**Speaker**: David Wittenberg (Brandeis)

**Title**: Rigorous Modeling of Hybrid Systems using Interval
Arithmetic Constraints

**Abstract**:
Hybrid systems research tries to rigorously model systems which
have analog components described by ODEs (Ordinary Differential
Equations), and very small digital components, often described as
programs. Hybrid systems techniques are usually used in areas
such as aircraft safety where errors are extremely expensive.
Because hybrid systems are often used to prove safety properties,
it is critical to have a rigorous analysis.

This talk describes some of the problems in using a computer to simulate a hybrid system. One of the major issues is that FP (Floating Point numbers) have none of the nice properties that the Reals (or even the Rationals) have. I will start by discussing the properties of FP, and then describe "Interval Arithmetic", a technique by which we can do calculations over FP and prove useful properties about those calculations. I will then briefly define hybrid systems, and describe the particular one I've been modeling.

Finally, I will talk about the system we've built, and how it rigorously models a hybrid system, even when the ODEs describing that system are discontinuous.

This talk is self-contained, and assumes very little background in either mathematics or computer science.