Multi-Objective Model Predictive Control

Abdelillah Otmane Cherif, Dmitry Balandin


Multi-objective optimization design recently has attracted great attention of the researchers in solving engineering problems that have conflicting objectives.
Although several control specifications which are often irreconcilable can be considered in the single objective function, choosing the appropriate weighting functions are another challenge faced by control designers. In this paper, a new Model Predictive Control scheme based on the multi-objective optimization is proposed in which at each sampling time, the MPC control action is chosen automatically among the set of Pareto optimal solutions based on the Nash Bargaining Solution from Game Theory. This method is independent of the system type. It is applied on the nonlinear systems along with TP transformation to design multi-objective MPC. As a result, LMIs and convex optimization techniques can be utilized to provide an on-line solution for the multi-objective MPC design. The proposed method is executed on a complex nonlinear system.  It is shown through the examples that the proposed method can execute approvingly compared to other methods in the literature of the control systems.

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Hernández Castellanos CI, Ober-Blöbaum S, Peitz S. Explicit multiobjective modelpredictive control for nonlinear systems under uncertainty. Int J Robust Nonlinear Control. 2020; 30:7593–7618.

OTMANE CHERIF Abdelillah; BALANDIN Dmitry Vladimirovich. Robust Model Predictive Control Design. International scientific journal «Modern Information Technologies and IT-Education», [S.l.], v. 17, n. 4, dec. 2021. ISSN 2411-1473. Available at:

Y. Y. Baranyi, P. and P. V´arlaki, Tensor product model transformation in polytopic model–based control. Taylor & Francis Group, LLC, 2014.

M. V. Kothare, V. Balakrishnan, and M. Morari, Robust constrained model predictive control using linear matrix inequalities, Automatica, vol. 32, no. 10, pp. 1361–1379, 1996.

F. A. Cuzzola, J. C. Geromel, and M. Morari, An improved approach for constrained robust model predictive control, Automatica, vol. 38, no. 7, pp. 1183 – 1189, 2002.

S. Yu, C. Bohm, H. Chen, and F. Allgower, Stabilizing model predictive control for lpv systems subject to constraints with parameter-dependent control law, in American Control Conference, 2009. ACC ’09., June 2009, pp. 3118–3123.

J. Engwerda, LQ Dynamic Optimization and Differential Games. Wiley, 2005.

A. Bemporad and D. M. de la Pea, Multiobjective model predictive control, Automatica, vol. 45, no. 12, pp. 2823 – 2830, 2009.

K. Binmore, A. Rubinstein, and A. Wolinsky, The nash bargaining solution in economic modelling, The RAND Journal of Economics, pp. 176–188, 1986.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, A fast and elitist multiobjective genetic algorithm: Nsga-ii, IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182 –197, apr 2002.

P. Baranyi, Tp model transformation as a way to lmi-based controller design, Industrial Electronics, IEEE Transactions on, vol. 51, no. 2, pp. 387–400, 2004.

L. Wang, Model predictive control system design and implementation using MATLAB R . Springer Science & Business Media, 2009.

J. J. V. Garca, V. G. Garay, E. I. Gordo, F. A. Fano, and M. L. Sukia, Intelligent multi-objective nonlinear model predictive control (imo-nmpc): Towards the on-line optimization of highly complex control problems, Expert Systems with Applications, vol. 39, no. 7, pp. 6527 – 6540, 2012.

Groetzner, P., Werner, R., 2021. Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach. Eur. J. Oper. Res . doi:

H. A. Hindi, B. Hassibi and S. P. Boyd, Multiobjective optimal control via finite dimensional q-parametrization and linear matrix inequalities, American Control Conference 1998. Proceedings of the 1998, vol. 5, pp. 3244-3249, 1998.

A. Otmane cherif, Shimmy vibration control using robust model predictive control, Int-Journal of Open Information Technologies, Vol 10, No 4, pp 24-30, 2022


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