This paper considers the adaptive error feedback regulation problem for 1D heat equation with general harmonic disturbance anti-collocated with control. We first construct an auxiliary system in which the control and the anti-collocated disturbance become collocated and the measured error becomes the output. Then we design an error feedback adaptive servomechanism for this system, which includes estimators for the parameters characterizing the disturbance and the reference signals. The control is thus designed to regulate the tracking error to zero and to keep the states bounded.

In this paper, we are concerned with boundary output feedback stabilization of two parallel coupled string equations with matched external disturbance. By the method proposed by Feng and Guo in [IEEE Transactions on Automatic Control, 62(2017), pp. 3774-3787], we design a disturbance estimator first which is used to cancel effect of disturbance in the feedback loop. The other part of output feedback controller is designed to make system stable. Then operator semigroup and Lyapunov function methods are adopted to prove that the closed-loop system admits a unique solution in state space, the solution of original system is asymptotically stable and the one of the disturbance estimator system is bounded. Finally, numerical simulation are presented to validate the theoretical results.

In this paper, we are concerned with boundary output feedback stabilization of a transport equation with non-local term. First, a boundary state feedback controller is designed by a backstepping approach. The closed-loop system is proved to be exponentially stable by the equivalence between original and target system. Then, we design an output feedback controller based on an infinite-dimensional observer. It is shown that the result closed-loop system is also exponentially stable. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed feedback controller.