Semidefinite Programming and Reachable Sets of Dissipative Bilinear Control Systems

Details Semidefinite Programming and Reachable Sets of Dissipative Bilinear Control Systems Semidefinite Programming and Reachable Sets of Dissipative Bilinear Control Systems

2005-04-14

arxiv.org/abs/math/0504308v2

Mathematics

Optimization and Control

A shorter version of this paper will appear in the 44th IEEE Conference on Decision and Control and European Control Conferenc

Scientific paper

In this manuscript, we investigate optimal control problems which arise in connection with manipulation of dissipative quantum dynamics. These problems motivate the study of a class of dissipative bilinear control systems. For these systems it is shown that the optimal solution and the reachable set can be found by solving a semidefinite program. In practice, solutions to these problems generate optimal methods for control of quantum mechanical phenomena in presence of dissipation. In the area of coherent spectroscopy, this translates into the maximum signal to noise ratio that can be obtained in a spectroscopy experiment.

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