Optimal control of electric vehicle by Short-term Costate Estimation method of Pontryagin's minimum principle

Pontryagin's minimum principle (PMP) is a foundational theory to obtain optimal control of dynamic systems by the change of their state and cost function over time. Compared to programming-based optimization methods, it offers the advantage of providing rapid computation and an algebraic comprehension of the optimal solution. However, particularly for large-scale systems, constructing their costate dynamics and ensuring numerical stability is quite a difficult task. This study introduces a novel method called as the Short-term Costate Estimation method based on PMP (SCEMP). It aims to efficiently obtain optimal control for largescale systems by employing an iterative algorithm cored by the PMP. The objective is to minimize energy consumption while a car is running, achieved by regulating the distribution ratio of traction torque between the front and rear wheels. The key concept of SCEMP lies in obtaining a discrete optimal control through the sequential process of forward integration of the state equation and backward integration of the costate equation within a pre-defined near-future time frame. Costate dynamics is formulated with a cost function evaluated within a surrogate model, which not only offers a simplified representation of the plant dynamics but also serves as a reference model for controlling the plant model. Verification is conducted within a simulation environment. The SCEMP achieved results that approached the global optimum obtained from Dynamic Programming (DP) within a margin of up to 1%, while requiring approximately one-tenth of the computation time needed by DP.