Control of parabolic PDE systems with time varying spatial boundary conditions using a novel nonlinear backstepping scheme

In this paper, an extension of backstepping controller for parabolic PDE systems (Heat Transfer Process) with timevarying spatial boundary is studied. The PDE system dynamics is transformed to an exponentially stable target system via a new nonlinear backstepping transformation. The exponential stability of the closedloop system is established by using a proper Lyapunov function. Finally, numerical simulation is provided to support the effectiveness of the proposed controller.