Min-max Economic Model Predictive Control

This paper proposes a min-max Economic Model Predictive Control approach for discrete time uncertain systems: a MPC min-max strategy where the worst-case performance with respect to uncertainties is optimized. Unfortunately, many min-max MPC formulations yield intractable optimization problems with exponential complexity, for this reason a min-max algorithm for a certain type of model uncertainty is derived in this paper. The transformation of the original problem into a second-order cone program is the most remarkable feature meaning that the min-max problem is written as a convex program. The result is an optimization problem with polynomial complexity.

[1]  Joos Vandewalle,et al.  The use of convex programming on fuzzy model based predictive control , 1999, Proceedings of the 1999 IEEE International Symposium on Intelligent Control Intelligent Systems and Semiotics (Cat. No.99CH37014).

[2]  John Bagterp Jørgensen,et al.  The potential of Economic MPC for power management , 2010, 49th IEEE Conference on Decision and Control (CDC).

[3]  Alberto Bemporad,et al.  Robust model predictive control: A survey , 1998, Robustness in Identification and Control.

[4]  John Bagterp Jørgensen,et al.  Economic MPC for Power Management in the SmartGrid , 2011 .

[5]  Xianzhong Chen,et al.  Distributed economic MPC: Application to a nonlinear chemical process network , 2012 .

[6]  J. D. Perkins,et al.  Process control structure selection based on economics , 2000 .

[7]  Panagiotis D. Christofides,et al.  Economic model predictive control of switched nonlinear systems , 2013, Syst. Control. Lett..

[8]  Moritz Diehl,et al.  A Lyapunov Function for Economic Optimizing Model Predictive Control , 2011, IEEE Transactions on Automatic Control.

[9]  David Angeli,et al.  Fundamentals of economic model predictive control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[10]  James B. Rawlings,et al.  Economic Dynamic Real-Time Optimization and Nonlinear Model-Predictive Control on Infinite Horizons , 2009 .

[11]  Bing Chu,et al.  Using economic Model Predictive Control to design sustainable policies for mitigating climate change , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[12]  Peng Xu,et al.  Demand reduction in building energy systems based on economic model predictive control , 2012 .

[13]  Lorenz T. Biegler,et al.  Optimizing process economics online using model predictive control , 2013, Comput. Chem. Eng..

[14]  John Bagterp Jørgensen,et al.  Robust economic MPC for a power management scenario with uncertainties , 2011, IEEE Conference on Decision and Control and European Control Conference.

[15]  Lorenz T. Biegler,et al.  Lyapunov stability of economically oriented NMPC for cyclic processes , 2011 .

[16]  Ian T. Cameron,et al.  Control studies on a model evaporation process — constrained state driving with conventional and higher relative degree systems , 1994 .

[17]  Michael Nikolaou,et al.  MPC: Current practice and challenges , 2012 .

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

[19]  David Angeli,et al.  Economic optimization using model predictive control with a terminal cost , 2011, Annu. Rev. Control..

[20]  James B. Rawlings,et al.  Optimizing Process Economic Performance Using Model Predictive Control , 2009 .