# Learning-Based Model Predictive Control for Piecewise Affine Systems with Feasibility Guarantees

arXiv: https://arxiv.org/abs/2412.00490 · HTML: https://mlsanity.com/paper/2412.00490/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2024.

## Built on by (most cited first, 1 of 1)

- [Reinforcement Learning with Distributed MPC for Fuel-Efficient Platoon Control with Discrete Gear Transitions](https://mlsanity.com/paper/2601.18294/) (2026)

## Abstract (arXiv)

Online model predictive control (MPC) for piecewise affine (PWA) systems requires the online solution to an optimization problem that implicitly optimizes over the switching sequence of PWA regions, for which the computational burden can be prohibitive. Alternatively, the computation can be moved offline using explicit MPC; however, the online memory requirements and the offline computation can then become excessive. In this work we propose a solution in between online and explicit MPC, addressing the above issues by partially dividing the computation between online and offline. To solve the underlying MPC problem, a policy, learned offline, specifies the sequence of PWA regions that the dynamics must follow, thus reducing the complexity of the remaining optimization problem that solves over only the continuous states and control inputs. We provide a condition, verifiable during learning, that guarantees feasibility of the learned policy's output, such that an optimal continuous control input can always be found online. Furthermore, a method for iteratively generating training data offline allows the feasible policy to be learned efficiently, reducing the offline computational burden. A numerical experiment demonstrates the effectiveness of the method compared to both online and explicit MPC.