Backstepping boundary control for first order hyperbolic PDEs and application to systems with actuator and sensor delays

We consider a problem of boundary feedback stabilization of first order hyperbolic partial differential equations (PDEs). These equations serve as a model for such physical phenomena as traffic flows, chemical reactors, and heat exchangers. We design controllers using a backstepping method, which has been recently developed for parabolic PDEs. With the integral transformation and boundary feedback the unstable PDE is converted into a "delay line" system which converges to zero in finite time. We then apply this procedure to finite-dimensional systems with actuator and sensor delays to recover a well-known infinite-dimensional controller (analog of the Smith predictor for unstable plants). We also show that the proposed method can be used for boundary control of the a Korteweg-de Vries-like third order PDE. The designs are illustrated with simulations.