Application of Optimal Control Theory to the Crashworthiness of a Passenger Vehicle Model

Optimal control theory concepts are thought to be useful in understanding the problem of determining safe deceleration characteristics for a crashing vehicle. These deceleration waveforms are to be computed such that passenger belt forces are minimized. Using both a linear one-degree-of-freedom model and a nonlinear two-degree-of-freedom model for a frontal collision, this problem is shown to be equivalent to the minimization of a performance or cost function when the terminal time is not fixed a priori, but is determined by terminal constraints. While the maximum principle is applied directly to find the optimal deceleration waveform for the linear problem, the steepest ascent method is used to optimize iteratively the nonlinear problem. Passenger seatbelt forces which resulted from using these optimal waveforms were compared with those forces which resulted from using step and ramp functions. Results showed that the seat belt forces resulting from the optimally derived deceleration signals were considerably smaller than those using step and ramp functions. With further effort, these results could possibly be used as design guides.