Two equivalence theorems of different kinds of optimal control problems for Schr\"{o}dinger equations

Y. Zhang

Two equivalence theorems of different kinds of optimal control problems for Schr\"{o}dinger equations

Optimization and Control 2013-01-29 v1

Authors: Y. Zhang

Abstract

This paper builds up two equivalence theorems for different kinds of optimal control problems of internally controlled Schr\"{o}dinger equations. The first one concerns with the equivalence of the minimal norm and the minimal time control problems. (The minimal time control problems are also called the first type of optimal time control problems.) The targets of the aforementioned two kinds of problems are the origin of the state space. The second one deals with the equivalence of three optimal control problems which are optimal target control problems, optimal norm control problems and the second type of optimal time control problems. These two theorems were estabilished for heat equations in [18] and [17] respectively.

Keywords

optimal control problems Schrödinger equations equivalence theorems minimal norm control minimal time control optimal target control internal control

Cite

@article{arxiv.1301.6321,
  title  = {Two equivalence theorems of different kinds of optimal control problems for Schr\"{o}dinger equations},
  author = {Y. Zhang},
  journal= {arXiv preprint arXiv:1301.6321},
  year   = {2013}
}

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27 pages