TY - INPR A1 - Grapentin, Andreas A1 - Heidler, Kirstin A1 - Korsch, Dimitri A1 - Kumar Sah, Rakesh A1 - Kunzmann, Nicco A1 - Henning, Johannes A1 - Mattis, Toni A1 - Rein, Patrick A1 - Seckler, Eric A1 - Groneberg, Björn A1 - Zimmermann, Florian ED - Hentschel, Uwe ED - Richter, Daniel ED - Polze, Andreas T1 - Embedded operating system projects N2 - In today’s life, embedded systems are ubiquitous. But they differ from traditional desktop systems in many aspects – these include predictable timing behavior (real-time), the management of scarce resources (memory, network), reliable communication protocols, energy management, special purpose user-interfaces (headless operation), system configuration, programming languages (to support software/hardware co-design), and modeling techniques. Within this technical report, authors present results from the lecture “Operating Systems for Embedded Computing” that has been offered by the “Operating Systems and Middleware” group at HPI in Winter term 2013/14. Focus of the lecture and accompanying projects was on principles of real-time computing. Students had the chance to gather practical experience with a number of different OSes and applications and present experiences with near-hardware programming. Projects address the entire spectrum, from bare-metal programming to harnessing a real-time OS to exercising the full software/hardware co-design cycle. Three outstanding projects are at the heart of this technical report. Project 1 focuses on the development of a bare-metal operating system for LEGO Mindstorms EV3. While still a toy, it comes with a powerful ARM processor, 64 MB of main memory, standard interfaces, such as Bluetooth and network protocol stacks. EV3 runs a version of 1 1 Introduction Linux. Sources are available from Lego’s web site. However, many devices and their driver software are proprietary and not well documented. Developing a new, bare-metal OS for the EV3 requires an understanding of the EV3 boot process. Since no standard input/output devices are available, initial debugging steps are tedious. After managing these initial steps, the project was able to adapt device drivers for a few Lego devices to an extent that a demonstrator (the Segway application) could be successfully run on the new OS. Project 2 looks at the EV3 from a different angle. The EV3 is running a pretty decent version of Linux- in principle, the RT_PREEMPT patch can turn any Linux system into a real-time OS by modifying the behavior of a number of synchronization constructs at the heart of the OS. Priority inversion is a problem that is solved by protocols such as priority inheritance or priority ceiling. Real-time OSes implement at least one of the protocols. The central idea of the project was the comparison of non-real-time and real-time variants of Linux on the EV3 hardware. A task set that showed effects of priority inversion on standard EV3 Linux would operate flawlessly on the Linux version with the RT_PREEMPT-patch applied. If only patching Lego’s version of Linux was that easy... Project 3 takes the notion of real-time computing more seriously. The application scenario was centered around our Carrera Digital 132 racetrack. Obtaining position information from the track, controlling individual cars, detecting and modifying the Carrera Digital protocol required design and implementation of custom controller hardware. What to implement in hardware, firmware, and what to implement in application software – this was the central question addressed by the project. N2 - Heutzutage sind eingebettete Systeme allgegenwärtig. Allerdings unterscheiden sie sich in vielen Aspekten von traditionellen Desktop-System – dazu gehören vorhersagbares Zeitverhalten („Echtzeit“), die Verwaltung von knappen Ressourcen (Speicher, Netzwerk), zuverlässige Kommunikationsprotokolle, Energiemanagement, spezialisierte Benutzungsschnittstellen („headless“), Systemkonfiguration, Programmiersprachen (zur Unterstützung von Software-Hardware-Co-Design) und Modellierungstechniken. In diesem technischen Bericht präsentieren die Autoren Ergebnisse aus der Vorlesung „Betriebssysteme für Embedded Computing“, die von der Fachgruppe „Betriebssysteme und Middleware“ am HPI in Wintersemester 2013/14 angeboten wurde. Schwerpunkte der Vorlesung und der begleitenden Projekte waren Prinzipien von Echtzeit-Computing. Die Studenten hatten die Möglichkeit, praktische Erfahrungen mit einer Reihe von verschiedenen Betriebssystemen und Anwendungen zu sammeln und präsentieren ihre Erfahrungen mit hardwarenaher Programmierung. Die Projekte adressieren das gesamte Spektrum von der Bare-Metal-Programmierung über die Nutzung eines Echtzeitbetriebssystem bis zur Anwendung des vollen Software-Hardware-Co-Design-Zyklus‘. Drei herausragende Projekte sind das Herzstück dieses technischen Berichts. Projekt 1 konzentriert sich auf die Entwicklung eines Bare-Metal-Betriebssystems für LEGO Mindstorms EV3. Obwohl es ein Spielzeug ist, kommt es mit einem leistungsstarken ARM-Prozessor, 64 MB Hauptspeicher und Standardschnittstellen wie Bluetooth und einem