  Differential stability of convex discrete optimal control problems in Banach
spaces is studied in this paper. By using some recent results of An and Yen
[Appl. Anal. 94, 108--128 (2015)] on differential stability of parametric
convex optimization problems under inclusion constraints, we obtain an upper
estimate for the subdifferential of the optimal value function of a parametric
convex discrete optimal control problem, where the objective function may be
nondifferentiable. If the objective function is differentiable, the obtained
upper estimate becomes an equality. It is shown that the singular
subdifferential of the just mentioned optimal value function always consists of
the origin of the dual space.
