Estimating the left boundary condition of coupled 1-D linear hyperbolic PDEs from right boundary sensing

Abstract : In this paper, we develop an adaptive observer for n + 1 coupled first-order 1-D hyperbolic PDEs for estimation of unknown parameters appearing in the left boundary condition using only measurements at the right boundary. Proof of boundedness of the estimated parameters and sufficient conditions for convergence are offered and the result is demonstrated in a simulation.