Recently proposed discrete-model representation of turbo-charged diesel engines are recast in state-space form and used in an optimal control study. It is known that the turbo-charger has considerable influence on the dynamical behaviour of the engine and this is accounted for by incorporating a weighting of the air-fuel ratio in the performance index. This leads to a rather unusual form of the quadratic performance functional and the optimal controls are determined using both dynamic programming and discrete minimum principle techniques. This leads to extensions and some simplification of known theoretical results.