Learning to Solve Parametric Mixed-Integer Optimal Control Problems via Differentiable Predictive Control

We propose a novel approach to solving input- and state-constrained parametric mixed-integer optimal control problems using Differentiable Predictive Control (DPC). Our approach follows the differentiable programming paradigm by learning an explicit neural policy that maps control parameters to integer- and continuous-valued decision variables. This policy is optimized via stochastic gradient descent by differentiating the quadratic model predictive control objective through the closed-loop finite-horizon response of the system dynamics. To handle integrality constraints, we incorporate three differentiable rounding strategies. The approach is evaluated on a conceptual thermal energy system, comparing its performance with the optimal solution for different lengths of the prediction horizon. The simulation results indicate that our self-supervised learning approach can achieve near-optimal control performance while significantly reducing inference time by avoiding online optimization, thus implying its potential for embedded deployment even on edge devices.