[Paper Review] Constrained optimal control of monotone systems with applications to battery fast-charging

Ross Drummond, Nicola E. Courtier+3 more|arXiv (Cornell University)|Jan 18, 2023

Advanced Battery Technologies Research4 citations

TL;DR

This paper establishes necessary conditions for optimal fast-charging control in lithium-ion batteries using monotone control systems theory, proving that optimal solutions for constrained problems must 'ride' a constraint at some point during charging. The key contribution is a theoretical foundation for bang-and-ride control policies, showing that active constraint engagement is essential for optimality in monotone systems, with direct application to battery charging protocols that balance speed, safety, and longevity.

ABSTRACT

Enabling fast charging for lithium ion batteries is critical to accelerating the green energy transition. As such, there has been significant interest in tailored fast-charging protocols computed from the solutions of constrained optimal control problems. Here, we derive necessity conditions for a fast charging protocol based upon monotone control systems theory.

Motivation & Objective

• To develop a theoretical framework for constrained optimal control in monotone systems applicable to battery fast-charging.
• To explain why experimentally successful protocols like CC-CV are optimal by deriving necessary conditions for optimality.
• To establish that optimal controls for monotone systems must actively engage at least one constraint at some time during the charging process.
• To provide a rigorous mathematical basis for bang-and-ride control policies in battery systems under safety and performance constraints.
• To address the limitations of prior model-based and data-driven approaches by introducing a theory-driven, analytically grounded method for optimal control design.

Proposed method

• Theoretical analysis of constrained optimal control problems in monotone control systems under assumptions (H1)–(H4), including monotonicity of system dynamics and constraints.
• Derivation of necessity conditions using control theory, showing that a control cannot be optimal if no constraint is active in any future time window.
• Application of the maximum principle and monotonicity properties to characterize optimal control structure.
• Use of a single particle model (SPM) with electrochemical and thermal dynamics to model battery behavior, including state-of-charge, relaxation voltage, and temperature.
• Numerical validation using a hybrid equivalent circuit model coupled with thermal dynamics, with cost function maximizing state-of-charge over time.
• Comparison of numerically computed optimal solutions with bang-and-ride control to verify theoretical predictions.

Experimental results

Research questions

• RQ1 Under what conditions is a bang-and-ride control policy optimal for constrained monotone systems?
• RQ2 Why do established fast-charging protocols like CC-CV perform well in practice, and can this be explained theoretically?
• RQ3 How can monotonicity in system dynamics be leveraged to derive necessary conditions for optimal control in battery charging?
• RQ4 What role do active constraints play in determining the structure of optimal charging profiles?
• RQ5 Can the theoretical necessity of constraint engagement be verified in realistic battery models with thermal and electrochemical dynamics?

Key findings

• The necessary condition for optimality in monotone control systems is that at least one constraint must be active at some point during the charging process.
• Optimal fast-charging protocols for lithium-ion batteries must engage constraints such as current, voltage, or temperature limits at some time, validating the bang-and-ride control structure.
• Numerical simulations of a battery model with electrochemical and thermal dynamics confirm that the optimal control closely matches a bang-and-ride policy.
• The optimal control strategy derived from the theoretical framework matches the solution obtained via a moment-measure numerical routine, validating the analytical approach.
• The results explain the empirical success of CC-CV charging by showing it naturally satisfies the necessary condition of constraint engagement.
• The framework provides a theoretical basis for designing fast-charging protocols that are both efficient and safe, with explicit mathematical justification for constraint usage.