Min-max Differential Inequalities for Polytopic Tube MPC


  • M.E. Villanueva, H. Hu, X. Feng, B. Houska


  • In Proceedings of the
    American Control Conference,
    Philadelphia, USA, pages 1170–1174, July, 2019.


This paper is concerned with robust, tube-based MPC for control systems with bounded time-varying disturbances. In tube MPC, predicted trajectories are replaced by a robust forward invariant tube (RFIT), a set-valued function enclosing all possible state trajectories under a given feedback control law, regardless of the uncertainty realization. In this paper, the main idea is to characterize RFITs with polytopic cross-sections via a min-max differential inequality for their support functions. This result leads to a conservative but tractable polytopic tube MPC formulation, which can be solved using existing optimal control solvers. The corresponding theoretical developments are illustrated by a numerical case study.



author = {Feng, X. and Hu, H. and Villanueva, M.E. and Houska, B.},
title = {Min-max differential inequalities for polytopic {T}ube {MPC}},
booktitle = {In Proceedings of the American Control Conference, Philadelphia, USA},
year = {2019},
pages = {1170–1174},