Netzwerkprotokollstapel. Auf dem EV3 läuft spezielle Linux-Version – die Quellen sind auf der Lego-Website verfügbar. Allerdings sind viele Geräte und deren Treiber-Software urheberrechtlich geschützt und nicht gut dokumentiert. Die Entwicklung eines neuen Bare-Metal-Betriebssystem für den EV3 erfordert ein Verständnis des EV3-Bootvorgangs. Da keine Standard-Ein-/Ausgabegeräte zur Verfügung stehen, sind anfängliche Debug-Schritte mühsam. Nach dem Absolvieren dieser ersten Schritte war das Projekt in der Lage, Gerätetreiber für einige Lego-Geräte anzupassen um einen Demonstrator (die Segway-Anwendung) erfolgreich auf dem neuen Betriebssystem laufen zu lassen. Projekt 2 befasst sich mit dem EV3 aus einer anderen Perspektive. Der EV3 wird mit einer üblichen EV3 Linux-Version betrieben – im Prinzip kann der RT_PREEMPT-Patch jedes Linux-System in ein Echtzeitbetriebssystem verwandeln, indem er das Verhalten einer Anzahl von Synchronisationskonstrukten im Herzen des Betriebssystems anpasst. Priority Inversion ist ein Problem, das durch Protokolle wie Prioritätsvererbung oder Priority Ceiling gelöst wird. Heutige Echtzeit-Betriebssysteme implementieren mindestens eines dieser Protokolle. Die zentrale Idee des Projekts war der Vergleich der Nicht-Echtzeit und Echtzeit-Varianten von Linux auf der EV3-Hardware. Ein Task-Set, das die Auswirkungen der Prioritätsumkehr auf Standard-EV3 Linux zeigt, würde ohne Probleme auf der Linux-Version mit dem RT_PREEMPT-Patch betrieben werden können. Wenn nur das Patchen Lego-Version von Linux war so einfach wäre... Projekt 3 nimmt den Begriff des Echtzeit-Computing ernst. Das Anwendungsszenario wurde um unsere Carrera Digital 132 Bahn angeordnet. Das Sammeln von Positionsinformationen, die Steuerung einzelner Fahrzeuge, die Erfassung und Änderung des Carrera Digital-Protokolls erfordert die Konzeption und Umsetzung von spezialisierter Controller-Hardware. Die zentrale Fragestellung dieses Projekts war, was in Hardware, in Firmware oder in der Anwendungssoftware zu implementieren ist. T3 - Technische Berichte des Hasso-Plattner-Instituts für Digital Engineering an der Universität Potsdam - 90 KW - Echtzeit KW - eingebettete Systeme KW - Betriebssysteme KW - Erfahrungsbericht KW - LEGO Mindstorms EV3 KW - RT_PREEMT-Patch KW - Carrera Digital D132 KW - real-time KW - embedded systems KW - operating systems KW - experience report KW - LEGO Mindstorms EV3 KW - RT_PREEMT patch KW - Carrera Digital D132 Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-69154 SN - 978-3-86956-296-4 SN - 1613-5652 SN - 2191-1665 IS - 90 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Fedchenko, Dmitry A1 - Tarkhanov, Nikolai Nikolaevich T1 - An index formula for Toeplitz operators N2 - We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first order partial differential equations in a bounded domain of Euclidean space with infinitely differentiable boundary. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3(2014)12 KW - Toeplitz operators KW - Fredholm property KW - index Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72499 SN - 2193-6943 VL - 3 IS - 12 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Dereudre, David A1 - Roelly, Sylvie T1 - Path-dependent infinite-dimensional SDE with non-regular drift : an existence result N2 - We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither small or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy. Our result strongly improves the previous ones obtained for free dynamics with a small perturbative drift. The originality of our method leads in the use of the specific entropy as a tightness tool and on a description of such stochastic differential equation as solution of a variational problem on the path space. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3(2014)11 KW - Infinite-dimensional SDE KW - non-Markov drift KW - non-regular drift KW - variational principle KW - specific entropy Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72084 SN - 2193-6943 VL - 3 IS - 11 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Makhmudov, Olimdjan A1 - Tarkhanov, Nikolai Nikolaevich T1 - The first mixed problem for the nonstationary Lamé system N2 - We find an adequate interpretation of the Lamé operator within the framework of elliptic complexes and study the first mixed problem for the nonstationary Lamé system. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3(2014)10 KW - Lamé system KW - evolution equation KW - first boundary value problem Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-71923 SN - 2193-6943 VL - 3 IS - 10 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Conforti, Giovanni A1 - Léonard, Christian A1 - Murr, Rüdiger A1 - Roelly, Sylvie T1 - Bridges of Markov counting processes : reciprocal classes and duality formulas N2 - Processes having the same bridges are said to belong to the same reciprocal class. In this article we analyze reciprocal classes of Markov counting processes by identifying their reciprocal invariants and we characterize them as the set of counting processes satisfying some duality formula. