Funnel-based Reachability Control of Unknown Nonlinear Systems using Gaussian Processes

TL;DR

This paper presents a method to design reachability controllers for unknown nonlinear systems by learning their dynamics with Gaussian processes and applying funnel-based control, validated through numerical experiments.

Contribution

It introduces a novel approach combining Gaussian process learning with funnel-based control for unknown nonlinear systems, providing probabilistic guarantees.

Findings

Successful controller synthesis for unknown systems

Probabilistic guarantees on system behavior

Effective numerical validation

Abstract

This paper aims to synthesize a reachability controller for an unknown dynamical system. We first learn the unknown system using Gaussian processes and the (probabilistic) guarantee on the learned model. Then we use the funnel-based controller synthesis approach using this approximated dynamical system to design the controller for a reachability specification. Finally, the merits of the proposed method are shown using a numerical example.