Robust Multi-Modal Hamilton-Jacobi Reachability Prognostics: An Application to Battery Health Management
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Abstract
This paper presents a novel and robust prognostics frame-
work for battery health management based on Hamilton–
Jacobi reachability analysis. A two-dimensional degradation
state space is constructed from the state of health, obtained
from discharge-capacity measurements, and a normalized
impedance feature extracted from electrochemical impedance
spectroscopy. Within this joint state space, a failure region is
defined to capture both capacity fade and impedance growth
under a unified EOL criterion. The Hamilton–Jacobi partial
differential equation is then solved backward in a minimum-
time-to-reach setting to generate state-dependent remaining
useful life maps. To account for battery-to-battery variability,
uncertainty in the degradation dynamics is estimated empiri-
cally from experimental data and incorporated through nom-
inal, worst-case, and best-case drift scenarios, thereby yield-
ing corresponding remaining useful life predictions. The re-
sulting maps are computed offline and interpolated online,
making the framework computationally efficient in deploy-
ment. Validation on the NASA battery dataset shows that the
proposed approach delivers physically interpretable remain-
ing useful life estimates together with informative uncertainty
bounds that successfully encapsulate the true remaining use-
ful life trajectories.
How to Cite
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Hamilton-Jacobi Reachability, Battery Health management, Prognostics, Uncertainty Quantification
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