Kernel-based multi-step predictors for data-driven analysis and control of nonlinear systems through the velocity form

TL;DR

This paper introduces kernel-based methods for constructing multi-step predictors of nonlinear systems in velocity form, enabling data-driven analysis and control with stability guarantees.

Contribution

It presents a novel kernel-based framework for multi-step prediction of nonlinear systems in velocity form, respecting their structure and facilitating control design.

Findings

Efficient multi-step predictor for nonlinear systems.

Data-driven analysis and control with stability guarantees.

Structured kernel formulation respects system dynamics.

Abstract

We propose kernel-based approaches for the construction of a single-step and multi-step predictor of the velocity form of nonlinear (NL) systems, which describes the time-difference dynamics of the corresponding NL system and admits a highly structured representation. The predictors in turn allow to formulate completely data-driven representations of the velocity form. The kernel-based formulation that we derive, inherently respects the structured quasi-linear and specific time-dependent relationship of the velocity form. This results in an efficient multi-step predictor for the velocity form and hence for nonlinear systems. Moreover, by using the velocity form, our methods open the door for data-driven behavioral analysis and control of nonlinear systems with global stability and performance guarantees.