arXiv subjects

Moritz Heinlein

Publications and source records attributed to Moritz Heinlein.

4 recordsLinked to original sources

arXiv2026

Large-scale workflow placement in serverless computing using integer nonlinear programming

Serverless edge computing has become a powerful cloud framework that enables the execution of large workflows without the need for the user to manage the underlying servers and edge devices. In this work, we address the challenge of deploying these workflows on a large number of different existing servers and edge devices such that monetary costs for the users and workflow evaluation times are minimized. To this end, the workflow and cloud node attributes are modeled in a mathematical framework. As a result, we present a novel model of the optimal placement problem as a nonlinear integer program. To solve both the issues of scaling towards a larger number of cloud/edge nodes as well as decomposed knowledge of node attributes, we propose a novel decomposition strategy. In a case study, we show the beneficial scaling properties of the decomposition approach and a mean improvement of 10% against a simple deployment heuristic.

cs.DC↗

arXiv2025

Ellipsoidal partitions for improved multi-stage robust model predictive control

Ellipsoidal tube-based model predictive control methods effectively account for the propagation of the reachable set, typically employing linear feedback policies. In contrast, scenario-based approaches offer more flexibility in the feedback structure by considering different control actions for different branches of a scenario tree. However, they face challenges in ensuring rigorous guarantees. This work aims to integrate the strengths of both methodologies by enhancing ellipsoidal tube-based MPC with a scenario tree formulation. The uncertainty ellipsoids are partitioned by halfspaces such that each partitioned set can be controlled independently. The proposed ellipsoidal multi-stage approach is demonstrated in a human-robot system, highlighting its advantages in handling uncertainty while maintaining computational tractability.

eess.SY↗

arXiv2024

On the risk levels of distributionally robust chance constrained problems

In this paper, we discuss the utilization of perturbed risk levels (PRLs) for the solution of chance-constrained problems via sampling-based approaches. PRLs allow the consideration of distributional ambiguity by rescaling the risk level of the nominal chance constraint. Explicit expressions of the PRL exist for some discrepancy-based ambiguity sets. We propose a discrepancy functional not included in previous comparisons of different PRLs based on the likelihood ratio, which we term ,,relative variation distance" (RVD). If the ambiguity set can be described by the RVD, the rescaling of the risk level with the PRL is in contrast to other discrepancy functionals possible even for very low risk levels. We derive distributionally robust one- and two-level guarantees for the solution of chance-constrained problems with randomized methods. We demonstrate the viability of the derived guarantees for a randomized MPC under distributional ambiguity.

math.OC↗

arXiv2024

Robust Model Predictive Control Exploiting Monotonicity Properties

Robust model predictive control algorithms are essential for addressing unavoidable errors due to the uncertainty in predicting real-world systems. However, the formulation of such algorithms typically results in a trade-off between conservatism and computational complexity. Monotone systems facilitate the efficient computation of reachable sets and thus the straightforward formulation of a robust model predictive control approach optimizing over open-loop predictions. We present an approach based on the division of reachable sets to incorporate feedback in the predictions, resulting in less conservative strategies. The concept of mixed-monotonicity enables an extension of our methodology to non-monotone systems. The potential of the proposed approaches is demonstrated through a nonlinear high-dimensional chemical tank reactor cascade case study.

eess.SY↗