Concurrent learning adaptive boundary observer design for linear coupled hyperbolic partial differential equation systems

Abstract

This paper proposes a novel concurrent learning-based adaptive boundary observer designed to tackle the joint estimation problem of system states and unknown parameters for a class of hyperbolic partial differential equation systems under the circumstance of unsatisfied persistent excitation conditions. By leveraging concurrent learning technique, an adapted data points selection algorithm is employed concurrently with current data to construct the adaptation law of unknown parameters, which overcomes the limitations imposed by persistent excitation conditions and ensures exponential convergence of estimation errors of unknown parameters under finite excitation conditions. Furthermore, combining the ideas of backstepping and swapping filters on the basis of uncertain estimation, a concurrent learning-based adaptive boundary observer is designed, accompanied by rigorous theoretical analysis and proofs to demonstrate its capability of achieving exponential convergence in estimation. Finally, the corresponding illustrative simulations are given to show the effectiveness of the proposed methodology.