Adaptive Control of a Scalar 1-D Linear Hyperbolic PDE with Uncertain Transport Speed Using Boundary Sensing

Abstract

We solve an adaptive boundary control problem for an 1-D linear hyperbolic partial differential equation (PDE) with an uncertain in-domain source parameter and uncertain transport speed using boundary sensing only. Convergence of the parameters to their true values is achieved in finite-time. Since linear hyperbolic PDEs are finite-time convergent in the non-adaptive case, finite-time parameter convergence leads to the system state converging in finite-time. This is achieved by combining a recently derived transport speed estimation scheme using boundary sensing only, with the swapping scheme for hyperbolic PDEs and a least-squares identifier of an event-triggering type. The method is demonstrated in simulations.