Sliding-Mode Boundary Control of an Uncertain Parabolic PDE–ODE Cascade With Dynamic Actuation and Unmatched Disturbance

Dynamic boundary control design is addressed for an uncertain heat process in order to regulate its state to a constant set-point value while also rejecting a smooth unmatched boundary disturbance. The diffusivity parameter is unknown a priori, and a control signal is applied to the plant at its boundary through a first-order dynamic actuation with uncertain time constant, thereby yielding a coupled PDE/ODE representation of the overall system dynamics. The proposed output feedback design is sliding mode based, and it is made under collocated sensing. Its Lyapunov stability analysis is developed in the Sobolev state space H2(0,1) to additionally conclude the uniform pointwise-in-space exponential stabilization of the closed-loop error dynamics. Numerical simulations are involved to corroborate the theoretical findings.