A characterization of irreducible infeasible subsystems in flow networks

Infeasible network flow problems with supplies and demands can be characterized via violated cut-inequalities of the classical Gale-Hoffman theorem. Written as a linear program, irreducible infeasible subsystems (IISs) provide a different means of infeasibility characterization. In this article, we answer a question left open in the literature by showing a one-to-one correspondence between IISs and Gale-Hoffman-inequalities in which one side of the cut has to be weakly connected. We also show that a single max-flow computation allows one to compute an IIS. Moreover, we prove that finding an IIS of minimal cardinality in this special case of flow networks is strongly NP-hard

Combinatorial Optimization

Combinatorial Optimization is a very active field that benefits from bringing together ideas from different areas, e.g., graph theory and combinatorics, matroids and submodularity, connectivity and network flows, approximation algorithms and mathematical programming, discrete and computational geometry, discrete and continuous problems, algebraic and geometric methods, and applications. We continued the long tradition of triannual Oberwolfach workshops, bringing together the best researchers from the above areas, discovering new connections, and establishing new and deepening existing international collaborations

Tight integration of cache, path and task-interference modeling for the analysis of hard real time systems

Traditional timing analysis for hard real-time systems is a two-step approach consisting of isolated per-task timing analysis and subsequent scheduling analysis which is conceptually entirely separated and is based only on execution time bounds of whole tasks. Today this model is outdated as it relies on technical assumptions that are not feasible on modern processor architectures any longer. The key limiting factor in this traditional model is the interfacing from micro-architectural analysis of individual tasks to scheduling analysis — in particular path analysis as the binding step between the two is a major obstacle. In this thesis, we contribute to traditional techniques that overcome this problem by means of by passing path analysis entirely, and propose a general path analysis and several derivatives to support improved interfacing. Specifically, we discuss, on the basis of a precise cache analysis, how existing metrics to bound cache-related preemption delay (CRPD) can be derived from cache representation without separate analyses, and suggest optimizations to further reduce analysis complexity and to increase accuracy. In addition, we propose two new estimation methods for CRPD based on the explicit elimination of infeasible task interference scenarios. The first one is conventional in that path analysis is ignored, the second one specifically relies on it. We formally define a general path analysis framework in accordance to the principles of program analysis — as opposed to most existing approaches that differ conceptually and therefore either increase complexity or entail inherent loss of information — and propose solutions for several problems specific to timing analysis in this context. First, we suggest new and efficient methods for loop identification. Based on this, we show how path analysis itself is applied to the traditional problem of per-task worst-case execution time bounds, define its generalization to sub-tasks, discuss several optimizations and present an efficient reference algorithm. We further propose analyses to solve related problems in this domain, such as the estimation of bounds on best-case execution times, latest execution times, maximum blocking times and execution frequencies. Finally, we then demonstrate the utility of this additional information in scheduling analysis by proposing a new CRPD bound

Hierarchical control for multi-domain coordination of vehicle energy systems with switched dynamics

This dissertation presents a hierarchical control framework for vehicle energy management. As a result of increasing electrification, legacy integration and control approaches for vehicle energy systems have become limiting factors of performance and cannot accommodate the requirements of next-generation systems. Addressing this requires control frameworks that coordinate dynamics across multiple physical domains and timescales, enabling transformative improvements in capability, efficiency, and safety. To capture multi-domain storage and exchange of energy, a graph-based dynamic modeling approach is proposed and experimentally validated. This modeling approach is then leveraged for model-based control, in which the complex task of energy management is decomposed into a hierarchical network of model predictive controllers that coordinate decision-making across subsystems, physical domains, and timescales. The controllers govern both continuous and switched dynamic behaviors, addressing the hybrid nature of modern vehicle energy systems. The proposed hierarchical control framework is evaluated in application to a hardware-in-the-loop electro-thermal testbed representative of a scaled aircraft energy system, where it achieves significantly improved capability, efficiency, and safety as compared to legacy control approaches. Next, the structural information embedded in the graph-based modeling approach is shown to facilitate analysis. Closed-loop stability of decentralized MPC frameworks is guaranteed by analyzing the passivity of switched nonlinear graph-based systems and augmenting their controllers with a local passivity-based constraint. Lastly, a hierarchical control formulation guaranteeing satisfaction of state and input constraints for a class of switched graph-based systems is presented. This formulation is demonstrated in application to thermal management using both simulation and experimental implementation

