Mihaly Petreczky

Center for Imaging Science

Department of Biomedical Engineering

The Johns Hopkins University

**Identification and Realization Theory for Hybrid Systems**

Hybrid systems are dynamical systems which exhibit both continuous and
discrete behavior. Such systems arise naturally in a number of
fields, including control theory, signal processing,
computer vision, communication networks and even
systems biology.

Our goal is to infer a hybrid dynamical system model based on the
observed external behavior. The observed behavior can be
a stochastic process or an input-output map.

We will address the following questions:

1.Under which conditions can the observed
behavior be represented by a hybrid dynamical system ?

2.When is a hybrid dynamical system a minimal representation of
the observed behavior?
Does such a minimal hybrid representation exist ?
Is it unique ?

3. How to compute/construct a (preferably minimal)
hybrid dynamical system from the observed behavior ?

We will also indicate the relationship between the solution of the above problems for hybrid systems and the solution for other classes of dynamical input-output systems.

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