Optimal bang-bang control for SU(1,1) coherent states

In this paper, the problem of achieving an arbitrary SU(1,1) coherent state is considered via switching the control field back and forth between admissible values with minimal number of switching times. When the controlled system Hamiltonian is hyperbolical or parabolical, the results show that the minimal switching number is one or two, which lies on whether the argument of the involved control is adjustable or not, and is independent of the target SU(1,1) coherent state. While for the elliptical case, the results indicate that the minimal number of switches needed depends on the target SU(1,1) coherent state and is provided as a function of it. In this case, one switch can also be saved if the argument of the involved control is adjustable. The theory developed here can also be extended to solve the optimal bang-bang control problem for a general SU(1,1) time evolution.