07 Fakultät Konstruktions-, Produktions- und Fahrzeugtechnik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/8
Browse
20 results
Search Results
Item Open Access Analysis and design of MPC frameworks for dynamic operation of nonlinear constrained systems(2021) Köhler, Johannes; Allgöwer, Frank (Prof. Dr.-Ing.)Item Open Access Understanding the mechanisms of robustness in intracellular protein signalling cascades and gene expression(2018) Paul, Debdas; Radde, Nicole (Prof. Dr. rer. nat.)We seek to understand the structural as well as the mechanistic basis of robustness in intracellular protein signalling cascades and in transcriptional regulation of gene expression. For protein signalling cascades, we employ a comparison based study involving a single, a double and a cascade of two double phosphorylation-dephosphorylation (PD) cycles. Using deterministic modelling approaches based on ordinary differential equations (ODE), we observe that the cascade of two double PD cycles exhibits robust output behaviour compared to that of a single and a double PD cycle upon constant as well as time- varying input perturbations. Furthermore, a system theoretic analysis reveals that the protein phosphorylation cascades act as an efficient low-pass filter that attenuates the noise mimicked as high-frequency input signals. Afterwards, we extend the study for a stochastic environment. Simulation results based on the stochastic simulation algorithm (SSA) reveal a novel phenomenon called dynamic sequestration that plays an ambivalent role as an intrinsic noise filter. Overall, the analysis indicates that complexity can be one of the basic principles of robust biological designs such as intracellular protein signalling cascades. A major function of intracellular signalling cascades is to transmit the extracellular signal to the nucleus to initiate the process of gene expression. Gene expression is an intrinsically stochastic process that results into cell-to-cell variability in protein and messenger RNA (mRNA) levels, often termed as the expression noise. In spite of such noise, how cells achieve robustness is therefore a fundamental biological problem. We conclude the thesis by introducing a rule-based modelling approach based on the Kappa (κ) platform with the goal to understand the underlying mechanisms that ensure robust cellular functioning during gene expression. In particular, we introduce a gene expression model that keeps the process of transcription and excludes the process of translation. Therefore, we quantify the expression noise using mRNA which is the end product of transcription. Besides, the motivation behind adopting a rule-based modelling approach is that unlike the ODE-based approach, the former subsumes the combinatorial complexity arises due to various binding configurations of transcription factors (TF) for regulation of gene expression and offers a compact graphical representation of the same. Afterwards, the representation is transformed into an equivalent set of executable κ rules that are simulated using the SSA to obtain distributions of mRNA copy numbers corresponding to different regulatory mechanisms.Item Open Access A systems science view on cell death signalling(2007) Eißing, Thomas; Allgöwer, Frank (Prof. Dr.-Ing.)This thesis provides new insight into cellular signal transduction by integrating biological knowledge into mathematical models, which are subsequently analysed using systems theoretic methods. Signal transduction has been dissected using molecular and genomic approaches providing exciting insight into the biochemistry of life. However, a detailed understanding of its dynamic properties remains elusive. The application of systems science ideas to biology is promising to put the pieces of molecular information back together, as important properties of life arise at the system level only. For example, certain signalling pathways convert graded input signals into all-or-none output signals constituting biological switches. These are implicated in cellular memory and decisions. One such decision is whether or not to undergo programmed cell death (apoptosis). Apoptosis is an important physiological process crucially involved in the development and homoeostasis of multicellular organisms. Switches, such as in apoptosis, can be represented by ordinary differential equation models showing bistable behaviour. Different biochemical mechanisms generating bistability in reaction schemes as encountered in apoptosis are presented