Mixed-Integer Nonlinear Differentiable Predictive Control for Underground Pumped Hydro Energy Storage Systems

Abstract:This paper extends Mixed-Integer Differentiable Predictive Control (MI-DPC) to multi-modal discrete decisions and nonconvex polynomial dynamics arising in Underground Pumped Hydro Energy Storage Systems (UPHES). A neural policy mapping problem parameters to continuous setpoints and integer mode selections via a Gumbel-Softmax layer is trained in a self-supervised manner by differentiating the expectation of the finite horizon control objective through the nonlinear dynamics model. Three methodological contributions enable this extension: a parallel differentiable simulator that preserves gradient magnitude, a Transformer encoder that captures long-range temporal dependencies, and a Gumbel-Softmax temperature annealing schedule that regularizes the combinatorial search. We demonstrate the framework on day-ahead scheduling of a UPHES, a large-scale mixed-integer optimal control problem with nonlinear unit performance curves and volume-head coupling. MI-DPC achieves only 1.6% suboptimality relative to a piecewise mixed-integer quadratic programming baseline, while providing five orders of magnitude speedup in online scheduling time.

6 pages, 5 figures. Accepted for publication in the 2026 65th IEEE Conference on Decision and Control (CDC)

Systems and Control (eess.SY); Machine Learning (cs.LG)

arXiv:2609.17964 [eess.SY]

(or arXiv:2609.17964v1 [eess.SY] for this version)

https://doi.org/10.48550/arXiv.2609.17964 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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