  We propose a scheme for inverse engineering control in open quantum systems.
Starting from an undetermined time evolution operator, a time-dependent
Hamiltonian is derived in order to guide the system to attain an arbitrary
target state at a predefined time. We analyze the fidelity of our control
protocol under noise with respect to the stochastic fluctuation of the linear
parameters of the Hamiltonian during the time evolution. For a special family
of Hamiltonians for two-level systems, we show that the control evolution of
the system under noise can be categorized into two standard decohering
processes: dephasing and depolarization, for both Markovian and non- Markovian
conditions. In particular, we illustrate our formalism by analysing the
robustness of the engineered target state.
