Exact Learning of Linear Model Predictive Control Laws using Oblique Decision Trees with Linear Predictions

TL;DR

This paper presents a novel data-driven method using oblique decision trees with linear predictions to learn explicit MPC laws, achieving high interpretability, computational efficiency, and verified stability for safety-critical control systems.

Contribution

It introduces a gradient-based training algorithm for ODT-LP models that replicate linear MPC laws with proven stability and improved evaluation speed, enhancing safety-critical control applications.

Findings

ODT-LP models replicate MPC performance accurately.

Evaluation time reduced by orders of magnitude.

Enables formal verification of control logic.

Abstract

Model Predictive Control (MPC) is a powerful strategy for constrained multivariable systems but faces computational challenges in real-time deployment due to its online optimization requirements. While explicit MPC and neural network approximations mitigate this burden, they suffer from scalability issues or lack interpretability, limiting their applicability in safety-critical systems. This work introduces a data-driven framework that directly learns the Linear MPC control law from sampled state-action pairs using Oblique Decision Trees with Linear Predictions (ODT-LP), achieving both computational efficiency and interpretability. By leveraging the piecewise affine structure of Linear MPC, we prove that the Linear MPC control law can be replicated by finite-depth ODT-LP models. We develop a gradient-based training algorithm using smooth approximations of tree routing functions to learn this structure from grid-sampled Linear MPC solutions, enabling end-to-end optimization. Input-to-state stability is established under bounded approximation errors, with explicit error decomposition into learning inaccuracies and sampling errors to inform model design. Numerical experiments demonstrate that ODT-LP controllers match MPC's closed-loop performance while reducing online evaluation time by orders of magnitude compared to MPC, explicit MPC, neural network, and random forest counterparts. The transparent tree structure enables formal verification of control logic, bridging the gap between computational efficiency and certifiable reliability for safety-critical systems.