  Maximally entangled states (MES) are highly valued in quantum information
processing. In quantum control, the creation of MES is typically treated as a
state transfer problem with a predefined MES as the target. However, this
approach is limited by the requirement to predetermine the MES structure. This
paper introduces an improved quantum Lyapunov control approach that relies on
the quantum entanglement measure to construct the Lyapunov function, instead of
using the distance between quantum states. This strategy enables the
preparation of any MES, regardless of whether its structure is known
beforehand, using a single control scheme. The proposed entanglement control
technique is unaffected by the number of entangled subsystems since it targets
the entanglement measure as a scalar. Initially applied to bipartite pure
states, this method demonstrates its capability to generate Bell states and
their equivalents. Subsequent applications to bipartite mixed states and
multipartite systems illustrate that the technique can produce MES with
unspecified structures.
