  In this paper, a backstepping control of the one-phase Stefan Problem, which
is a 1-D diffusion Partial Differential Equation (PDE) defined on a time
varying spatial domain described by an ordinary differential equation (ODE), is
studied. A new nonlinear backstepping transformation for moving boundary
problem is utilized to transform the original coupled PDE-ODE system into a
target system whose exponential stability is proved. The full-state boundary
feedback controller ensures the exponential stability of the moving interface
to a reference setpoint and the ${\cal H}_1$-norm of the distributed
temperature by a choice of the setpint satisfying given explicit inequality
between initial states that guarantees the physical constraints imposed by the
melting process.
