Performance output tracking and robustness of multi-dimensional heat equation with non-collocated control and unmatched disturbance

Abstract

We consider performance output tracking for a boundary controlled multi-dimensional heat equation with possibly unknown internal nonlinear uncertainty and external disturbance on one part and control on the rest of the boundary. The active disturbance rejection control (ADRC) approach is adopted in investigation. With partial boundary measurement only, we propose an extended state observer which is used to estimate both system state and total disturbance, design a servomechanism and an output feedback controller. Three control objectives have been achieved: a) the performance output is exponentially tracking the arbitrary given reference signal; b) all internal signals are uniformly bounded; c) the closed-loop system is internally asymptotically stable whenever both the reference signal and the disturbance vanish or belong to the spaces H1(0, ∞; L1(Γ 1 )) and L2(0, ∞; L2(Γ 0 )), respectively. In addition, when boundary measurement is suffered from the noise, it is shown that the proposed controller is robust to the measurement noise.