Learning controllers from data via kernel-based interpolation

TL;DR

This paper introduces a data-driven control design approach for nonlinear systems using kernel-based interpolation, enabling stabilization and invariant set computation through semidefinite programming.

Contribution

It presents a novel kernel-based interpolation method for control design that incorporates deterministic error bounds and guarantees stability.

Findings

Successfully stabilizes nonlinear systems using data-driven kernels.

Provides positively invariant sets for closed-loop systems.

Implemented via semidefinite programming.

Abstract

We propose a data-driven control design method for nonlinear systems that builds on kernel-based interpolation. Under some assumptions on the system dynamics, kernel-based functions are built from data and a model of the system, along with deterministic model error bounds, is determined. Then, we derive a controller design method that aims at stabilizing the closed-loop system by cancelling out the system nonlinearities. The proposed method can be implemented using semidefinite programming and returns positively invariant sets for the closed-loop system.