Multiple agent hybrid control: carrier manifolds and chattering approximations to optimal control

Developing complete foundations for multiple-agent hybrid control is an arduous task and also requires important mathematical design choices. It involves synthesizing in a coherent fashion theorems and algorithms from a variety of fields. We discuss the notion of carrier manifold and of chattering approximations to optimal controls on carrier manifolds. The new idea we introduce here, beyond the hybrid systems models and the autonomous agents model for hybrid distributed autonomous control, is the idea of a carrier manifold modelling a distributed agent antonomous hybrid system. Thus the cost functions to be ε-optimised by choice of measure valued control are to be regarded as on the corresponding carrier manifold