Getting Robustness Against Unstructured Uncertainty: A Tube-Based MPC Approach

This note extends tube-based model predictive control to the control of nonlinear systems with unmodeled dynamics. The problem of obtaining robustness against unstructured uncertainty is converted into the easier problem of achieving robustness against an additional bounded disturbance while satisfying an additional output constraint. The output constraint depends on the maximum l∞ gain of the unstructured dynamics.

[1]  Manfred Morari,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[2]  D. Bernstein,et al.  Induced convolution operator norms for discrete-time linear systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[3]  D. Angeli.  Intrinsic robustness of global asymptotic stability , 1999 .

[4]  Eduardo Sontag,et al.  Formulas relating KL stability estimates of discrete-time and sampled-data nonlinear systems , 1999 .

[5]  Eduardo Sontag,et al.  Input-to-state stability for discrete-time nonlinear systems , 1999, at - Automatisierungstechnik.

[6]  B. Kouvaritakis,et al.  Receding horizon H/sub /spl infin// predictive control for systems with input saturation , 2000 .

[7]  David Q. Mayne,et al.  Robustifying model predictive control of constrained linear systems , 2001 .

[8]  Luigi Chisci,et al.  Systems with persistent disturbances: predictive control with restricted constraints , 2001, Autom..

[9]  Massimo Canale,et al.  Robust design of predictive controllers in presence of unmodeled dynamics , 2001 .

[10]  D. Limón,et al.  Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[11]  Eduardo D. Sontag,et al.  A small-gain theorem with applications to input/output systems, incremental stability, detectability, and interconnections , 2002, J. Frankl. Inst..

[12]  J. Löfberg.  Minimax approaches to robust model predictive control , 2003 .

[13]  Alessandro Casavola,et al.  Robust constrained predictive control of uncertain norm-bounded linear systems , 2004, Autom..

[14]  Stephen J. Wright,et al.  Closed‐loop behavior of nonlinear model predictive control , 2004 .

[15]  Yuandan Lin,et al.  REMARKS ON INPUT-TO-OUTPUT STABILITY FOR DISCRETE TIME SYSTEMS , 2005 .

[16]  Eduardo F. Camacho,et al.  Min-Max MPC using a tractable QP Problem , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[17]  Eduardo F. Camacho,et al.  On the stability of constrained MPC without terminal constraint , 2006, IEEE Transactions on Automatic Control.

[18]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[19]  María M. Seron,et al.  A systematic method to obtain ultimate bounds for perturbed systems , 2007, Int. J. Control.

[20]  Chaohong Cai,et al.  Asymptotic characterizations of input-output-to-state stability for discrete-time systems , 2007, Syst. Control. Lett..

[21]  R. Findeisen,et al.  On Disturbance Attenuation of Nonlinear Moving Horizon Control , 2007 .

[22]  Chaohong Cai,et al.  Input-output-to-state stability for discrete-time systems , 2008, Autom..

[23]  Graham C. Goodwin,et al.  Robust output-feedback model predictive control for systems with unstructured uncertainty , 2008, Autom..

[24]  Thomas Parisini,et al.  Robust Model Predictive Control of Nonlinear Systems With Bounded and State-Dependent Uncertainties , 2009, IEEE Transactions on Automatic Control.

[25]  D. Limón,et al.  Input-to-State Stability: A Unifying Framework for Robust Model Predictive Control , 2009 .

[26]  Eric C. Kerrigan,et al.  Control of Constrained Discrete-Time Systems With Bounded $\ell_{2}$ Gain , 2009, IEEE Transactions on Automatic Control.

[27]  David Q. Mayne,et al.  Tube‐based robust nonlinear model predictive control , 2011 .

[28]  David Q. Mayne,et al.  Tube-based model predictive control for nonlinear systems with unstructured uncertainty , 2011, IEEE Conference on Decision and Control and European Control Conference.

[29]  S. Raković.  Invention of Prediction Structures and Categorization of Robust MPC Syntheses , 2012 .