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Because they represent physical systems with propagation delays, hyperbolicsystems are well suited for feedforward control. This is especially true whenthe delay between a disturbance and the output is larger than the controldelay. In this paper, we address the design of feedforward controllers for ageneral class of $2 \times 2$ hyperbolic systems with a single disturbanceinput located at one boundary and a single control actuation at the otherboundary. The goal is to design a feedforward control that makes the systemoutput insensitive to the measured disturbance input. We show that, for thisclass of systems, there exists an efficient ideal feedforward controller whichis causal and stable. The problem is first stated and studied in the frequencydomain for a simple linear system. Then, our main contribution is to show howthe theory can be extended, in the time domain, to general nonlinear hyperbolicsystems. The method is illustrated with an application to the control of anopen channel represented by Saint- Venant equations where the objective is tomake the output water level insensitive to the variations of the input flowrate. Finally, we address a more complex application to a cascade of poolswhere a blind application of perfect feedforward control can lead todetrimental oscillations. A pragmatic way of modifying the control law to solvethis problem is proposed and validated with a simulation experiment.

Feedforward boundary control of $2 \times 2$ nonlinear hyperbolic systems with application to Saint-Venant equations