Immersion-based model predictive control of constrained nonlinear systems: Polyflow approximation

TL;DR

This paper introduces a novel offline method to embed nonlinear systems into high-dimensional linear models, enabling efficient convex model predictive control and addressing computational challenges in nonlinear MPC.

Contribution

The authors propose a polyflow approximation technique that uses algebraic immersibility conditions to create linear embeddings, facilitating convex MPC for nonlinear systems.

Findings

Enables offline computation of high-dimensional linear models for nonlinear systems.

Allows convex online MPC problem formulation for constrained nonlinear systems.

Provides a Koopman operator interpretation of the embedding approach.

Abstract

In the framework of Model Predictive Control (MPC), the control input is typically computed by solving optimization problems repeatedly online. For general nonlinear systems, the online optimization problems are non-convex and computationally expensive or even intractable. In this paper, we propose to circumvent this issue by computing a high-dimensional linear embedding of discrete-time nonlinear systems. The computation relies on an algebraic condition related to the immersibility property of nonlinear systems and can be implemented offline. With the high-dimensional linear model, we then define and solve a convex online MPC problem. We also provide an interpretation of our approach under the Koopman operator framework.