Bang-Ride Optimal Control: Monotonicity, External Positivity, and Fast Battery Charging

TL;DR

This paper analyzes a class of optimal control problems with bang-ride solutions, focusing on their structure, properties, and implications for fast battery charging, providing a theoretical foundation for heuristic strategies.

Contribution

It formalizes the bang-ride control pattern, connects it to external positivity, and offers a theoretical basis for efficient heuristic charging algorithms.

Findings

Bang-ride solutions activate all constraints and enable efficient computation.

Heuristics following the maximum feasible input satisfy optimality conditions under certain monotonicity.

External positivity of costate dynamics explains the effectiveness of heuristic charging strategies.

Abstract

This work studies a class of optimal control problems with scalar inputs and general constraints, whose solutions follow a bang-ride pattern that always activates a constraint and enables efficient numerical computation. As a motivating example, fast battery charging leads to computationally demanding optimal control problems when detailed electrochemical models are used. Recently proposed optimization-free heuristics reduce this computational cost while producing input profiles observed in practice, following a bang-ride pattern and applying the maximum feasible input. We investigate when such heuristics satisfy necessary optimality conditions. By leveraging Pontryagin's maximum principle, we unify and formalize existing insights on the bang-ride structure and on the optimal control attaining the maximum feasible input under monotonicity. We further establish a novel connection between the structured optimal control and the external positivity of the costate dynamics. These results provide a rigorous theoretical foundation for heuristic charging strategies and explain the efficiency of optimization-free algorithms.