Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach

K. Flaßkamp, S. Ober-Blöbaum, S. Peitz, in: O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation, Springer, Cham, 2020.

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Many dynamical systems possess symmetries, e.g. rotational and translational invariances of mechanical systems. These can be beneficially exploited in the design of numerical optimal control methods. We present a model predictive control scheme which is based on a library of precomputed motion primitives. The primitives are equivalence classes w.r.t. the symmetry of the optimal control problems. Trim primitives as relative equilibria w.r.t. this symmetry, play a crucial role in the algorithm. The approach is illustrated using an academic mobile robot example.
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Advances in Dynamics, Optimization and Computation
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Flaßkamp K, Ober-Blöbaum S, Peitz S. Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach. In: Junge O, Schütze O, Froyland G, Ober-Blöbaum S, Padberg-Gehle K, eds. Advances in Dynamics, Optimization and Computation. Cham: Springer; 2020. doi:10.1007/978-3-030-51264-4_9
Flaßkamp, K., Ober-Blöbaum, S., & Peitz, S. (2020). Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach. In O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, & K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation. Cham: Springer. https://doi.org/10.1007/978-3-030-51264-4_9
@inbook{Flaßkamp_Ober-Blöbaum_Peitz_2020, place={Cham}, title={Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach}, DOI={10.1007/978-3-030-51264-4_9}, booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer}, author={Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Peitz, Sebastian}, editor={Junge, Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle, KathrinEditors}, year={2020} }
Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Sebastian Peitz. “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach.” In Advances in Dynamics, Optimization and Computation, edited by Oliver Junge, Oliver Schütze, Gary Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle. Cham: Springer, 2020. https://doi.org/10.1007/978-3-030-51264-4_9.
K. Flaßkamp, S. Ober-Blöbaum, and S. Peitz, “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach,” in Advances in Dynamics, Optimization and Computation, O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, and K. Padberg-Gehle, Eds. Cham: Springer, 2020.
Flaßkamp, Kathrin, et al. “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach.” Advances in Dynamics, Optimization and Computation, edited by Oliver Junge et al., Springer, 2020, doi:10.1007/978-3-030-51264-4_9.

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