Boundary control of non-linear hyperbolic systems — Migrating object approach

The paper presents part of the created systematic methodology of solving optimal control problems formulated for systems with subsystems (possibly analog) that are changing scale, dimension or symmetry. In the paper we are interested in controlled processes that can be described by hyperbolic equations. The system described by such equation can locally change its qualitative properties. In the considered case the local behaviour is approximated by a parabolic system. New model (semantics) is introduced to model the emerging subsystem. The introduced invariant measure chosen for migrating object is used to identify the local properties and choose a unique local value.