@article{16294, 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 Since the standard multi-parametric programming approach is no longer valid in this situation, we instead use interpolation between different entries of the library.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.}}, author = {{Ober-Blöbaum, Sina and Peitz, Sebastian}}, journal = {{International Journal of Robust and Nonlinear Control}}, pages = {{380--403}}, title = {{{Explicit multiobjective model predictive control for nonlinear systems with symmetries}}}, doi = {{10.1002/rnc.5281}}, volume = {{31(2)}}, year = {{2021}}, } @article{16297, abstract = {{In real-world problems, uncertainties (e.g., errors in the measurement, precision errors) often lead to poor performance of numerical algorithms when not explicitly taken into account. This is also the case for control problems, where optimal solutions can degrade in quality or even become infeasible. Thus, there is the need to design methods that can handle uncertainty. In this work, we consider nonlinear multi-objective optimal control problems with uncertainty on the initial conditions, and in particular their incorporation into a feedback loop via model predictive control (MPC). In multi-objective optimal control, an optimal compromise between multiple conflicting criteria has to be found. For such problems, not much has been reported in terms of uncertainties. To address this problem class, we design an offline/online framework to compute an approximation of efficient control strategies. This approach is closely related to explicit MPC for nonlinear systems, where the potentially expensive optimization problem is solved in an offline phase in order to enable fast solutions in the online phase. In order to reduce the numerical cost of the offline phase, we exploit symmetries in the control problems. Furthermore, in order to ensure optimality of the solutions, we include an additional online optimization step, which is considerably cheaper than the original multi-objective optimization problem. We test our framework on a car maneuvering problem where safety and speed are the objectives. The multi-objective framework allows for online adaptations of the desired objective. Alternatively, an automatic scalarizing procedure yields very efficient feedback controls. Our results show that the method is capable of designing driving strategies that deal better with uncertainties in the initial conditions, which translates into potentially safer and faster driving strategies.}}, author = {{Hernández Castellanos, Carlos Ignacio and Ober-Blöbaum, Sina and Peitz, Sebastian}}, journal = {{International Journal of Robust and Nonlinear Control}}, pages = {{7593--7618}}, title = {{{Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty}}}, doi = {{10.1002/rnc.5197}}, volume = {{30(17)}}, year = {{2020}}, } @inbook{29413, author = {{Flaßkamp, K. and Ober-Blöbaum, Sina and Peitz, S. }}, booktitle = {{Advances in Dynamics, Optimization and Computation}}, editor = {{Junge, Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}}, pages = {{209--237}}, publisher = {{Springer International Publishing}}, title = {{{Symmetry in optimal control: A multiobjective model predictive control approach}}}, year = {{2020}}, } @article{19993, author = {{Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Worthmann, Karl}}, journal = {{MCSS}}, pages = {{455--485}}, title = {{{Symmetry and motion primitives in model predictive control}}}, volume = {{31}}, year = {{2019}}, } @article{8756, abstract = {{We present a new algorithm for model predictive control of non-linear systems with respect to multiple, conflicting objectives. The idea is to provide a possibility to change the objective in real-time, e.g. as a reaction to changes in the environment or the system state itself. The algorithm utilises elements from various well-established concepts, namely multiobjective optimal control, economic as well as explicit model predictive control and motion planning with motion primitives. In order to realise real-time applicability, we split the computation into an online and an offline phase and we utilise symmetries in the open-loop optimal control problem to reduce the number of multiobjective optimal control problems that need to be solved in the offline phase. The results are illustrated using the example of an electric vehicle where the longitudinal dynamics are controlled with respect to the concurrent objectives arrival time and energy consumption.}}, author = {{Peitz, Sebastian and Schäfer, Kai and Ober-Blöbaum, Sina and Eckstein, Julian and Köhler, Ulrich and Dellnitz, Michael}}, issn = {{2405-8963}}, journal = {{Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC)}}, number = {{1}}, pages = {{8674--8679}}, title = {{{A multiobjective MPC approach for autonomously driven electric vehicles}}}, doi = {{10.1016/j.ifacol.2017.08.1526}}, volume = {{50}}, year = {{2017}}, }