Bridging microscopic hydrogen-tunneling physics with macroscopic predictive control — multiscale modeling and formal guarantees.
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 $(298$–$333\,\mathrm{K})$.
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 $T \to 0^+$.
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 $T \to 0^+$.
At $T = 120\,\mathrm{K}$ (deep cryogenic, $D_{\mathrm{ratio}} = 4.23\times$), the quantum-informed controller produces a transient that classical Arrhenius-based MPC cannot match by any choice of weights.
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).
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.
Full manuscript currently under review at IEEE TCST. Open access on Preprints.org.
Implementation in Julia 1.12 with OSQP and JuMP.jl. Repository release accompanies the camera-ready paper.
Nuchkrua, T., Boonto, S., Liu, X.
"Quantum-Transport-Informed Digital-Twin MPC for
Metal-Hydride Hydrogen Storage."
Submitted, IEEE TCST, 2026.