Boundary Parameter and State Estimation in General Linear Hyperbolic PDEs

We develop an adaptive observer that estimates boundary parameters and the system states in general heterodirectional linear systems of m+n coupled hyperbolic partial differential equations. The observer uses boundary sensing only, and is based on the swapping design, where filters are constructed that can be used to express the system states as linear static combinations of the unknown parameters and the filters states. Standard parameter identification laws can then be applied. Proof of boundedness of the estimates is offered, and sufficient conditions ensuring exponential convergence to their true values is derived. The theory is verified in a simulation.