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

TL;DR

This paper introduces a hybrid learning-based MPC approach for PWA systems that balances online and offline computation, guaranteeing feasibility and reducing complexity compared to traditional methods.

Contribution

It proposes a partially offline-online MPC method with a verifiable feasibility condition and an iterative training data generation process for PWA systems.

Findings

Reduces online computational complexity compared to traditional MPC.

Guarantees feasibility of the control policy during online operation.

Demonstrates improved efficiency over purely online or explicit MPC in experiments.

Abstract

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.