Abstract
In recent years, Economic Model Predictive Control has emerged as a variant of traditional (tracking) MPC which aims at maximizing economic profitability by directly minimizing, over a receding prediction horizon, the costs incurred in system’s operation. Several design alternatives have been proposed in the literature, as well as suitable tools for the analysis of stability and performance of the different design methods. This note provides the authors’ perspective on some of the most relevant results that appeared within this framework as well as, for interested readers, references to the technical papers where such results have first been discussed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Amrit, R., Rawlings, J.B., Angeli, D.: Economic optimization using model predictive control with a terminal cost. Annu. Rev. Control 35, 178–186 (2011)
Angeli, D., Rawlings, J.B.: Receding horizon cost optimization and control for nonlinear plants. In: 8th IFAC Symposium on Nonlinear Control Systems (NOLCOS), Bologna (2010)
Angeli, D., Amrit, R., Rawlings, J.B.: On average performance and stability of economic model predictive control. IEEE Trans. Autom. Control 57(7), 1615–1626 (2012)
Angeli, D., Casavola, A., Tedesco, F.: Theoretical advances on economic model predictive control with time-varying costs. Annu. Rev. Control 41, 218–224 (2016)
Bayer, F.A., Müller, M.A., Allgöwer, F.: Tube-based robust economic model predictive control. J. Process Control 24(8), 1237–1246 (2014)
Bayer, F.A., Müller, M.A., Allgöwer, F.: Min-max economic model predictive control approaches with guaranteed performance. In: 55th IEEE Conference on Decision and Control (CDC), Las Vegas, pp. 3210–3215 (2016)
Bayer, F.A., Lorenzen, M., Müller, M.A., Allgöwer, F.: Robust economic model predictive control using stochastic information. Automatica 74, 151–161 (2016)
Chisci, L., Rossiter, J.A., Zappa, G.: Systems with persistent disturbances: predictive control with restricted constraints. Automatica 37(7), 1019–1028 (2001)
Diehl, M., Amrit, R., Rawlings, J.B.: A Lyapunov function for economic optimizing model predictive control. IEEE Trans. Autom. Control 56(3), 703–707 (2011)
Dong, Z., Angeli, D.: A generalized approach to economic model predictive control with terminal penalty functions. In: IFAC World Congress, Toulouse (2017)
Dorfman, R., Samuelson, P.A., Solow, R.M.: Linear Programming and Economic Analysis. Dover Publications, New York (1987); Reprint of the 1958 original
Ellis, M., Liu, J., Christofides, P.D.: Economic Model Predictive Control: Theory, Formulations and Chemical Process Applications. Advances in Industrial Control. Springer, Berlin (2017)
Fagiano, L., Teel, A.: Generalized terminal state constraint for model predictive control. Automatica 49(9), 2622–2631 (2013)
Faulwasser, T., Bonvin, D.: On the design of economic NMPC based on approximate turnpike properties. In: 54th IEEE Conference on Decision and Control (CDC), Osaka, pp. 4964–4970 (2015)
Faulwasser, T., Korda, M., Jones, C.N., Bonvin, D.: Turnpike and dissipativity properties in dynamic real-time optimization and economic MPC. In: 53rd IEEE Conference on Decision and Control (CDC), Los Angeles, pp. 2734–2739 (2014)
Finlay, L., Gaitsgory, V., Lebedev, I.: Duality in linear programming problems related to deterministic long run average problems of optimal control. SIAM J. Control Optim. 47(4), 1667–1700 (2008)
Grüne, L.: Economic receding horizon control without terminal constraints. Automatica 493, 725–734 (2013)
Grüne, L., Müller, M.A.: On the relation between strict dissipativity and turnpike properties. Syst. Control Lett. 90, 45–53 (2016)
Grüne, L., Pannek, J.: Nonlinear Model Predictive Control: Theory and Algorithms. Communications and Control Engineering Series, 2nd edn. Springer, New York (2017)
