Adaptive Output Regulation of a Class of 1-D Hyperbolic PDEs With Unknown Boundary Scaled Parameters

This article considers the problem of adaptive output regulation of a class of 1-D anticollocated hyperbolic partial differential equations (PDEs). The model is subject to unknown scaled parameters in both the boundary condition and boundary measurement. An adaptive boundary observer, providing online estimates of the system state and parameters, is designed. Particularly, to realize that the pure boundary state at left side tracks a reference signal, a challenging problem with the estimate of the true value of unknown scaled parameter appearing in measurement (at the left side) is tackled in this article. It is shown that the proposed observer is exponentially convergent, and furthermore, the exponential output regulation and stabilization are achieved.