Direct Predictive Boundary Control of a First-order Quasilinear Hyperbolic PDE

摘要

We present a method for the boundary control of a system governed by one hyperbolic PDE with a non-local coupling term by state feedback. The method is an extension of recently developed controllers for semilinear systems. The design consists of three steps: predicting the states up to the time when they are affected by the delayed input; virtually moving the input to the uncontrolled boundary (which makes characterizing stability trivial); and constructing the inputs by, starting with the desired boundary values at the uncontrolled boundary, solving an ODE governing the dynamics on the system's characteristic lines backwards in time. The controller steers the system to the origin in finite time. A discussion of potential extensions of the presented method is given.