  In this work, we review several results on development and application of
incoherent version of GRAPE (Gradient Ascent Pulse Engineering) approach,
inGRAPE, to optimization for open quantum systems driven by both coherent and
incoherent controls. In the incoherent control approach, the environment serves
as a control together with coherent field, and decoherence rates become
generally time-dependent. For a qubit, explicit analytic expressions for
evolution of the density matrix were obtained by solving a cubic equation via
Cardano method. We discuss applications of incoherent GRAPE method to high
fidelity gate generation for open one- and two-qubit systems and surprising
properties of the underlying control landscapes, forming two groups - smooth
single peak landscapes for Hadamard, C-NOT and C-Z gates, and more complicated
with two peaks for T (or $\pi/8$) gate. For a qutrit, a formulation of the
environment-assisted incoherent control with time-dependent decoherence rates
is provided.
