  A stable and fast path linking arbitrary pair of quantum states is commonly
desired for the engineering protocols inspired by stimulated Raman adiabatic
passage, such as shortcut to adiabaticity and holonomic transformation. It has
immediate applications in quantum control and quantum computation and is
fundamental about the exact solution of a time-dependent Schr\"odinger
equation. We construct a universal control framework based on the system
dynamics within an ancillary picture, in which the system Hamiltonian is
diagonal so that no transition exists among the ancillary bases during the time
evolution. Practically the desired evolution path can be obtained by the von
Neumann equation for the parametric ancillary bases. We demonstrate that our
control framework can be reduced to the nonadiabatic holonomic quantum
transformation, the Lewis-Riesenfeld theory for invariant, and the
counterdiabatic driving method under distinct scenarios and conditions. Also it
can be used to achieve the cyclic transfer of system population that could be a
hard or complex problem for the existing methods. For the state engineering
over a finite-dimensional quantum system, our work can provide a full-rank
nonadiabatic time-evolution operator.
