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

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.