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 large-scale 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.