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

In this paper, an extension of back stepping controller for a class of parabolic Partial Differential Equation systems (The Heat Transfer Process) with time-varying spatial boundary condition is fully studied. The PDE system dynamics is first transformed to an exponentially stable target system via a new nonlinear and invertible back stepping transformation with two gain kernel functions. The exponential stability of the closed-loop system is established by using a proper Lyapunov function and knowing the fact that the introduced back stepping transformation has a unique inverse transformation. Finally, numerical simulation is provided to support the effectiveness of the proposed controller.