TY - JOUR

T1 - A computationally efficient robust model predictive control framework for uncertain nonlinear systems

AU - Koehler, Johannes

AU - Soloperto, Raffaele

AU - Müller, Matthias A.

AU - Allgöwer, Frank

N1 - Funding information: Manuscript received October 22, 2019; revised February 25, 2020; accepted March 15, 2020. Date of publication March 23, 2020; date of current version January 28, 2021. This work was supported by the German Research Foundation under Grant GRK 2198/1-277536708, Grant AL 316/12-2, and Grant MU 3929/1-2-279734922. The work of Raffaele Soloperto was supported by the International Max Planck Research School for Intelligent Systems. Recommended by Associate Editor E. C. Kerrigan. (Corresponding author: Johannes Köhler.) Johannes Köhler, Raffaele Soloperto, and Frank Allgöwer are with the Institute for Systems Theory and Automatic Control, University of Stuttgart, 70550 Stuttgart, Germany (e-mail: johannes.koehler@ist.uni-stuttgart.de; raffaele.soloperto@ist.uni-stuttgart.de; mueller@irt.uni-hannover.de).

PY - 2020/3/23

Y1 - 2020/3/23

N2 - In this article, we present a nonlinear robust model predictive control (MPC) framework for general (state and input dependent) disturbances. This approach uses an online constructed tube in order to tighten the nominal (state and input) constraints. To facilitate an efficient online implementation, the shape of the tube is based on an offline computed incremental Lyapunov function with a corresponding (nonlinear) incrementally stabilizing feedback. Crucially, the online optimization only implicitly includes these nonlinear functions in terms of scalar bounds, which enables an efficient implementation. Furthermore, to account for an efficient evaluation of the worst case disturbance, a simple function is constructed offline that upper bounds the possible disturbance realizations in a neighborhood of a given point of the open-loop trajectory. The resulting MPC scheme ensures robust constraint satisfaction and practical asymptotic stability with a moderate increase in the online computational demand compared to a nominal MPC. We demonstrate the applicability of the proposed framework in comparison to state-of-the-art robust MPC approaches with a nonlinear benchmark example.

AB - In this article, we present a nonlinear robust model predictive control (MPC) framework for general (state and input dependent) disturbances. This approach uses an online constructed tube in order to tighten the nominal (state and input) constraints. To facilitate an efficient online implementation, the shape of the tube is based on an offline computed incremental Lyapunov function with a corresponding (nonlinear) incrementally stabilizing feedback. Crucially, the online optimization only implicitly includes these nonlinear functions in terms of scalar bounds, which enables an efficient implementation. Furthermore, to account for an efficient evaluation of the worst case disturbance, a simple function is constructed offline that upper bounds the possible disturbance realizations in a neighborhood of a given point of the open-loop trajectory. The resulting MPC scheme ensures robust constraint satisfaction and practical asymptotic stability with a moderate increase in the online computational demand compared to a nominal MPC. We demonstrate the applicability of the proposed framework in comparison to state-of-the-art robust MPC approaches with a nonlinear benchmark example.

KW - constrained control

KW - Nonlinear model predictive control (MPC)

KW - robust MPC

KW - uncertain systems

UR - http://www.scopus.com/inward/record.url?scp=85100388305&partnerID=8YFLogxK

U2 - 10.1109/TAC.2020.2982585

DO - 10.1109/TAC.2020.2982585

M3 - Article

VL - 66

SP - 794

EP - 801

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 2

M1 - 9044326

ER -