Control Problems for Nonlinear Hyperbolic Equations

Abstract. The talk is concerned with the effect of boundary conditions on the solution of an hyperbolic system of conservation laws in one-space variable, from the point of view of control theory, where one assumes that the evolution of the system can be affected by an external controller acting through the boundary conditions and thus regards the boundary data (or a partial number of their components) as boundary input controls. In the talk are discussed some results concerning the finite time exact controllability and the asymptotic stabilizzability of a first order hyperbolic system relative to general boundary conditions. Moreover, it is addressed the problem of determining an optimal solution of an hyperbolic system of balance laws relative to certain classes of cost functionals with boundary or distributed controls.