Boundary observer design for a class of semi-linear hyperbolic PDE systems with recycle loop

ABSTRACT

The present manuscript considers the observer design problem for a class of scalar semi-linear hyperbolic partial differential equation (PDE) systems with a recycle loop through the boundary point. The design method of Kazantzis and Kravaris [(1998). Nonlinear observer design using Lyapunov's auxiliary theorem. Systems & Control Letters, 34(5), 241–247] developed for the nonlinear finite dimensional systems observer design is extended to semi-linear hyperbolic PDE systems. The observer design problem is tackled through a first-order associated PDE. Due to the existence of spatial partial derivative operator, Lyapunov's Auxiliary Theorem originated from finite-dimensional systems can be no longer applied to seek conditions ensuring solvability of the associated PDE. In this manuscript, a new theorem is formulated and proved to ensure the solvability. The solution for the associated PDE is locally analytic nonlinear coordinate transformation which provides foundation for observer realization and a series solution approach is developed. Simulation examples are presented to study the performance of the proposed observer.

KEYWORDS:

• Semi-linear hyperbolic PDEs
• boundary observer
• semi-linear observer
• single-step
• output injection

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Stevan Dubljevic  http://orcid.org/0000-0002-1889-1599