Exact Controllability For Subcritical Open Canals And Quasilinear Hyperbolic Systems In A Star-like Network

In this paper,various controllability problems for unsteady flows in subcritical star-like network of open canals are studied,and the conclusions are extended to the exact controllability for a star-like network of quasilinear hyperbolic systems.In this paper,we first obtain the existence and uniqueness of the semi-global C1 solution for unsteady flows in subcritical star-like network of open canals,and realize the exact controllability for it when only the control is applied at the multiple node or the control number is arbitrarily allocated between the multiple node and some simple nodes.On this basis,this paper is further extended and obtained existence and uniqueness of semi-global C1 solutions for a star-like network consisting of general quasilinear hyperbolic systems.By apply control to multiple node,multiple node and simple node at the same time,and simple node on the side with a larger number of equations,various exact controllability for quasilinear hyperbolic systems in a star-like network is realized by structural method.