Abstract
In this paper, we analyze the solvability of the optimal control problem for a nonlinear Schr\"{o}dinger equation. A Lions-type functional is considered as the objective functional. First, it is shown that the optimal control problem has at least one solution. Later, the Frechet differentiability of the objective functional is proved and a formula is obtained for its gradient. Finally, a necessary optimality condition is derived.
Publisher
International Journal of Optimization and Control: Theories and Applications
Subject
Applied Mathematics,Control and Optimization
Reference35 articles.
1. Liu, Wu-M., & Kengne, E. (2019). Schrodinger Equations in Nonlinear Systems, Springer Nature Singapore Pte. Ltd., Singapore.
2. Zhuravlev, V. M. (1996). Models of nonlinear wave processes that allow for soliton solutions. Journal of Experimental and Theoretical Physics, 83 (6), 1235-1245.
3. Elhia, M., Balatif, O., Boujalla, L., & Rachik, M. (2021). Optimal control problem for a tuberculosis model with multiple infectious compartments and time delays. An International Journal of Optimization and Control: Theories & Applications, 11 (1), 75-91.
4. Gisser, M., & Sanchez, D. A. (1980). Competition Versus Optimal Control in Groundwater Pumping. Water Resources Research, 16 (4), 638-642.
5. Imer, O. C., Yuksel, S., & Basar, T. (2006). Optimal control of LTI systems over unreliable communication links. Automatica, 42, 1429 – 1439.