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Optimal Control for Klein-Gordon-Schrödinger Quantum System in Complex Hilbert Space

Optimal control problem for Klein-Gordon-Schrödinger quantum system is originally considered in complex Hilbert space at the framework of variational method. In particular, existence of weak solution and existence of optimal quantum control are proved, respectively. Necessary optimality condition is deduced for quadratic cost function. Finally, Band-Bang principle is found for specified admissible set of control space.