On the optimal braking of wheeled vehicles

The standard approach for designing ABS systems is to devise a control law to enforce operation at (or close to) the maximum of the friction force vs. slip curve. This “maximum friction” approach is based on the assumption that the friction force generated at the tire/ground interface can be accurately represented as a (static) function of the slip coefficient with a distinct maximum. Under this assumption, we provide a formal proof of this “maximum friction” approach using optimal control theory. The optimal control is shown to be singular and can be written in a state feedback form