A variational approach to constrained controllability for distributed systems

We consider linear distributed control systems of the form y′(t)=Ay(t)+Bu(t) where A generates a strongly continuous semigroup (etA)t⩾0 on an infinite dimensional Hilbert space Y. We suppose that the control operator B is bounded from the (Hilbert) control space U to Y. Taking into account eventual control constraint (such as saturation), we study the problem of exact controllability by using a variational approach. Applications to hyperbolic-like systems of the form z″(t)+Az(t)=Bu(t) are treated.