Physics-informed Gaussian Processes as Linear Model Predictive Controller
This work addresses control problems in engineering by proposing an incremental method that integrates Gaussian Processes with model predictive control for improved stability.
The paper tackles controlling linear time-invariant systems for tracking by introducing a physics-informed Gaussian Process controller that enforces linear ODE constraints, achieving open-loop stability as proven theoretically and demonstrated numerically.
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.