Backstepping control of PDEs with time-varying domain

In this work a PDE backstepping-based control law for one-dimensional unstable heat equation with time-varying spatial domain is developed. The underlying parabolic partial differential equation (PDE) with time-varying domain is the model emerging from process control applications such as crystal growth. In backstepping control law synthesis, a characteristic feature is that the PDE describing the transformation kernel of the associated Volterra integral is time-dependent. In this work, the kernel PDE is solved numerically and the state-feedback controller is simulated for the application of temperature regulation in the Czochralski crystal growth process.