Fast Physics-Informed Model Predictive Control Approximation for Lyapunov Stability

TL;DR

This paper introduces a Physics-Informed MPC surrogate model (PI-MPCS) that approximates traditional MPC control with enhanced stability and robustness, significantly reducing computational load for real-time applications like quadcopter landing.

Contribution

The paper presents a novel deterministic surrogate model that integrates system dynamics and Lyapunov stability to efficiently approximate MPC control in resource-constrained settings.

Findings

Achieves approximately two times speed-up over standard MPC.

Demonstrates stable control on non-linear quadcopter landing tasks.

Effectively maintains stability for out-of-distribution states.

Abstract

At the forefront of control techniques is Model Predictive Control (MPC). While MPCs are effective, their requisite to recompute an optimal control given a new state leads to sparse response to the system and may make their implementation infeasible in small systems with low computational resources. To address these limitations in stability control, this research presents a small deterministic Physics-Informed MPC Surrogate model (PI-MPCS). PI-MPCS was developed to approximate the control by an MPC while encouraging stability and robustness through the integration of the system dynamics and the formation of a Lyapunov stability profile. Empirical results are presented on the task of 2D quadcopter landing. They demonstrate a rapid and precise MPC approximation on a non-linear system along with an estimated two times speed up on the computational requirements when compared against an MPC. PI-MPCS, in addition, displays a level of stable control for in- and out-of-distribution states as encouraged by the discrete dynamics residual and Lyapunov stability loss functions. PI-MPCS is meant to serve as a surrogate to MPC on situations in which the computational resources are limited.