Min-max Differential Inequalities for Polytopic Tube MPC

Authors

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

Reference

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

Abstract

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.

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Bibtex

@INPROCEEDINGS{Feng2019,
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},
}