Sufficiency Theorem for Discontinuous Optimal Cost Surfaces.
NAVAL RESEARCH LAB WASHINGTON D C
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A V-type function is introduced for the purpose of modeling the optimal cost surfaces OCS of a very general class of optimal control processes, especially state-constrained processes. This classification of the OCS builds from the assumption that the OCS is the countable union of disjoint submanifolds. The V-type function is particularly suitable for handling OCSs that are discontinuous at submanifolds of codimension 1 of the state space. A discontinuous nontransversality condition is presented which keeps trajectories from entering any submanifold of the OCS from a discontinuous edge. A sufficiency theorem using the V-type function is given. This theorem states that if certain conditions are met by a control policy, than it is optimal. The defining of these conditions, together with the sufficiency theorem, provides a classification of the OCS for general optimal control processes with state constraints. An example is provided to demonstrate the implementation of the results.
- Numerical Mathematics