Sufficient conditions in free final time optimal control problems. A comment
Abstract By an application of sufficient conditions, assume that an optimal pair ( χ τ (·), u τ (·)) and an adjoint function p τ (·) were found in the control problem in question with the final time τ fixed but arbitrary. Then a sufficient condition for one of these pairs, say χ τ ∗ (·) , u τ ∗ (·) to be optimal in the corresponding free final time problem is that the Hamiltonian, with ( χ τ ( t ), u τ ( τ −), p τ ( τ ), τ) inserted, is nonnegative (nonpositive) to the left (right) of τ ∗ .