Abstract
Motivated by our recent works on the optimal value function in parametric optimal control problems under linear state equations, in this paper we study of the first-order behavior of the value function of a parametric convex optimal control problem with a convex cost function and linear state equations. By establishing an abstract result on the subdifferential of the value function to a parametric convex mathematical programming problem, we derive a formula for computing the subdifferential and the singular subdifferential of the value function to a parametric convex optimal control problem. By virtue of the convexity, several assumptions used in the above papers, like the existence of a local upper Lipschitzian selection of the solution map, as well as the V-inner semicontinuity of the solution map, are no longer needed.
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