A new solution property in optimal control: The lens

We consider a new property of an optimal control problem called a lens.A lens is an interior point in the state–control phase plane where—given the value of the state variable—there is only one control value satisfying the necessary optimality conditions and—given the value of the control variable—there is only one state value satisfying the necessary optimality conditions.We build a simple model that generates a lens and give necessary and sufficient conditions under which a lens occurs.