Benchmarking Computational Time of Dynamic Programming for Autonomous Vehicle Powertrain Control

Dynamic programming (DP) has been used for optimal control of hybrid powertrain and vehicle speed optimization particularly in design phase for over a couple of decades. With the advent of autonomous and connected vehicle technologies, automotive industry is getting closer to implementing predictive optimal control strategies in real time applications. The biggest challenge in implementation of optimal controls is the limitation on hardware which includes processor speed, IO speed, and random access memory. Due to the use of autonomous features, modern vehicles are equipped with better onboard computational resources. In this paper we present a comparison between multiple hardware options for dynamic programming. The optimal control problem considered, is the optimization of travel time and fuel economy by tuning the torque split ratio and vehicle speed while maintaining charge sustaining operation. The system has two states - battery state of charge and vehicle speed, and two inputs namely, total torque and torque split ratio. First, we develop a Matlab® based program to solve the optimal control problem. The Matlab® code is optimized for performance and memory on PC. Secondly, we deploy the code in C++ based application using hand written code. The code is prepared to be able to use with parallel processing. Finally, we compare four different hardware options for computational efficiency. The hardware options considered are a single core on a PC (7th gen intel Xeon processor), a cluster, a GPU (NVDIA DRIVE™ PX2) and an Android smartphone. The GPU chosen is specifically designed for automotive applications, and an android phone is chosen since it is the most realistic situation. The results of this paper suggest that the DP can be used in real time applications if the problem can be simplified to 1 state 2 input case.