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 9 KW - counting process KW - bridge KW - reciprocal class KW - duality formula Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-71855 SN - 2193-6943 VL - 3 IS - 9 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Flandoli, Franco A1 - Högele, Michael T1 - A solution selection problem with small stable perturbations N2 - The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is a general alpha-stable process. It is proved that extremal solutions are selected and the probability of selection is computed. Detailed analysis of the characteristic function of an exit time form on the half-line is performed, with a suitable decomposition in small and large jumps adapted to the singular drift. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 8 KW - stochastic differential equations KW - singular drifts KW - zero-noise limit KW - Peano phenomena KW - non-uniqueness Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-71205 SN - 2193-6943 VL - 3 IS - 8 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Pornsawad, Pornsarp A1 - Böckmann, Christine T1 - Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems N2 - This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 7 KW - ill-posed problems KW - Runge-Kutta methods KW - regularization methods KW - Hölder-type source condition KW - stopping rules Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70834 SN - 2193-6943 VL - 3 IS - 7 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Conforti, Giovanni A1 - Dai Pra, Paolo A1 - Roelly, Sylvie T1 - Reciprocal class of jump processes N2 - Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of compound Poisson processes whose jumps belong to a finite set A in R^d. We propose a characterization of the reciprocal class as the unique set of probability measures on which a family of time and space transformations induces the same density, expressed in terms of the reciprocal invariants. The geometry of A plays a crucial role in the design of the transformations, and we use tools from discrete geometry to obtain an optimal characterization. We deduce explicit conditions for two Markov jump processes to belong to the same class. Finally, we provide a natural interpretation of the invariants as short-time asymptotics for the probability that the reference process makes a cycle around its current state. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 6 KW - reciprocal processes KW - stochastic bridges KW - jump processes KW - compound Poisson processes Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70776 SN - 2193-6943 VL - 3 IS - 6 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Högele, Michael A1 - Pavlyukevich, Ilya T1 - Metastability of Morse-Smale dynamical systems perturbed by heavy-tailed Lévy type noise N2 - We consider a general class of finite dimensional deterministic dynamical systems with finitely many local attractors each of which supports a unique ergodic probability measure, which includes in particular the class of Morse–Smale systems in any finite dimension. The dynamical system is perturbed by a multiplicative non-Gaussian heavytailed Lévy type noise of small intensity ε > 0. Specifically we consider perturbations leading to a Itô, Stratonovich and canonical (Marcus) stochastic differential equation. The respective asymptotic first exit time and location problem from each of the domains of attractions in case of inward pointing vector fields in the limit of ε-> 0 has been investigated by the authors. We extend these results to domains with characteristic boundaries and show that the perturbed system exhibits a metastable behavior in the sense that there exits a unique ε-dependent time scale on which the random system converges to a continuous time Markov chain switching between the invariant measures. As examples we consider α-stable perturbations of the Duffing equation and a chemical system exhibiting a birhythmic behavior. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 5 KW - hyperbolic dynamical system KW - Morse-Smale property KW - stable limit cycle KW - small noise asymptotic KW - multiplicative noise Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70639 SN - 2193-6943 VL - 3 IS - 5 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Sultanov, Oskar A1 - Kalyakin, Leonid A1 - Tarkhanov, Nikolai Nikolaevich T1 - Elliptic perturbations of dynamical systems with a proper node N2 - The paper is devoted to asymptotic analysis of the Dirichlet problem for a second order partial differential equation containing a small parameter multiplying the highest order derivatives. It corresponds to a small perturbation of a dynamical system having a stationary solution in the domain. We focus on the case where the trajectories of the system go into the domain and the stationary solution is a proper node. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 4 KW - dynamical system KW - singular perturbation KW - asymptotic methods Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70460 SN - 2193-6943 VL - 3 IS - 4 PB - Universitätsverlag Potsdam CY - Potsdam ER -