and compared in this thesis. Bifurcation studies reveal structural and parametric requirements for bistability. In combination with reported kinetic information, inconsistencies in the literature view of apoptosis signalling in humans are revealed. An additional regulatory mechanism is proposed, which is now supported by experimental evidence. Extended robustness analyses indicate that the cell has achieved a favourable robustness-performance trade-off, imposed by network structure and evolutionary constraints. On the one hand, inhibitors of apoptosis function as noise filters and reduce variability caused by the stochastic nature of reactions. Further, qualitative properties such as bistability are comparably robust to parameter changes supporting proper decisions. On the other hand, quantitative aspects are comparably sensitive. This allows for variability in a population, as observed in experiments, and which is likely important for physiological function as recently indicated in immunological studies. The analyses further indicate that the trade-off leads to fragilities. For example, an up-regulation of inhibitors of apoptosis, as observed in certain cancers, can not only desensitise cells to apoptotic stimuli, as also suggested by experimental studies, but can contribute to cancer aggressiveness and progression through additional mechanisms. Thereby, the analyses provide insight of pharmaceutical relevance. Several results presented in this thesis are not restricted to apoptosis signalling only, but are conceptually relevant to various other signal transduction pathways.Item Open Access Control of uncertain systems with l1 and quadratic performance objectives(2007) Rieber, Jochen M.; Allgöwer, Frank (Prof. Dr.-Ing.)This thesis presents novel analysis and synthesis concepts for linear control systems with parametric uncertainties. Different performance objectives such as L1, H-infinity, H2, and quadratic performance are considered. In the analysis section, upper bounds on the L-infinity-gain (or the L1-norm) of uncertain systems are developed. These bounds exhibit different degrees of computational effort and accuracy. In particular, a new direct approach for determining the robust L-infinity-gain is proposed. The synthesis sections introduce an efficient formulation of H-infinity and H2 constraints in a general linear multi-objective control framework. Moreover, a novel control structure for the design of parameter-varying controllers is developed. Using this structure, a scheme for the synthesis of linear parameter-varying output-feedback controllers in the L1 control framework is presented for the first time. In addition, it is shown how the control structure is applicable to other norm-based frameworks like quadratic performance control and in particular H-infinity control. The analysis and synthesis conditions proposed in this thesis are expressed as computationally tractable optimization problems, in particular in form of linear matrix inequalities, semi-definite programs, or iterations thereof. Several detailed examples, including a flight control problem with time-varying dynamics, demonstrate the properties and the applicability of the proposed methods.Item Open Access Delay robustness in cooperative control(2010) Münz, Ulrich; Allgöwer, Frank (Prof. Dr.-Ing.)The robustness of various cooperative control schemes on large scale networked systems with respect to heterogeneous communication and coupling delays is investigated. The presented results provide delay-dependent and delay-independent conditions that guarantee consensus, rendezvous, flocking, and synchronization in different classes of multi-agent systems (MAS). All conditions are scalable to arbitrarily large multi-agent systems with non-identical agent dynamics. In particular, conditions for linear agents, for nonlinear agents with relative degree one, and for a class of nonlinear agents with relative degree two are presented. The interconnection topology between the agents is in most cases represented by an undirected graph. The results for nonlinear agents with relative degree one hold also for the more general case of directed graphs with switching topologies. Different delay configurations are investigated and compared. These configurations represent different ways how the delays affect the coupling between the agents. The presented robustness analysis considers constant, time-varying, and distributed delays in order to take different sources of delays into account. The