Infinite-Horizon Differentiable Model Predictive Control

TL;DR

This paper introduces a differentiable MPC framework using the algebraic Riccati equation for stable, safe control, enabling gradient-based learning with proven stability and constraint satisfaction.

Contribution

It derives the analytical derivative of the DARE solution, allowing differentiable MPC for the first time, and integrates an augmented Lagrangian method for feasible, constrained optimization.

Findings

Framework achieves stable, safe control in numerical studies

Enables gradient-based learning for MPC

Maintains feasibility and constraints during training

Abstract

This paper proposes a differentiable linear quadratic Model Predictive Control (MPC) framework for safe imitation learning. The infinite-horizon cost is enforced using a terminal cost function obtained from the discrete-time algebraic Riccati equation (DARE), so that the learned controller can be proven to be stabilizing in closed-loop. A central contribution is the derivation of the analytical derivative of the solution of the DARE, thereby allowing the use of differentiation-based learning methods. A further contribution is the structure of the MPC optimization problem: an augmented Lagrangian method ensures that the MPC optimization is feasible throughout training whilst enforcing hard constraints on state and input, and a pre-stabilizing controller ensures that the MPC solution and derivatives are accurate at each iteration. The learning capabilities of the framework are demonstrated in a set of numerical studies.