2013/01/27 by Y. Zhang, Zhang, Y.
Engineering · Mathematics · #Advanced Mathematical Physics Problems #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1301.6321
openalex publication_date 2013/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper builds up two equivalence theorems for different kinds of optimal control problems of internally controlled Schrödinger 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.