  We develop and analyze a new method for manipulation of energy in a quantum
harmonic oscillator using coherent, e.g., electromagnetic, field and incoherent
control. Coherent control is typically implemented by shaped laser pulse or
tailored electromagnetic field. Incoherent control is implemented by engineered
environment, whose mean number of excitations at the frequency of the
oscillator is used as a control variable. An approach to coherent and
incoherent controls design based on the speed gradient algorithms in general,
finite and differential forms is proposed. It is proved that the differential
form is able to completely manipulate the energy of the oscillator: an
arbitrary energy can be achieved starting from any initial state of the
oscillator. The key instrument which allows for complete energy manipulation in
this case is the use of the engineered environment. A robustified
speed-gradient control algorithm in differential form is also proposed. It is
shown that the proposed robustified control algorithm ensures exponential
stability of the closed loop system which is preserved for sampled-data
control.
