Continuous state-feedback tracking of an uncertain heat diffusion process

A spatially distributed form of a second-order sliding-mode control algorithm is suggested for the feedback control of a heat process subject to unmeasurable, sufficiently smooth, persistent disturbances of arbitrary shape. In order to obtain a continuous control input, while retaining similar properties of robustness as those usually endowing the discontinuous control systems, a dynamic input-extension technique is exploited by adding an integrator at the input side and by applying a discontinuous distributed input to the integrator. We present a constructive Lyapunov analysis of the closed-loop performance that yields simple controller tuning conditions guaranteeing the asymptotic tracking of a sufficiently smooth reference trajectory despite the presence of norm-bounded persistent disturbances. Numerical simulations confirm the effectiveness of the proposed approach.