Worst-case complexity analysis of inexact gradient methods applied to predictive control

Details

Supervisors

Bianchin, Gianluca ; Nunes Grapiglia, Geovani

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

enIn modern control applications, Model Predictive Control (MPC) is a powerful framework capable of handling multivariate systems and constraints. However, its reliance on solving an optimization problem at each timestep can be computationally expensive, in particular for model uncertainties and real-time constraints. This thesis investigates the use of inexact first-order optimization methods within a real-time MPC framework when the model is subject to bounded disturbances. The primary objective is to quantify the impact of gradient inaccuracies (caused by model mismatch) on the performance of (projected) gradient methods applied to both convex and nonconvex cost functions. The analysis focuses on the derivation of explicit worst-case complexity bounds that relate the number of iterations required to achieve a specified level of stationarity to the disturbance magnitude. These bounds are validated through extensive numerical simulations for linear time-invariant systems, covering different classes of cost functions. Furthermore, the study experimentally shows how inexact gradient methods can be effectively integrated into real-time MPC controllers, showing their robustness in both stable and unstable system scenarios. This work contributes theoretical insights and practical strategies for deploying efficient and robust control algorithms in computationally constrained environments and for disturbed dynamical systems.