Controlled Invariant Sets for Gaussian Process State Space Models

TL;DR

This paper introduces a method to compute probabilistic invariant sets for nonlinear systems modeled with Gaussian processes, enabling data-driven control with safety guarantees.

Contribution

It proposes a semidefinite programming approach for designing controllers that maximize the probability of staying within invariant sets under input constraints.

Findings

Validated on a quadrotor in simulation and real-world tests.

Achieved high probability of trajectories remaining within safe bounds.

Demonstrated effectiveness of the approach for safety-critical control.

Abstract

We compute probabilistic controlled invariant sets for nonlinear systems using Gaussian process state space models, which are data-driven models that account for unmodeled and unknown nonlinear dynamics. We propose a semidefinite programming scheme for designing state-feedback controllers that maximize the probability of the trajectories staying within a probabilistic controlled invariant set while satisfying input constraints. The results are validated on a quadrotor, both in simulation and on a physical platform.