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.Keywords Parametric convex discrete optimal control problem · Optimal value function · Subdifferentials · Linear operator with closed range · Adjoint operator. Mathematics Subject Classification (2000)

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In this paper, we study second-order necessary optimality conditions for a discrete optimal control problem with nonconvex cost functions and state-control constraints. By establishing an abstract result on second-order necessary optimality conditions for a mathematical programming problem, we derive second-order necessary optimality conditions for a discrete optimal control problem.