Trajectory tracking problem for a class of 2-D hyperbolic PDEs

The trajectory tracking problem (TTP) refers to the procedure of finding an input control which steers the system output to follow a predefined path. In this paper we investigate the TTP for controlled systems governed by a class of 2-D hyperbolic PDEs in which we target a perfect matching of an output with a desired trajectory. The controller as well as the corresponding state response are explicitly given by means of the target trajectory and the solutions of appropriate kernel PDEs. The approach is based on backstepping techniques, the Laplace transform, and the Green's functions.