  Quantum Lyapunov control uses a feedback control methodology to determine
control fields which are applied to control quantum systems in an open-loop
way. In this work, we adopt two Lyapunov control schemes to prepare an edge
state for a fermionic chain consisted of cold atoms loaded in an optical
lattice. Such a chain can be described by the Harper model. Corresponding to
the two schemes, state distance and state error Lyapunov functions are
considered. The results show that both the schemes are effective to prepare the
edge state within a wide range of parameters. We found that the edge state can
be prepared with high fidelity even \textbf{if} there are moderate fluctuations
in on-site or hopping potentials. Both control schemes can be extended to
similar chains (3$m+d$, $d$=2) of different lengths. Since regular amplitude
control field is easier to apply in practice, amplitude-modulated control
fields are used to replace the unmodulated one to prepare the edge state. Such
control approaches provide tools to explore edge states for one dimensional
topological materials.
