Error Bounds in Nonlinear Model Predictive Control with Linear Differential Inclusions of Parametric-Varying Embeddings

TL;DR

This paper derives explicit deterministic error bounds for nonlinear systems using LPV embeddings and linear differential inclusions within MPC, improving accuracy over traditional linearization methods.

Contribution

It introduces a novel approach to compute exact polytopic error bounds in nonlinear MPC using LDIs, reducing conservatism compared to existing linearization-based methods.

Findings

Derived explicit polytopic error bounds for nonlinear systems

Validated the approach on a classical control benchmark (unbalanced disk)

Demonstrated reduced conservatism over traditional linearization schemes

Abstract

In this work, we provide deterministic error bounds for the actual state evolution of nonlinear systems embedded with the linear parametric variable (LPV) formulation and steered by model predictive control (MPC). The main novelty concerns the explicit derivation of these deterministic bounds as polytopic tubes using linear differential inclusions (LDIs), which provide exact error formulations compared to linearization schemes that introduce additional error and deteriorate conservatism. The analysis and method are certified by solving the regulator problem of an unbalanced disk that stands as a classical control benchmark example.