In real-world problems, uncertainties (eg, errors in the measurement, precision errors, among others) often lead to poor performance of numerical algorithms when not explicitly taken into account. This is also the case for control problems, where in the case of uncertainties, optimal solutions can degrade in quality or they can even become unfeasible. Thus, there is the need to design methods that can handle uncertainty. In this work, we consider nonlinear multiobjective optimal control problems with uncertainty on the initial conditions, and in particular their incorporation into a feedback loop via model predictive control. 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. In order to reduce the numerical cost of the offline phase—which grows exponentially with the parameter dimension—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 multiobjective optimization problem. We test our framework on a car maneuvering problem where safety and speed are the objectives. The multiobjective framework allows for online adaptations of the desired objective. 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.
Hernández Castellanos, CI, Ober-Blöbaum, S, Peitz, S. Explicit multiobjective model predictive control for nonlinear systems under uncertainty. Int J Robust Nonlinear Control. 2020; 30: 7593– 7618. https://doi.org/10.1002/rnc.5197