Infinite-horizon differentiable Model Predictive Control

Conference item

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.

Authors: East, S; Gallieri, M; Masci, J; Koutnik, J; Cannon, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: ICLR
• Journal: Proceedings of ICLR 2020
• Publication date: 2020-04-06
• Acceptance date: 2020-04-06
• Event title: International Conference on Learning Representations (ICLR 2020)
• Event location: Millennium Hall, Addis Ababa ETHIOPIA
• Event website: https://iclr.cc/
• Event start date: 2020-04-26
• Event end date: 2020-05-01
• Language: English
• Keywords: FFR; Model Predictive Control; imitation Learning; safe Learning; Riccati equation