Hierarchic Control For A Coupled Fourth Order Parabolic Equation

In this paper,we study the hierarchical control for a coupled fourth-order parabolic equation,i.e.,the null controllability of the equation based on the Stackelberg-Nash strategy.First of all,the existence and uniqueness of Nash equilibrium pairs of the original system are proved for any given leader control,and their explicit expression is provided.Next,we investigate the null controllability of Nash equilibrium to the corresponding optimal system.Finally,by duality theory,we prove the observability inequality of the adjoint system.The key to proving the observability inequality is to establish a new Carleman estimate for a coupled fourth-order parabolic system.