Bisimulation relations for dynamical, control, and hybrid systems

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 ...

Bisimulation Relations for Dynamical and Control Systems

Bisimulation of Dynamical Systems

A general notion of bisimulation is studied for dynamical systems. An algebraic characterization of bisimulation together with an algorithm for computing the maximal bisimulation relation is derived using geometric control theory. Bisimulation of dynamical systems is shown to be a concept which unifies the system-theoretic concepts of state space equivalence and state space reduction, and which...

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...

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...