Effective computation for nonlinear systems

Abstract:

 Nonlinear dynamical and control systems are an important source of
applications for theories of computation over the the real numbers, since
these systems are usually to complicated to study analytically, but may be
extremely sensitive to numerical error. Further, computer-assisted proofs
and specification verification problems require a rigorous treatment of
numerical errors. In this talk I will describe how to provide a semantics
for effective computations on sets and maps, and discuss the computability
of some important operators. I will show how these operations have been
implemented in the tool Ariadne, and give examples of the use of Ariadne for
the analysis, design and verification of nonlinear and hybrid systems.