In this work, we perform an analysis of the quantum control landscapes for three- and four-level approximations of a transmon system. We consider three- and four-level approximating Hamiltonians and investigate a possibility for the appearance of higher-order traps in the control landscape of maximizing the mean value of a quantum observable. As a result, we find that the null control is a trap of the third order for the three-level approximation and of the fifth order for the four-level approximation. We perform a numerical analysis of the influence of the fifth-order trap on the efficiency of local search optimization using GRAPE algorithm.