Boundary controller design and well-posedness analysis of semi-linear parabolic PDE systems

This paper addresses the boundary control design problem of a class of nonlinear distributed parameter systems described by a scalar semi-linear parabolic partial differential equation (PDE). A simple boundary controller design is developed under the domain-averaged measurement for the PDE system. The suggested controller is easily implemented since only a boundary actuator is utilized. Based on the Lyapunov direct method and the contraction semigroup theory, it is shown that the closed-loop system is well-posed and is exponentially stable. Finally, the effectiveness of the proposed control methods is illustrated by a numerical example.