Online Ecological Gearshift Strategy via Neural Network with Soft-Argmax Operator

TL;DR

This work tackles online ecological gearshift for a 2-speed EV by casting gear selection as a mixed-integer MPC problem aimed at minimizing energy consumption. It introduces an outer convexification approach to relax binary gear controls and a neural network optimizer that uses soft-argmax to approximate binary decisions in a differentiable training loop. Compared with Bonmin, the proposed NN-based method achieves comparable energy savings with significantly faster solution times, enabling real-time operation. The approach demonstrates practical impact for eco-driving and provides a framework for extending to broader MIMPC problems.

Abstract

This paper presents a neural network optimizer with soft-argmax operator to achieve an ecological gearshift strategy in real-time. The strategy is reformulated as the mixed-integer model predictive control (MIMPC) problem to minimize energy consumption. Then the outer convexification is introduced to transform integer variables into relaxed binary controls. To approximate binary solutions properly within training, the soft-argmax operator is applied to the neural network with the fact that all the operations of this scheme are differentiable. Moreover, this operator can help push the relaxed binary variables close to 0 or 1. To evaluate the strategy effect, we deployed it to a 2-speed electric vehicle (EV). In contrast to the mature solver Bonmin, our proposed method not only achieves similar energy-saving effects but also significantly reduces the solution time to meet real-time requirements. This results in a notable energy savings of 6.02% compared to the rule-based method.

Figures (5)

• Figure 1: Neural Network Optimizer Scheme.
• Figure 2: Soft-argmax for binary controls.
• Figure 3: Online control strategy.
• Figure 4: Gearshift comparison for NEDC of 2-speed EV.
• Figure 5: Motor efficiency comparison of working condition.

Theorems & Definitions (2)

• Remark 1
• Remark 2