results are applied to several typical applications and simulations illustrate the findings. The main contributions of this thesis include: (i) Consensus and rendezvous in single integrator MAS are robust to arbitrarily large delays even on switching topologies. However, the convergence rate of this MAS is delay-dependent and scalable convergence rate conditions are presented. (ii) Consensus and rendezvous in relative degree two MAS are robust to sufficiently small delays. Local, scalable conditions are derived for these MAS that guarantee consensus and rendezvous for bounded delays. (iii) Finally, the derived delay robustness analysis for general linear MAS allows for the first time to compare different delay configurations in a unifying framework.Item Open Access Physics-informed regression of implicitly-constrained robot dynamics(2022) Geist, Andreas René; Allgöwer, Frank (Prof. Dr.-Ing.)The ability to predict a robot’s motion through a dynamics model is critical for the development of fast, safe, and efficient control algorithms. Yet, obtaining an accurate robot dynamics model is challenging as robot dynamics are typically nonlinear and subject to environment-dependent physical phenomena such as friction and material elasticities. The respective functions often cause analytical dynamics models to have large prediction errors. An alternative approach to analytical modeling forms the identification of a robot’s dynamics through data-driven modeling techniques such as Gaussian processes or neural networks. However, solely data-driven algorithms require considerable amounts of data, which on a robotic system must be collected in real-time. Moreover, the information stored in the data as well as the coverage of the system’s state space by the data is limited by the controller that is used to obtain the data. To tackle the shortcomings of analytical dynamics and data-driven modeling, this dissertation investigates and develops models in which analytical dynamics is being combined with data-driven regression techniques. By combining prior structural knowledge from analytical dynamics with data-driven regression, physics-informed models show improved data-efficiency and prediction accuracy compared to using the aforementioned modeling techniques in an isolated manner.Item Open Access Uncertainty and robustness analysis of biochemical reaction networks via convex optimisation and robust control theory(2009) Waldherr, Steffen; Allgöwer, Frank (Prof. Dr.-Ing.)In the area of systems biology, dynamical models of biochemical reaction networks are used to derive model-based predictions about the related biological processes. This thesis provides new methods to study how parametric uncertainty affects such predictions. The focus of this study is on predictions about the steady states and the type of dynamical behaviour, such as bistability or oscillations. Concerning steady states, the problem of uncertainty analysis is investigated. For a given extent of parametric uncertainty, the objective is to compute bounds on the variations in the steady states. In view of an underlying feasibility problem, a method based on semidefinite programming is developed to solve this problem. The approach is also applied to compute a measure for the robustness of the location of steady states in the presence of parametric uncertainty. Regarding the effect of parametric uncertainty on the type of dynamical behaviour, the robustness problem is considered. A robustness measure is defined by the extent of parametric uncertainty for which no local bifurcations occur. An approach to solve the robustness problem with frequency domain methods is investigated. The proposed feedback loop breaking method allows to characterise parametric uncertainties for which the type of dynamical behaviour is robust. On the one hand, a lower bound on the corresponding robustness measure is computed by providing Positivstellensatz infeasibility certificates for the underlying equations. On the other hand, the feedback loop breaking concept is adopted for the design of a bifurcation search algorithm in a high-dimensional parameter space. The results of the search algorithm thereby provide an upper bound on the robustness measure. In addition, the novel concept of kinetic perturbations is introduced. This is a class of specific parametric uncertainties which are particularly useful for the analysis of biochemical reaction networks. It is shown that a robustness analysis is performed efficiently for