Finite-time parameter estimation based boundary control for a class of 2×2 hyperbolic partial differential equation systems with uncertain transport speeds

This article investigates the boundary control problem for a class of (Formula presented.) hyperbolic partial differential equation systems with uncertain transport speeds, in which both state feedback and output feedback cases are considered. The least-square method is utilized to achieve the finite-time parameter estimation based on the parametric models. During parameter estimation, proper actuation signals are designed via contradiction method to avoid the singular problems. With the estimated parameters, control laws are designed by the backstepping method for both state-feedback case and output-feedback case. Finally, simulation studies are provided to illustrate the efficiency of our results.