Data-driven Nonlinear Predictive Control for Feedback Linearizable Systems

TL;DR

This paper introduces a data-driven predictive control method for nonlinear systems that uses noisy data and basis functions to achieve stability and feasibility, demonstrated on a double inverted pendulum.

Contribution

It develops a robust, data-driven nonlinear predictive control scheme that handles noisy data and nonlinearities without parametric modeling, ensuring stability.

Findings

Recursive feasibility of the control scheme

Practical exponential stability of the closed-loop system

Successful application to a double inverted pendulum

Abstract

We present a data-driven nonlinear predictive control approach for the class of discrete-time multi-input multi-output feedback linearizable nonlinear systems. The scheme uses a non-parametric predictive model based only on input and noisy output data along with a set of basis functions that approximate the unknown nonlinearities. Despite the noisy output data as well as the mismatch caused by the use of basis functions, we show that the proposed multistep robust data-driven nonlinear predictive control scheme is recursively feasible and renders the closed-loop system practically exponentially stable. We illustrate our results on a model of a fully-actuated double inverted pendulum.