  In this paper, we study a non-canonical extension of a supergravity-motivated
model acting as a vivid counterexample to the cosmic no-hair conjecture due to
its unusual coupling between scalar and electromagnetic fields. In particular,
a canonical scalar field is replaced by the string-inspired Dirac-Born-Infeld
one in this extension. As a result, exact anisotropic inflationary solutions
for this Dirac-Born-Infeld model are figured out under a constant-roll
condition. Furthermore, numerical calculations are performed to verify that
these anisotropic constant-roll solutions are indeed attractive during their
inflationary phase.
