Optimal control of nonlinear systems provides a major challenge in control engineering. Constraints on the input signals are common to many real-world applications and render the problem even more complicated to be tackled. This paper proposes a method to map the input constraints by nonlinear functions to the state equations of the system, afterwards an approximation of the solution of the resulting optimization problem is calculated by means of a dynamic extension to the state of the system. The approach is applied in the control of test benches for internal combustion engines, where speed and torque references need to be tracked at the crankshaft of the engine. Simulation results using a high-quality simulator, also regarding effects that have not been included in the model for controller design, show the performance of the proposed approach.