Equivalence of Several Kinds of Optimal Controls

Connections of time optimal control problems with other kinds of optimal control problems can allow us to get properties for one kind of optimal control problems through studying another kind of optimal control problems. In Fattorini (J SIAM Control 2: 54–59, 1964) (see also Fattorini (J SIAM Control 2:54–59, 1964)), the author derived the Pontryagin Maximum Principle for minimal time controls (or minimal norm controls) via the Pontryagin Maximum Principle for minimal norm controls (or minimal time controls).