Robust and stochastic model predictive control: Are we going in the right direction?

Abstract Motivated by requirements in the process industries, the largest user of model predictive control, we re-examine some features of recent research on this topic. We suggest that some proposals are too complex and computationally demanding for application in this area and make some tentative proposals for research on robust and stochastic model predictive control to aid applicability

[1]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[2]  Francesco Borrelli,et al.  Scenario model predictive control for lane change assistance on highways , 2015, 2015 IEEE Intelligent Vehicles Symposium (IV).

[3]  Eric C. Kerrigan,et al.  Optimization over state feedback policies for robust control with constraints , 2006, Autom..

[4]  Frank Allgöwer,et al.  Constraint-Tightening and Stability in Stochastic Model Predictive Control , 2015, IEEE Transactions on Automatic Control.

[5]  Sergio Grammatico,et al.  A Scenario Approach for Non-Convex Control Design , 2014, IEEE Transactions on Automatic Control.

[6]  Giuseppe Carlo Calafiore,et al.  Robust Model Predictive Control via Scenario Optimization , 2012, IEEE Transactions on Automatic Control.

[7]  Giuseppe Carlo Calafiore,et al.  Uncertain convex programs: randomized solutions and confidence levels , 2005, Math. Program..

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

[9]  Marco C. Campi,et al.  The Exact Feasibility of Randomized Solutions of Uncertain Convex Programs , 2008, SIAM J. Optim..

[10]  R. Bhushan Gopaluni,et al.  Model Predictive Control in Industry: Challenges and Opportunities , 2015 .

[11]  D. Q. Mayne,et al.  Suboptimal model predictive control (feasibility implies stability) , 1999, IEEE Trans. Autom. Control..

[12]  Mark Rice,et al.  A numerically robust state-space approach to stable-predictive control strategies , 1998, Autom..

[13]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[14]  Marko Bacic,et al.  Model predictive control , 2003 .

[15]  John Lygeros,et al.  A randomized approach to Stochastic Model Predictive Control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[16]  James A. Primbs,et al.  Stochastic Receding Horizon Control of Constrained Linear Systems With State and Control Multiplicative Noise , 2007, IEEE Transactions on Automatic Control.

[17]  Basil Kouvaritakis,et al.  Explicit use of probabilistic distributions in linear predictive control , 2010, Autom..

[18]  John Lygeros,et al.  Stochastic Model Predictive Control using a combination of randomized and robust optimization , 2013, 52nd IEEE Conference on Decision and Control.

[19]  David Q. Mayne,et al.  Robust model predictive control of constrained linear systems with bounded disturbances , 2005, Autom..

[20]  Stephen J. Wright,et al.  Conditions under which suboptimal nonlinear MPC is inherently robust , 2011, Syst. Control. Lett..

[21]  Giuseppe Carlo Calafiore,et al.  Random Convex Programs , 2010, SIAM J. Optim..

[22]  David Q. Mayne,et al.  Invariant approximations of the minimal robust positively Invariant set , 2005, IEEE Transactions on Automatic Control.

[23]  Giuseppe Carlo Calafiore,et al.  The scenario approach to robust control design , 2006, IEEE Transactions on Automatic Control.

[24]  R. Tempo,et al.  Randomized Algorithms for Analysis and Control of Uncertain Systems , 2004 .

[25]  S. Raković,et al.  Explicit use of probabilistic distributions in linear predictive control , 2010, at - Automatisierungstechnik.

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

[27]  Roberto Tempo,et al.  Randomized methods for design of uncertain systems: Sample complexity and sequential algorithms , 2013, Autom..

[28]  John Lygeros,et al.  On Stability and Performance of Stochastic Predictive Control Techniques , 2013, IEEE Transactions on Automatic Control.

[29]  Lars Grne,et al.  Nonlinear Model Predictive Control: Theory and Algorithms , 2011 .

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

[31]  David Q. Mayne,et al.  Model predictive control: Recent developments and future promise , 2014, Autom..

[32]  Stefano Di Cairano,et al.  Decomposition via ADMM for scenario-based Model Predictive Control , 2015, 2015 American Control Conference (ACC).

[33]  Stefano Di Cairano,et al.  An Industry Perspective on MPC in Large Volumes Applications: Potential Benefits and Open Challenges , 2012 .

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

[35]  David Q. Mayne,et al.  An apologia for stabilising terminal conditions in model predictive control , 2013, Int. J. Control.

[36]  Alberto Bemporad,et al.  Scenario-based model predictive control of stochastic constrained linear systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[37]  Sergio Grammatico,et al.  On the sample size of random convex programs with structured dependence on the uncertainty , 2015, Autom..