On determining the submanifolds of state space where the optimal value surface has an infinite derivative
The problem of obtaining the optimal value surface of an optimal control process is investigated. In practice, the optimal cost surface often possesses an infinite derivative at points of certain submanifolds of the state space. A necessary condition is derived with which the equations of such submanifolds can be established without solving first the entire optimal control problem. The necessity of the condition is proved in a theorem, but only for submanifolds having one dimension less than the dimension of the state space. Three examples are provided to illustrate the utility of the condition.
KeywordsState Space Optimal Control Problem Function Versus Optimal Control Theory Grad Versus
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