals with relations on manifolds. We ...

A composition theorem for bisimulation functions

The standard engineering approach to modelling of complex systems is highly compositional. In order to be able to understand (or to control) the behavior of a complex dynamical systems, it is often desirable, if not necessary, to view this system as an interconnection of smaller interacting subsystems, each of these subsystems having its own functionalities. In this paper, we propose a composit...

Bisimulation Relations for Dynamical and Control Systems

Unifying bisimulation relations for discrete and continuous systems

The fundamental notion of bisimulation has inspired various notions of system equivalences in concurrency theory. Many notions of bisimulation for various discrete systems have been recently unified in the abstract category theoretical formulation of bisimulation due to Joyal, Nielsen and Winskel. In this paper, we adopt their framework and unify the notions of bisimulation equivalences for dis...