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

In this work, we provide deterministic error bounds for the actual state evolution of nonlinear systems that can be embedded in linear parameter-varying (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). We provide exact error formulations compared to other approaches based on linearization schemes that inevitably introduce additional errors and deteriorate performance. The analysis and method are certified by solving the regulation problem of an unbalanced disk.