Efficient Uniform Feasible Set Sampling for Approximate Linear MPC

TL;DR

This paper introduces LMPC-HR, an efficient sampling method for linear MPC feasible sets that significantly reduces computation time, facilitating better training data generation for approximate MPC.

Contribution

The paper presents a novel linear MPC Hit-and-Run sampler that formulates boundary detection as a convex linear program, improving sampling efficiency.

Findings

LMPC-HR achieves an order of magnitude faster sampling than naive methods.

The method accurately generates uniform samples from the feasible set.

Numerical results validate the efficiency and effectiveness of the proposed sampler.

Abstract

Model Predictive Control (MPC) offers safe and near-optimal control but suffers from high computational costs. Approximate MPC (AMPC) mitigates this by learning a cheaper surrogate policy, typically by training a neural network on state-MPC input pairs. Generating training data is a major bottleneck, requiring solving the MPC for numerous states sampled from its feasible set. Since this feasible set is implicitly defined and unknown, efficient sampling is nontrivial but crucial. We propose the linear MPC Hit-and-Run (LMPC-HR) sampler for linear MPC with polyhedral constraints. We identify the feasible set boundaries along search directions, a crucial step within HR, by formulating the problem as a convex linear program, replacing expensive iterative searches with a single optimization step. A numerical study demonstrates that LMPC-HR achieves an order of magnitude reduction in computation time for generating uniformly distributed samples from the feasible set compared to naive baselines.