Observer-Based Output Regulation for an Uncertain Parabolic Partial Differential Equation

Abstract This paper presents a new observer-based output feedback boundary tracking control strategy to improve the tracking performance in an uncertain parabolic partial differential equation (PDE) with external disturbances. First, using the measurable signal of the distributed parameter system (DPS), a state observer is designed to estimate unknown disturbances and distributed states. Then, a disturbance-compensation-based output-feedback boundary control law is derived from the estimated values to realize the high-precision tracking performance for exogenous reference signal and effective compensation of external disturbances. Some lemmas and theorems are given to prove that the closed-loop system is exponentially stable. Finally, some numerical simulations demonstrate the effectiveness of the proposed method.