Universität Stuttgart
Permanent URI for this communityhttps://elib.uni-stuttgart.de/handle/11682/1
Browse
45 results
Search Results
Item Open Access Indefinite linear quadratic optimal control: periodic dissipativity and turnpike properties(2018) Berberich, JulianItem 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 Multivariable controller design for an industrial distillation column(1992) Allgöwer, Frank; Raisch, JörgIn this paper, we report our experience with the design of linear multivariable controllers for a staged binary distillation column with 40 trays. Controller design methods include H∞-minimization, DNA-design, CL-design and H2minimization. Results obtained at the real plant are shown.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 Mathematical modeling of the pituitary-thyroid feedback loop: role of a TSH-T3-shunt and sensitivity analysis(2018) Berberich, Julian; Dietrich, Johannes W.; Hoermann, Rudolf; Müller, Matthias A.Despite significant progress in assay technology, diagnosis of functional thyroid disorders may still be a challenge, as illustrated by the vague upper limit of the reference range for serum thyrotropin (TSH). Diagnostical problems also apply to subjects affected by syndrome T, i.e. those 10% of hypothyroid patients who continue to suffer from poor quality of life despite normal TSH concentrations under substitution therapy with levothyroxine (L-T4 ). In this paper, we extend a mathematical model of the pituitary-thyroid feedback loop in order to improve the understanding of thyroid hormone homeostasis. In particular, we incorporate a TSH-T3 –shunt inside the thyroid, whose existence has recently been demonstrated in several clinical studies. The resulting extended model shows good accordance with various clinical observations, such as a circadian rhythm in free peripheral triiodothyronine (FT3). Furthermore, we perform a sensitivity analysis of the derived model, revealing the dependence of TSH and hormone concentrations on different system parameters. The results have implications for clinical interpretation of thyroid tests, e.g. in the differential diagnosis of subclinical hypothyroidism.Item Open Access Identifiability and sensitivity analysis of heterogeneous cell population models(2013) Zeng, ShenIn this thesis, we introduce novel concepts to the modeling and analysis of heterogeneous cell populations. Heterogeneous cell populations can be interpreted as large populations of structurally identical cells with heterogeneous parameters and initial conditions. They appear in biological systems such as tissues of higher organisms or colonies of microorganisms. A well-known approach for the modeling of heterogeneous cell populations is the so called density-based approach, in which the state of a heterogeneous cell population is given by the probability density of the cell states. The evolution of the probability densities is in this approach given in terms of a partial differential equation. We extend this approach via a measure theoretical consideration, which exploits the probabilistic nature of the problem. The result of this novel ansatz is a framework in which the evolution of densities is described by operators. One of the key tasks in the analysis of heterogeneous cell population models is parameter estimation. For heterogeneous cell populations we want to estimate the probability density of parameters and initial conditions. However, to be able to perform parameter estimation, one always needs specific identifiability properties of a system. We formulate for the first time the concept of structural identifiability of a heterogeneous cell population model. It is revealed that this concept is closely related to observability of the corresponding single cell model. The connection between both concepts is studied and illuminated in a concrete example. The second emphasis of this thesis is the implementation of sensitivity analysis to the class of heterogeneous cell population models. Here we study sensitivity with respect to variations or misspecifications in the probability density of parameters and initial conditions.Item Open Access Moment dynamics of Zirconia particle formation for optimizing particle size distribution(2019) Halter, Wolfgang; Eisele, Rahel; Rothenstein, Dirk; Bill, Joachim; Allgöwer, FrankItem 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 Validation and analysis of linear distillation models for controller design(1993) Amrhein, Michael; Allgöwer, Frank; Marquardt, WolfgangIt is a nontrivial task to decide whether a model describes the main dynamic characteristics of a process and to determine which model is to be preferred for controller design. Techniques for examining lineal models for controller design are described in Section 2. One focus of this paper is on tools for analysing multivariable processes in the frequency domain, for example, condition number and dynamic relative gain array (RGA) analysis. The latter tool is extended by the phase information of the RGA. A novel evaluation tool involving the singular directions over frequency of the respective processes is introduced. In Section 3, a new linear low-order model is compared to five models from the literature using the analysis tools introduced in Section 2. The new model directly exploits wave propagation phenomena, and, therefore, will be called the wave model. Finally, Section 4 shows briefly result of the H∞-coutrolled column where the controller is designed on the basis of the wave model. Simulations with a detailed nonlinear distillation model show that very good control action can be achieved with this model. Moreover, the linear model allows to predict the nonlinear closed loop behavior quite accurately.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.