TY - JOUR

T1 - Model predictive control for linear uncertain systems using integral quadratic constraints

AU - Schwenkel, Lukas

AU - Köhler, Johannes

AU - Muller, Matthias A.

AU - Allgower, Frank

N1 - Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – AL 316/12-2 and MU 3929/1-2 - 279734922. F. Allgower is thankful that this work was funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – GRK 2198/1 - 277536708. L. Schwenkel thanks the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting him.

PY - 2022/4/29

Y1 - 2022/4/29

N2 - In this work, we propose a tube-based MPC scheme for state- and input-constrained linear systems subject to dynamic uncertainties characterized by dynamic integral quadratic constraints (IQCs). In particular, we extend the framework of $\rho$-hard IQCs for exponential stability analysis to external inputs. This result yields that the error between the true uncertain system and the nominal prediction model is bounded by an exponentially stable scalar system. In the proposed tube-based MPC scheme, the state of this error bounding system is predicted along with the nominal model and used as a scaling parameter for the tube size. We prove that this method achieves robust constraint satisfaction and input-to-state stability despite dynamic uncertainties and additive bounded disturbances. A numerical example demonstrates the reduced conservatism of this IQC approach compared to state-of-the-art robust MPC approaches for dynamic uncertainties.

AB - In this work, we propose a tube-based MPC scheme for state- and input-constrained linear systems subject to dynamic uncertainties characterized by dynamic integral quadratic constraints (IQCs). In particular, we extend the framework of $\rho$-hard IQCs for exponential stability analysis to external inputs. This result yields that the error between the true uncertain system and the nominal prediction model is bounded by an exponentially stable scalar system. In the proposed tube-based MPC scheme, the state of this error bounding system is predicted along with the nominal model and used as a scaling parameter for the tube size. We prove that this method achieves robust constraint satisfaction and input-to-state stability despite dynamic uncertainties and additive bounded disturbances. A numerical example demonstrates the reduced conservatism of this IQC approach compared to state-of-the-art robust MPC approaches for dynamic uncertainties.

KW - Additives

KW - Electron tubes

KW - Integral quadratic constraints

KW - Measurement uncertainty

KW - Numerical stability

KW - Predictive control for linear systems

KW - Robust control

KW - Uncertain systems

KW - Uncertainty

KW - uncertain systems

KW - Integral quadratic constraints (IQCs)

KW - robust control

KW - predictive control for linear systems

UR - http://www.scopus.com/inward/record.url?scp=85129617169&partnerID=8YFLogxK

U2 - 10.1109/TAC.2022.3171410

DO - 10.1109/TAC.2022.3171410

M3 - Article

AN - SCOPUS:85129617169

VL - 68

SP - 355

EP - 368

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 1

ER -