The air path of an internal combustion engine is a classical example of MIMO system with actuator constraints and high dynamic requirements. While the classical approach consists in using simple, decoupled heuristic controllers and empirical limitations, this paper proposes to state the problem in terms of an optimal control problem with input constraints and to solve it in a model based environment. To this end, a recently developed controller design - explicit MPC - is used to calculate the explicit solution of the state feedback control law offline and to store it in tables for online controller selection. The combination of plant and switched controller leads to a piecewise linear and discrete system – a special form of hybrid system. The approach has been tested on a production diesel engine yielding impressive improvements in terms of soot while compared with the basic application.