kinetic perturbations by use of the structured singular value. As a side result, the direct relation between kinetic perturbations and changes to the sensitivity of steady states in a biochemical reaction network is demonstrated. To complement the methodological results, a novel model for a specific biochemical signal transduction system within the TNF induced signalling network is constructed. The model is analysed with methods developed in this thesis. In addition to an illustrative application of the new methods, the findings of this analysis also provide new biological insight into TNF signal transduction.Item Open Access A novel overactuated quadrotor UAV(2015) Ryll, Markus; Allgöwer, Frank (Prof. Dr.-Ing.)Standard quadrotor UAVs are inherently underactuated as they posses only four independent control inputs - their four propeller spinning velocities. Therefore they only possess a limited mobility in space for the six dofs parameterizing the quadrotor position/orientation. This implies that for standard quadrotors it is impossible to follow an arbitrarily designed trajectory. A standard quadrotor for example cannot translate position while remaining horizontal. The common use of UAVs and quadrotors in particular is changing from common observer tasks to more applied flying service robot tasks including interaction with the environment. Here the loss of mobility on the basis of the inherent underactuation can constitute a limiting factor. In this thesis we will present a novel quadrotor UAV design that surmounts these limitations by additional four control inputs actuating the four propeller tilting angles. First, we will show that our novel quadrotor UAV with tilting propellers offers behavior as a fully-actuated flying vehicle with full actuation of the quadrotor position and orientation in space. Second, a comprehensive modeling and control framework for the proposed quadrotor is presented, and the hardware/software specifications of an experimental prototype will be introduced. Finally, the results of several simulations and real experiments are reported to illustrate the capabilities of the proposed novel UAV design.Item Open Access From static to dynamic couplings in consensus and synchronization among identical and non-identical systems(2010) Wieland, Peter; Allgöwer, Frank (Prof. Dr.-Ing.)In a systems theoretic context, the terms 'consensus' and 'synchronization' both describe the property that all individual systems in a group behave asymptotically identical, i.e., output or state trajectories asymptotically converge to a common trajectory. The objective of the present thesis is an improved understanding of some of the diverse coupling mechanisms leading to consensus and synchronization. A starting point is the observation that classical consensus and synchronization results commonly deal with two distinct facets of the problem: Consensus has regularly a strong focus on the interconnections and related constraints while the individual systems possess simple dynamics. Synchronization, in contrast, typically addresses questions about complex individual dynamical systems and puts weak emphasis on communication constraints. Very few results exist that address both facets simultaneously. A thorough analysis of static couplings in consensus algorithms provides explanations for this observation by unveiling limitations inherent to this type of couplings. Novel dynamic coupling mechanisms are proposed to overcome these limitations. These methods essentially rely on an internal model principle for consensus and synchronization derived in the thesis. This principle provides necessary conditions for consensus and synchronization in groups of non-identical systems, and it establishes a link to the output regulation problem. The fresh point of view revealed by this link eventually leads to a new hierarchical mechanism for consensus and synchronization, where coupling dynamics compensate for heterogeneity in the dynamical models of the individual systems as well as communication constraints. Applications include synchronization of linear systems and phase synchronization of exponentially stable oscillators.Item Open Access Die Phototaxis von Halobakterium salinarum - Mathematische Beschreibung stochastischer Prozesse(2006) Nutsch, Torsten; Gilles, Ernst Dieter (Prof. Dr.