Optimal control problem for head injury criterion

The optimal control of the deceleration of a particle moving along a straight line after an impact against a surface covered with an impact isolation coating is considered. The force applied to the particle by the surface is treated as the control variable, that is, the control force replaces the coating. The deceleration distance is minimized under the constrained value of the HIC functional - an integral criterion that is utilized in engineering biomechanics to evaluate the expected severity of impact-induced head injury of a human being. The solution indicates the limiting capabilities of the prevention from the head injuries in the case of traffic accidents, falling, or other occurrences by means of an appropriate coating of the surface against which impacts can occur.