Standard necessary conditions for optimal control problems with pathwise state constraints supply no useful information about minimizers in a number of cases of interest, e.g., when the left endpoint of state trajectories is fixed at x(0) and x(0) lies in the boundary of the state constraint set; in these cases a nonzero, but nevertheless trivial, set of multipliers exists. We give conditions for the existence of nontrivial multipliers. A feature of these conditions is that they allow nonconvex velocity sets and measurably time-dependent data. The proof techniques are based on refined estimates of the distance of a given state trajectory from the set of state trajectories satisfying the state constraint, originating in the dynamic programming literature.
Degenerate optimal control problems with state constraints
RAMPAZZO, FRANCO
2000
Abstract
Standard necessary conditions for optimal control problems with pathwise state constraints supply no useful information about minimizers in a number of cases of interest, e.g., when the left endpoint of state trajectories is fixed at x(0) and x(0) lies in the boundary of the state constraint set; in these cases a nonzero, but nevertheless trivial, set of multipliers exists. We give conditions for the existence of nontrivial multipliers. A feature of these conditions is that they allow nonconvex velocity sets and measurably time-dependent data. The proof techniques are based on refined estimates of the distance of a given state trajectory from the set of state trajectories satisfying the state constraint, originating in the dynamic programming literature.Pubblicazioni consigliate
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