(705g) A Multiparametric Programming-Based Approach for Multi-Objective Model Predictive Control

Optimal control problems can involve multiple, often conflicting objectives, which can consist of economic, safety or tracking performance criteria. Different approaches have been proposed in the literature for the development of multi-objective model predictive controllers (MOMPC), including the ε-constraint approach [1], the weight sum approach [2], objective prioritization [3] and by considering the switch between different cost functionals [4,5]. Furthermore, multiparametric programming has been utilized for the solution of MOMPC problems [6] and for the calculation of the optimal Pareto front for multi-objective optimization problems explicitly [7]. However, to our knowledge no approaches have been proposed in the literature for the exact explicit derivation of the Pareto front of MOMPC with more than one quadratic objective function.

This work presents a multiparametric-based approach for the derivation of the explicit Pareto front of MOMPC. In this context, we assume that there exist two or (possibly) more conflicting control objectives described by linear or convex quadratic functions and linear or quadratic constraints. The MOMPC problem is reformulated into a multiparametic Quadratically Constrained Quadratic Programming problem (mpQCQP), which can then be exactly solved using the algorithm proposed in [8]. As a result, we generate the Pareto optimal solutions of the optimal control problem as an explicit function of the system’s states, while the decision-maker is able to select the preferred control law, which has been calculated a priori. The proposed strategy is highlighted on a simple CSTR case study.

References:

[1] Zavala, V. M. A multiobjective optimization perspective on the stability of economic MPC. IFAC-PapersOnLine, 2015, 48(8), 974-980.

[2] Fairweather, M., Vallerio, M., Logist, F., Impe, J.F. Towards enhanced weight selection for (N)MPC via multi-objective optimization. Proceedings of the 22nd European Symposium on Computer Aided Process Engineering, 2012.

[3] He, D., Wang, L., & Sun, J. On stability of multiobjective NMPC with objective prioritization. Automatica, 2015, 57, 189-198.

[4] Magni, L., Scattolini, R., & Tanelli, M. Switched model predictive control for performance enhancement. International Journal of Control, 2008, 81(12), 1859-1869.

[5] Müller, M. A., & Allgöwer, F. Improving performance in model predictive control: Switching cost functionals under average dwell-time. Automatica, 2012, 48(2), 402-409.

[6] Bemporad, A.; Munoz de la Pena, D. Multiobjective model predictive control. Automatica, 2009, 45, 2823-2830.

[7] Oberdieck, R.; Pistikopoulos, E. N. Multi-objective optimization with convex quadratic cost functions: A multi-parametric programming approach. Computers & Chemical Engineering, 2016, 85, 36-39.

[8] Diangelakis, N. A.; Pappas, I. S.; Pistikopoulos, E. N. On multiparametric/explicit NMPC for Quadratically Constrained Problems. 6th IFAC Conference on Nonlinear Model Predictive Control; Elsevier, 2018, 400-405.