-Ing. Dr. h.c. mult.)Die Phototaxis von Halobacterium salinarum ist ein elegantes Beispielsystem für Signaltransduktion in Prokaryoten. Die Zellen verfügen über zwei verschiedene Typen von Photorezeptoren SRI und SRII, die für Licht verschiedener Wellenlängen empfindlich sind. An den Rezeptoren schließt sich ein molekulares Signaltransduktionsnetzwerk an, das das Schwimmverhalten der Zellen je nach äußerem Reiz beeinflusst. Ohne Stimulation wechseln die Zellen immer wieder zufällig zwischen der vorwärts- und rückwärts gerichteten Schwimmbewegung hin und her. Im Mittel geschieht das alle 12 Sekunden. Nach einer Schreckstimulation wird der Wechsel der Schwimmrichtung deutlich schneller eingeleitet, während die Zellen bei einer Lockstimulation die Dauer der aktuellen Schwimmrichtung noch länger ausdehnen. Beide Schwimmphasen verhalten sich sowohl im unstimulierten als auch im stimulierten Fall symmetrisch zueinander. Im Gegensatz zu den gängigen Motormodellen von E. coli befindet sich der Schaltprozess von Halobacterium salinarum nicht im thermischen Gleichgewicht. Vielmehr handelt es sich hier um einen energieverbrauchenden Kreisprozess, der nacheinander unterschiedliche Phasen in einer bestimmten Vorzugsrichtung durchläuft. In einem ersten Schritt konnten mittels Analyse von experimentellen Ergebnissen 8 verschiedene Funktionszustände (Phasen) des halobakteriellen Schaltprozesses identifiziert werden (4 Phasen pro Schwimmrichtung). Die Stopp-Phase ist leicht durch Beobachten der Schwimmbewegung zu erkennen. Sie dauert sowohl im stimulierten als auch im unstimulierten Fall im Mittel 0,43 Sekunden. Nach dieser Phase schwimmt die Zelle in der entgegengesetzten Richtung weiter. In den ersten 1-2 Sekunden nach dieser Richtungsumkehr reagiert sie allerdings verzögert (refraktär) auf einen Schreckreiz. Dieses Verhalten wird der Refraktär-Phase zugeordnet, deren Dauer durch einen Schreckreiz deutlich verlängert wird. Anschließend befindet sich der Schaltkomplex in der Kompetent-Phase. Hier ist der Motor 'kompetent', die Richtungsumkehr bei einem Schreckreiz zu aktivieren. Diese Aktivierung geschieht schließlich in der letzten Phase, der Aktiv-Phase. Danach stoppt der Motor, bevor die Funktionszustände in analoger Art und Weise in der entgegengesetzten Schwimmrichtung durchlaufen werden. In einem zweiten Schritt wurde die Kinetik der einzelnen Phasen aufgrund von gemessenen Häufigkeitsverteilungen von Prozessdauern bestimmt. Darauf hin konnte schließlich ein detailliertes Modell aufgestellt werden, das die einzelnen Phasen sowie die Kinetik ihrer Übergänge miteinander vereint. Es besteht aus 44 Untereinheiten, die sich synchron in einem der oben genannten Funktionszustände befinden. Mit Hilfe des aufgestellten Gesamtmodells, bestehend aus dem einfachen Modell der Signaltransduktion und dem detaillierten Modell des Schaltverhaltens, war es möglich die verschiedensten Experimente zu simulieren. Alle Simulationen zeigten eine recht gute, viele sogar eine sehr gute Übereinstimmung mit den experimentellen Ergebnissen. So kann das Modell z.B. die Häufigkeitsverteilung der Länge einer Schwimmphase sowohl im spontanen als auch im lichtinduzierten Fall bei Stimulation mit einem Schreck- oder Locksignal korrekt wiedergeben. Ebenso beschreibt es die mittlere Reaktionszeit der Zellen auf Einzel- und Doppelpulse aus blauem Licht. Diese Reaktionszeit ist proportional zum Kehrwert der applizierten Lichtmenge sowie proportional zur Dunkelpause zwischen beiden Pulsen und ihrem Tastverhältnis. Weiterhin ist das Gesamtmodell in der Lage, Experimente zu beschreiben, für die bisher keine Erklärung bekannt war. Dies ist z.B. bei der inversen Antwort auf einen Lockreiz der Fall. Eine Stimulation mit einem Orangelicht-Puls hat normalerweise eine Verringerung der Schalthäufigkeit der Zellen zur Folge. Wird ein solcher Puls allerdings bis zu 8 Sekunden nach einem Schreckreiz gegeben, hat er die entgegengesetzte Wirkung und lässt die Zellen erneut die Schwimmrichtung umkehren. Das Modell zeigt dasselbe Verhalten. Grund dafür ist die Refraktär-Phase, in der die Zellen nach dem Schreckreiz durch die erhöhte Konzentration des Schaltsignals 'festgehalten' werden. Der Orangelicht-Puls 'befreit' die Zellen wieder aus der Refraktär-Phase, indem er kurzzeitig die Schaltsignalkonzentration absenkt. Nach diesem Puls erhöht sich diese Konzentration wieder, weil die Adaptation an den noch andauernden Schreckreiz noch nicht abgeschlossen ist. Nun reagieren die Zellen aber mit einer erneuten Richtungsumkehr, da sie sich jetzt in der Kompetent-Phase befinden. Dadurch hat der Orangelicht-Puls, der normalerweise die Schalthäufigkeit verringert, eine inverse Wirkung.