Simultaneous Exact Boundary Controllability of Final State and Nodal Profile for Quasilinear Hyperbolic Systems

In this paper, we consider the problem about the simultaneous realization of exact boundary controllability of final state and nodal profile for general 1-D first order quasilinear hyperbolic systems. We show that by means of boundary controls, the system (hyperbolic equations together with boundary conditions) can drive any given initial data at \(t=0\) $t=0$ to any given final data at \(t=T\) $t=T$ , and the solution to the system fits exactly any given nodal profile on a boundary node or an internal node for certain subinterval \([T_1,T_2]\) $[T_1,T_2]$ of [0, T]. Moreover, we give an application of the main results to the system of traffic flow.