On static execution-time analysis

Proving timeliness is an integral part of the verification of safety-critical real-time systems. To this end, timing analysis computes upper bounds on the execution times of programs that execute on a given hardware platform. Modern hardware platforms commonly exhibit counter-intuitive timing behaviour: a locally slower execution can lead to a faster overall execution. Such behaviour challenges efficient timing analysis. In this work, we present and discuss a hardware design, the strictly in-order pipeline, that behaves monotonically w.r.t. the progress of a program's execution. Based on monotonicity, we prove the absence of the aforementioned counter-intuitive behaviour. At least since multi-core processors have emerged, timing analysis separates concerns by analysing different aspects of the system's timing behaviour individually. In this work, we validate the underlying assumption that a timing bound can be soundly composed from individual contributions. We show that even simple processors exhibit counter-intuitive behaviour - a locally slow execution can lead to an even slower overall execution - that impedes the soundness of the composition. We present the compositional base bound analysis that accounts for any such amplifying effects within its timing contribution. This enables a sound compositional analysis even for complex processors. Furthermore, we discuss hardware modifications that enable efficient compositional analyses.Echtzeitsysteme müssen unter allen Umständen beweisbar pünktlich arbeiten. Zum Beweis errechnet die Zeitanalyse obere Schranken der für die Ausführung von Programmen auf einer Hardware-Plattform benötigten Zeit. Moderne Hardware-Plattformen sind bekannt für unerwartetes Zeitverhalten bei dem eine lokale Verzögerung in einer global schnelleren Ausführung resultiert. Solches Zeitverhalten erschwert eine effiziente Analyse. Im Rahmen dieser Arbeit diskutieren wir das Design eines Prozessors mit eingeschränkter Fließbandverarbeitung (strictly in-order pipeline), der sich bzgl. des Fortschritts einer Programmausführung monoton verhält. Wir beweisen, dass Monotonie das oben genannte unerwartete Zeitverhalten verhindert. Spätestens seit dem Einsatz von Mehrkernprozessoren besteht die Zeitanalyse aus einzelnen Teilanalysen welche nur bestimmte Aspekte des Zeitverhaltens betrachten. Eine zentrale Annahme ist hierbei, dass sich die Teilergebnisse zu einer korrekten Zeitschranke zusammensetzen lassen. Im Rahmen dieser Arbeit zeigen wir, dass diese Annahme selbst für einfache Prozessoren ungültig ist, da eine lokale Verzögerung zu einer noch größeren globalen Verzögerung führen kann. Für bestehende Prozessoren entwickeln wir eine neuartige Teilanalyse, die solche verstärkenden Effekte berücksichtigt und somit eine korrekte Komposition von Teilergebnissen erlaubt. Für zukünftige Prozessoren beschreiben wir Modifikationen, die eine deutlich effizientere Zeitanalyse ermöglichen

Design optimisation of complex space systems under epistemic uncertainty

This thesis presents an innovative methodology for System Design Optimisation (SDO) through the framework of Model-Based System Engineering (MBSE) that bridges system modelling, Constrained Global Optimisation (CGO), Uncertainty Quantification (UQ), System Dynamics (SD) and other mathematical tools for the design of Complex Engineered and Engineering Systems (CEdgSs) under epistemic uncertainty. The problem under analysis has analogies with what is nowadays studied as Generative Design under Uncertainty. The method is finally applied to the design of Space Systems which are Complex Engineered Systems (CEdSs) composed of multiple interconnected sub-systems. A critical aspect in the design of Space Systems is the uncertainty involved. Much of the uncertainty is epistemic and is here modelled with Dempster Shafer Theory (DST). Designing space systems is a complex task that involves the coordination of different disciplines and problems. The thesis then proposes a set of building blocks, that is a toolbox of methodologies for the solution of problems which are of interest also if considered independently. It proposes then a holistic framework that couples these building blocks to form a SDO procedure. With regard to the building blocks, the thesis includes a network-based modelling procedure for CEdSs and a generalisation for CEdgSs where the system and the whole design process are both taken into account. Then, it presents a constraint min-max solver as an algorithmic procedures for the solution of the general Optimisation Under Uncertainty (OUU) problem. An extension of the method for the Multi-Objective Problems (MOP) is also proposed in Appendix as a minor result. A side contribution for the optimisation part refers to the extension of the global optimiser Multi Population Adaptive Inflationary Differential Evolution Algorithm (MP-AIDEA) with the introduction of constraint handling and multiple objective functions. The Constraint Multi-Objective Problem (CMOP) solver is however a preliminary result and it is reported in Appendix. Furthermore, the thesis proposes a decomposition methodology for the computational reduction of UQ with DST. As a partial contribution, a second approach based on a Binary Tree decomposition is also reported in Appendix. With regard to the holistic approach, instead, the thesis gives a new dentition and proposes a framework for system network robustness and for system network resilience. It finally presents the framework for the optimisation of the whole design process through the use of a multi-layer network model.This thesis presents an innovative methodology for System Design Optimisation (SDO) through the framework of Model-Based System Engineering (MBSE) that bridges system modelling, Constrained Global Optimisation (CGO), Uncertainty Quantification (UQ), System Dynamics (SD) and other mathematical tools for the design of Complex Engineered and Engineering Systems (CEdgSs) under epistemic uncertainty. The problem under analysis has analogies with what is nowadays studied as Generative Design under Uncertainty. The method is finally applied to the design of Space Systems which are Complex Engineered Systems (CEdSs) composed of multiple interconnected sub-systems. A critical aspect in the design of Space Systems is the uncertainty involved. Much of the uncertainty is epistemic and is here modelled with Dempster Shafer Theory (DST). Designing space systems is a complex task that involves the coordination of different disciplines and problems. The thesis then proposes a set of building blocks, that is a toolbox of methodologies for the solution of problems which are of interest also if considered independently. It proposes then a holistic framework that couples these building blocks to form a SDO procedure. With regard to the building blocks, the thesis includes a network-based modelling procedure for CEdSs and a generalisation for CEdgSs where the system and the whole design process are both taken into account. Then, it presents a constraint min-max solver as an algorithmic procedures for the solution of the general Optimisation Under Uncertainty (OUU) problem. An extension of the method for the Multi-Objective Problems (MOP) is also proposed in Appendix as a minor result. A side contribution for the optimisation part refers to the extension of the global optimiser Multi Population Adaptive Inflationary Differential Evolution Algorithm (MP-AIDEA) with the introduction of constraint handling and multiple objective functions. The Constraint Multi-Objective Problem (CMOP) solver is however a preliminary result and it is reported in Appendix. Furthermore, the thesis proposes a decomposition methodology for the computational reduction of UQ with DST. As a partial contribution, a second approach based on a Binary Tree decomposition is also reported in Appendix. With regard to the holistic approach, instead, the thesis gives a new dentition and proposes a framework for system network robustness and for system network resilience. It finally presents the framework for the optimisation of the whole design process through the use of a multi-layer network model