Safe Receding Horizon Mixed-Integer Differentiable Predictive Control for Degradation-Aware Battery Dispatch
We present a safe receding-horizon mixed-integer differentiable predictive control methodology for residential battery energy storage dispatch that combines neural-network speed with recursive feasibility guarantees. Unlike open-loop learning-to-optimize methods, it incorporates real-time state-of-charge feedback and sinusoidal time-of-day conditioning, enabling closed-loop re-planning at every timestep without re-solving a mixed-integer program. A differentiable rainflow cycle-counting layer enables self-supervised training of the mixed-integer policy on exact degradation physics. The controller is a hybrid closed-loop system pairing a neural mode-selection and continuous-action policy with a quadratic-programming safety filter that guarantees recursive feasibility independent of network weights or mode optimality. We establish mode-conditioned Lipschitz continuity and a conditional regret decomposition into training-quality, mode-mismatch, and forecast-error terms. On a 7-day net-metering evaluation, the method attains a 6.9% cost gap versus the closed-loop mixed-integer MPC benchmark with a 25x speedup (0.11 s vs 2.7 s per step), while average regret rises by under 4% across 0-30% forecast noise. The learned and benchmark modes agree at every step, so the bound reduces to its training-quality and forecast-error terms, both empirically validated.