Learning-enabled Acceleration of Scenario-based Model Predictive Control

Scenario-based Model Predictive Control (SBMPC) is a powerful tool for managing uncertainty in complex systems, but its computational burden grows rapidly with the number of scenarios and the prediction horizon. This paper addresses this bottleneck by proposing a learning-accelerated Alternating Direction Method of Multipliers (ADMM) algorithm. The authors reformulate the SBMPC problem into a consensus form that decouples scenario-dependent dynamics from non-anticipativity constraints, allowing for parallel updates across both scenarios and time steps.

To further accelerate the process, the authors integrate the Learning-Enabled ADMM Framework (LEAF). Instead of solving the primal optimization subproblems directly at each iteration, the framework uses Input Convex Neural Networks (ICNNs) to learn the Moreau envelope of the cost function. By approximating the gradient of this envelope, the algorithm replaces iterative optimization with efficient neural network forward passes and gradient computations.

The proposed framework was evaluated on a microgrid energy management problem involving battery storage, renewable generation, and load uncertainty. The authors compared their method against industry-standard nonlinear programming solvers, IPOPT and MadNLP. The results demonstrate that the learning-accelerated approach achieves substantial computational speedups while maintaining reliable closed-loop control performance. The ability to reuse learned models across different scenarios with similar cost structures further enhances the efficiency of the online control process.

Real-time control in environments like microgrids requires rapid decision-making under uncertainty. Traditional solvers often struggle to meet these real-time requirements as the complexity of the scenario set increases. By combining the structural benefits of ADMM decomposition with the speed of learned approximations, this work provides a scalable path for deploying sophisticated stochastic control strategies in time-sensitive applications.