Optimal control of the temperature in a catalytic converter

This paper is concerned with the optimization of the dynamics of the gas flow in an exhaust pipe. As a prototypical question the start up heating of the catalytic converter is considered. Reaching the optimal temperature in the converter rapidly competes against the costs, i.e., releasing too much unburnt fuel in the exhaust gases. The underlying model is a one dimensional small Mach number asymptotic gas dynamic model for a mixture of burnt and unburnt gases, formulated on a network consisting of the various pieces of the exhaust tube. For the optimization, adjoint calculus is applied on the continuous level. The resulting system is then discretized. Finally, numerical examples show the validity of this approach.