  We study the optimal value function for control problems on Banach spaces
that involve both continuous and discrete control decisions. For problems
involving semilinear dynamics subject to mixed control inequality constraints,
one can show that the optimal value depends locally Lipschitz continuously on
perturbations of the initial data and the costs under rather natural
assumptions. We prove a similar result for perturbations of the initial data,
the constraints and the costs for problems involving linear dynamics, convex
costs and convex constraints under a Slater-type constraint qualification. We
show by an example that these results are in a sense sharp.
