Explicit multiobjective model predictive control for nonlinear systems with symmetries

S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 31(2) (2021) 380–403.

Journal Article | English
Abstract
Model predictive control is a prominent approach to construct a feedback control loop for dynamical systems. Due to real-time constraints, the major challenge in MPC is to solve model-based optimal control problems in a very short amount of time. For linear-quadratic problems, Bemporad et al. have proposed an explicit formulation where the underlying optimization problems are solved a priori in an offline phase. In this article, we present an extension of this concept in two significant ways. We consider nonlinear problems and - more importantly - problems with multiple conflicting objective functions. In the offline phase, we build a library of Pareto optimal solutions from which we then obtain a valid compromise solution in the online phase according to a decision maker's preference. Since the standard multi-parametric programming approach is no longer valid in this situation, we instead use interpolation between different entries of the library. To reduce the number of problems that have to be solved in the offline phase, we exploit symmetries in the dynamical system and the corresponding multiobjective optimal control problem. The results are verified using two different examples from autonomous driving.
Publishing Year
Journal Title
International Journal of Robust and Nonlinear Control
Volume
31(2)
Page
380-403
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Ober-Blöbaum S, Peitz S. Explicit multiobjective model predictive control for nonlinear systems  with symmetries. International Journal of Robust and Nonlinear Control. 2021;31(2):380-403. doi:10.1002/rnc.5281
Ober-Blöbaum, S., & Peitz, S. (2021). Explicit multiobjective model predictive control for nonlinear systems  with symmetries. International Journal of Robust and Nonlinear Control, 31(2), 380–403. https://doi.org/10.1002/rnc.5281
@article{Ober-Blöbaum_Peitz_2021, title={Explicit multiobjective model predictive control for nonlinear systems  with symmetries}, volume={31(2)}, DOI={10.1002/rnc.5281}, journal={International Journal of Robust and Nonlinear Control}, author={Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2021}, pages={380–403} }
Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems  with Symmetries.” International Journal of Robust and Nonlinear Control 31(2) (2021): 380–403. https://doi.org/10.1002/rnc.5281.
S. Ober-Blöbaum and S. Peitz, “Explicit multiobjective model predictive control for nonlinear systems  with symmetries,” International Journal of Robust and Nonlinear Control, vol. 31(2), pp. 380–403, 2021, doi: 10.1002/rnc.5281.
Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems  with Symmetries.” International Journal of Robust and Nonlinear Control, vol. 31(2), 2021, pp. 380–403, doi:10.1002/rnc.5281.
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