Flatness-based design of state feedback controllers for heterodirectional hyperbolic systems

Abstract This paper introduces the hyperbolic controller canonical form (HCCF) for boundary-actuated heterodirectional hyperbolic systems with multiple input components. The HCCF is a special state representation that significantly simplifies the design of state feedback tracking controllers for stabilizing desired reference trajectories. The form exists if the system is exactly controllable and involves a number of transport equations with normalized transport velocities, which are coupled solely at the actuated boundary. Similar to finite-dimensional systems, the HCCF is derived from the parametrization of the system’s solutions in terms of a flat output. In the case of boundary-coupled systems without in-domain coupling, it is shown that the use of a special flat output always allows for the stabilization via static state feedback. The HCCF-based control design is illustrated for an example system.