Grüne, L., Stieler, M.: Asymptotic stability and transient optimality of economic MPC without terminal constraints. J. Process Control 24(8), 1187–1196 (2014)
Gaitsgory, V., Parkinson, A., Shvartsman, I.: Linear programming formulations of deterministic infinite horizon optimal control problems in discrete time. arXiv:1702.00857 (2017)
Keerthi, S.S., Gilbert, E.G.: Optimal infinite-horizon feedback control laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations. J. Optim. Theory Appl. 57, 265–293 (1988)
Langson, W., Chryssochoos, I., Raković, S.V., Mayne, D.Q.: Robust model predictive control using tubes. Automatica 40, 125–133 (2004)
Limon, D., Alvarado, I., Alamo, T., Camacho, E.F.: On the relation between strict dissipativity and turnpike properties. Automatica 44(9), 2382–2387 (2008)
Marlin, T.E., Hrymak, A.N.: Real-time operations optimization of continuous processes. In: Kantor, J.C., Garca, C.E., Carnahan, B. (eds.) Chemical Process Control-V, pp. 156–164. CACHE, AIChE (1997)
Mayne, D.Q., Seron, M.M., Raković, S.V.: Robust model predictive control of constrained linear systems with bounded disturbances. Automatica 41(2), 219–224 (2005)
Müller, M.A., Grüne, L.: Economic model predictive control without terminal constraints for optimal periodic behavior. Automatica 70, 128–139 (2016)
Müller, M.A., Angeli, D., Allgöwer, F.: Economic model predictive control with self-tuning terminal cost. Eur. J. Control 19(5), 408–416 (2013)
Müller, M.A., Angeli, D., Allgöwer, F.: On the performance of economic model predictive control with self-tuning terminal cost. J. Process Control 24(8), 1179–1186 (2014)
Müller, M.A., Angeli, D., Allgöwer, F., Amrit, R., Rawlings, J.B.: Convergence in economic model predictive control with average constraints. Automatica 50(12), 3100–3111 (2014)
Müller, M.A., Angeli, D., Allgöwer, F.: Transient average constraints in economic model predictive control. Automatica 50(11), 2943–2950 (2014)
Müller, M.A., Grüne, L., Allgöwer, F.: On the role of dissipativity in economic model predictive control. In: 5th IFAC Conference on Nonlinear Model Predictive Control, Seville, pp. 110–116 (2015)
Müller, M.A., Angeli, D., Allgöwer, F.: On necessity and robustness of dissipativity in economic model predictive control. IEEE Trans. Autom. Control 60(6), 1671–1676 (2015)
Raković, S.V., Kouvaritakis, B., Findeisen, R., Cannon, M.: Homothetic tube model predictive control. Automatica 48, 1631–1638 (2012)
Rakovic, S.V., Kouvaritakis, B., Cannon, M., Panos, C., Findeisen, R.: Parameterized tube model predictive control. IEEE Trans. Autom. Control 57, 2746–2761 (2012)
Rawlings,J.B., Mayne, D.Q.: Model Predictive Control: Theory and Design. Nob Hill Publishing, LLC, Madison (2009)
Rawlings, J.B., Bonne, D., Jörgensen, J.B., Venkat, A.N., Jörgensen, S.B.: Unreachable setpoints in model predictive control. IEEE Trans. Autom. Control 53(9), 2209–2215 (2008)
Sopasakis, P., Herceg, D., Patrinos, P., Bemporad, A.: Stochastic economic model predictive control for Markovian switching systems. arXiv:1610.10014.
Zanon, M., Gros, S., Diehl, D.: A tracking MPC formulation that is locally equivalent to economic MPC. J. Process Control 45, 30–42 (2016)
Zanon, M., Grüne, L., Diehl, M.: Periodic optimal control, dissipativity and MPC. IEEE Trans. Autom. Control 62(6), 2943–2949 (2017)
Zaslavski, A.J.: Turnpike Properties in the Calculus of Variations and Optimal Control. Springer, New York (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Angeli, D., Müller, M.A. (2019). Economic Model Predictive Control: Some Design Tools and Analysis Techniques. In: Raković, S., Levine, W. (eds) Handbook of Model Predictive Control. Control Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-77489-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-77489-3_7
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-77488-6
Online ISBN: 978-3-319-77489-3
eBook Packages: EngineeringEngineering (R0)