This paper considers the problem of tracking dynamic reference profiles for rotational speed and torque at the crankshaft of an internal combustion engine at a test bench. The test bench is equipped with a hydrodynamic dynamometer that can only load the internal combustion engine. A proper formulation of this tracking problem with input constraints by nonlinear functions to the state equations of the system and an extension of the state to approximately solve the resulting optimization problem is used to design a control law achieving at the same time a criterion of optimality. Simulation results using a high-quality simulator of the test bench show the performance of the proposed approach.