Quantum-Transport-Informed Digital-Twin MPC for Metal-Hydride Hydrogen Storage
Connecting microscopic hydrogen transport with macroscopic predictive control through a physics-consistent digital twin.
Abstract | Contributions | Theory | Results | Paper and code
From quantum transport to predictive control. Temperature-dependent diffusion informs the digital twin and parameter estimation. The twin supplies the MPC prediction model; reactor measurements feed back to update the twin. Curves and reactor geometry are schematic; evaluation uses physics-calibrated simulations.
A unified framework for quantum-aware hydrogen control.
Classical metal-hydride (MH) hydrogen-storage systems exhibit inherently slow absorption/desorption dynamics that worsen at low temperatures ($T \lesssim 200\,\mathrm{K}$), where quantum-mechanical transport effects — hydrogen tunneling and zero-point lattice vibrations — sustain measurable diffusion that classical Arrhenius kinetics cannot predict, causing systematic actuation bias and degraded closed-loop performance.
This work presents a quantum-transport-informed MPC framework with a parameter-level digital-twin estimation architecture, in which a temperature-dependent quantum correction factor $g_q(T)$, grounded in zero-point energy theory, augments the classical Arrhenius law and is propagated through a multi-fidelity hierarchy into the MPC prediction matrices, enforcing a physics-consistent parameter manifold $\Theta$ at every online weighted least-squares update.
Physics-calibrated simulations on the authors' LaNi$_5$-H$_2$ platform demonstrate 70.2% settling-time reduction over classical MPC and 50.0% over the authors' prior LARC, with complete overshoot elimination at $120\,\mathrm{K}$ and a zero-overshoot safety benefit persisting across the full operating range $(298$–$333\,\mathrm{K})$.
The study examines how this model mismatch affects predictive control.
Four contributions, theoretical and numerical.
Temperature-dependent correction factor $g_q(T)$, grounded in zero-point energy theory, augments the classical Arrhenius law for control-ready effective diffusion.
Microscopic quantum transport parameters propagate into macroscopic MPC prediction matrices via a multi-fidelity hierarchy, enforcing the manifold $\Theta$ at every update.
Huber-WLS regression identifies $[\mathcal{D}_0, E_a]^\top$ from noisy, sparse data. Lemma 2 proves $\mathcal{O}(N^{-1/2})$ bootstrap confidence-interval convergence.
Theorem 1: asymptotic stability with explicit exponential rate. Corollary 1: closed-form excess-cost bound — classical MPC's penalty is strictly positive at all finite $T$ and diverges as $T \to 0^+$.
Two results, anchored by physics.
Under Assumptions (A1)–(A3), the closed-loop system satisfies recursive feasibility, monotone Lyapunov decrease, and $\hat{c}_k \to r$ with rate determined by the physical bounds of $\Theta$.
Let $\delta_k \triangleq \mathbb{B}_q(T_k) - \mathbb{B}_c(T_k)$. Then $J^{\mathrm{class}}_k - J^{\mathrm{quant}}_k \ge 0$ with strict inequality for all finite $T_k$. The relative mismatch grows without bound as $T \to 0^+$.
Simulation Results
At $T = 120\,\mathrm{K}$ (deep cryogenic, $D_{\mathrm{ratio}} = 4.23\times$), the quantum-informed controller produces a faster transient than the classical Arrhenius-based MPC configuration used in the comparison.
Three controllers operate on the same true quantum plant: classical MPC, the authors' prior LARC (IEEE TIE 2022), and the proposed quantum-informed MPC. The zero-overshoot safety benefit holds across the full operating range $(120$–$333\,\mathrm{K})$, not only the cryogenic regime.
The advantage stems from the physics-consistent diffusion model, not from the MPC architecture alone — confirmed directly by Experiment 7 (Corollary 1 validation).
Eight experiments, mapped to theory.
A decade on the same LaNi$_5$ platform.
This work is the third in a series advancing control methodology for the authors' LaNi$_5$-H$_2$ experimental platform. The hardware-in-the-loop campaign currently in preparation will deploy the proposed framework on the same hardware that already validated our prior controllers.
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Preprint
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Implementation in Julia 1.12 with OSQP and JuMP.jl. Repository release accompanies the camera-ready paper.