Tracking in Minimum Time in General Linear Hyperbolic PDEs Using Collocated Sensing and Control

We solve a tracking problem for general heterodirectional linear 1-D hyperbolic partial differential equations. A full state feedback controller and an observer generating full state estimates from sensing co-located with the actuation are designed. Both converge in finite, minimum time. The two are then combined into an output feedback law achieving tracking in finite time given by the sum of the convergence times of the controller and observer.