Abstract. The paper is concerned with an optimal control problem on Formula: see text, where the dynamics is linear w.r.t. the control functions. For a terminal cost Formula: see text in a dense Formula: see text set of Formula: see text (i.e., in a countable intersection of open dense subsets), two main results are proved. Namely: the set Formula: see text of conjugate points is closed, with locally bounded Formula: see text-dimensional Hausdorff measure. Moreover, the set of initial points Formula: see text, which admit two or more globally optimal trajectories, is contained in the union of a locally finite family of embedded manifolds. In particular, the value function is continuously differentiable on an open, dense subset of Formula: see text.
Bressan et al. (Thu,) studied this question.
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