Fast Physics-Informed Model Predictive Control Approximation for Lyapunov Stability

TL;DR

PI-MPCS is meant to serve as a surrogate to MPC on situations in which the computational resources are limited and displays a level of stable control for in- and 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.

Figures (3)

• Figure 1: Test case 1 with initial state $s_0 = [2,6,0,0,0,0]$
• Figure 2: Test case 2 with initial state $s_0 = [0,5,0,0,0,0]$
• Figure 3: CPU time comparison between MPC (mean 3.2037 secs, standard deviation 0.5653 sec) and PI-MPCS (mean 1.7344 sec, standard deviation 0.5370 sec)

Theorems & Definitions (3)

• Definition 1: In-distribution states
• Definition 2: Out-of-distribution states
• Definition 3: Lyapunov stability profile