Necessary Properness Conditions in Periodic Control
This paper deals with optimal periodic control problems and, in particular, with the question of properness. Loosely speaking this means that there is a non-trivial optimal solution which is better than the best constant solution. Two new necessary conditions for properness are presented. First, it is shown, that properness cannot occur in a one-state variable problem if the optimal solution is unique. In other words, a necessary condition for properness is that the dimension of the state space is at least two. The second result is that properness can only occur if the Hamiltonian is non-concave in the state variables.
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