Detail:
Abstract: Motivated by the problem of time optimal control of two level quantum systems, we investigate the role of symmetries in general time-optimal control problems. If a symmetry is present the underlying (reduced) orbit space where the geodesics are studied is not simply a manifold but it has a reduced dimension and the structure of a stratified space. We study the relationship between singular strata and the critical and cut loci of the sub-Riemannian structure underlying the time-optimal control problem. We consider in detail problems with a K-P structure for which several simplifications are possible. We show how the knowledge of the stratified structure of the orbit space helps in the solution of the time optimal control problems and describe several examples of interest in quantum control.
Biosketch： Domenico D'Alessandro is a professor of Department of Mathematics, Iowa State University. He has published more than 80 papers in the research areas of Mathematical Physics, Systems and Control Theory, Quantum Theory and Quantum Information, Dierential Geometry and Lie Groups, Application of Control Theory to Bio-Medical Science. For his outstanding researches, he was awarded Iowa State University Foundation Award for Early Achievement in Research (2004), National Science Foundation CAREER Award (2003).
