Bang-Bang Property of Optimal Controls

In this chapter, we will study the bang-bang property of some time optimal control problems. The bang-bang property of such a problem says, in plain language, that any optimal control reaches the boundary of the corresponding control constraint set at almost every time. This property not only is mathematically interesting, but also has important applications. For instance, the uniqueness of time optimal control is an immediate consequence of the bang-bang property in certain cases.