Direct predictive control of a first-order quasilinear hyperbolic PDE

Abstract

We present a method for the boundary controlof a system governed by one hyperbolic PDE with a non-localcoupling term by state feedback. The method is an extensionof recently developed controllers for semilinear systems. Thedesign consists of three steps: predicting the states up to thetime when they are affected by the delayed input; virtuallymoving the input to the uncontrolled boundary (which makescharacterizing stability trivial); and constructing the inputs by,starting with the desired boundary values at the uncontrolledboundary, solving an ODE governing the dynamics on thesystem’s characteristic linesbackwardsin time. The controllersteers the system to the origin in finite time. A discussion ofpotential extensions of the presented method is given.