  In this paper, we study a class of stochastic time-inconsistent
linear-quadratic (LQ) control problems with control input constraints. These
problems are investigated within the more general framework associated with
random coefficients. This paper aims to further develop a new methodology,
which fundamentally differs from those in the standard control (without
constraints) theory in the literature, to cope with the mathematical
difficulties raised due to the presence of input constraints. We first prove
that the existence of an equilibrium solution is equivalent to the existence of
a solution to some forward-backward stochastic differential equations with
constraints. Under convex cone constraint, an explicit solution to equilibrium
for mean-variance portfolio selection can be obtained and proved to be unique.
Finally, some examples are discussed to shed light on the comparison between
our established results and standard control theory.
