Time-Optimal Problem for Hyperbolic Systems with Control Constraints

Perhaps the most widely studied type of problem in the mathematical theory of control is the time optimal control problem. The aim of control in this problem is to transform(or steering) any initial state y0 of a dynamic system into a desired stationary state (or to hitting a target set K ⊂ H ) in minimal time. i.e. the cost function in this problem is the time in which a system is driving to desired state. Such problems are physical meaningful only if constraints are imposed on the control variables u ∈ U ⊂ H since otherwise trivially the desired state could be achieved in zero time by the application of controls of infinite amplitude.