Physics-informed Gaussian Processes as Linear Model Predictive Controller

TL;DR

This paper presents a novel control algorithm for linear systems using Gaussian Processes constrained by differential equations, enabling stability guarantees and incorporating soft constraints through a Bayesian inference framework.

Contribution

It introduces a Gaussian Process-based Model Predictive Control method that enforces system dynamics and stability, with a novel approach to handling soft constraints via virtual setpoints.

Findings

Controller satisfies open-loop stability.

Incorporates soft constraints through virtual setpoints.

Demonstrated effectiveness in a numerical example.

Abstract

We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with constant coefficients. Control inputs for tracking are determined by conditioning the prior GP on the setpoints, i.e. control as inference. The resulting Model Predictive Control scheme incorporates pointwise soft constraints by introducing virtual setpoints to the posterior Gaussian process. We show theoretically that our controller satisfies open-loop stability for the optimal control problem by leveraging general results from Bayesian inference and demonstrate this result in a numerical example.