  We address the problem of constructing dynamically corrected gates for
non-Markovian open quantum systems in settings where limitations on the
available control inputs and/or the presence of control noise make existing
analytical approaches unfeasible. By focusing on the important case of
singlet-triplet electron spin qubits, we show how ideas from optimal control
theory may be used to automate the synthesis of dynamically corrected gates
that simultaneously minimize the system's sensitivity against both decoherence
and control errors. Explicit sequences for effecting robust single-qubit
rotations subject to realistic timing and pulse-shaping constraints are
provided, which can deliver substantially improved gate fidelity for
state-of-the-art experimental capabilities.
