Browsing by Author "Allgöwer, Frank (Prof. Dr.-Ing.)"

Now showing 1 - 14 of 14

Open Access
Analysis and design of MPC frameworks for dynamic operation of nonlinear constrained systems
(2021) Köhler, Johannes; Allgöwer, Frank (Prof. Dr.-Ing.)
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.
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.
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.
Open Access
Model predictive control for nonlinear continuous-time systems with and without time-delays
(2013) Reble, Marcus; Allgöwer, Frank (Prof. Dr.-Ing.)
The objective of this thesis is the development of novel model predictive control (MPC) schemes for nonlinear continuous-time systems with and without time-delays in the states which guarantee asymptotic stability of the closed-loop. The most well-studied MPC approaches with guaranteed stability use a control Lyapunov function as terminal cost. Since the actual calculation of such a function can be difficult, it is desirable to replace this assumption by a less restrictive controllability assumption. For discrete-time systems, the latter assumption has been used in the literature for the stability analysis of so-called unconstrained MPC, i.e., MPC without terminal cost and terminal constraints. The contributions of this thesis are twofold. In the first part, we propose novel MPC schemes with guaranteed stability based on a controllability assumption, whereas we extend different MPC schemes with guaranteed stability to nonlinear time-delay systems in the second part. In the first part of this thesis, we derive explicit stability conditions on the prediction horizon as well as performance guarantees for unconstrained MPC. Starting from this result, we propose novel alternative MPC formulations based on combinations of the controllability assumption with terminal cost and terminal constraints. One of the main contributions is the development of a unifying MPC framework which allows to consider both MPC schemes with terminal cost and terminal constraints as well as unconstrained MPC as limit cases of our framework. In the second part of this thesis, we show that several MPC schemes with and without terminal constraints can be extended to nonlinear time-delay systems. Due to the infinite-dimensional nature of these systems, the problem is more involved and additional assumptions are required in the controller design. We investigate different MPC schemes with and without terminal constraints and/or terminal cost terms and derive novel stability conditions. Furthermore, we pay particular attention to the calculation of the involved control design parameters.
Open Access
Modeling and parameter estimation for heterogeneous cell populations
(2013) Hasenauer, Jan; Allgöwer, Frank (Prof. Dr.-Ing.)
Most of the modeling performed in biology aims at achieving a quantitative description and understanding of the intracellular signaling pathways within a “typical cell”. However, in many biologically important situations even genetically identical cell populations show a heterogeneous response. This means that individual members of the cell population behave differently. Such situations require the study of cell-to-cell variability and the development of models for heterogeneous cell populations. The main contribution of this thesis is the development of unifying modeling frameworks for signal transduction and proliferation processes in heterogeneous cell populations. These modeling frameworks allow for the detailed description of individual cells as well as differences between them. In contrast to many existing modeling approaches, the proposed frameworks allow for a direct comparison of model predictions with available data. Beyond this, the proposed population models can be simulated efficiently and, by exploiting the model structures, we are able to develop model-tailored Bayesian parameter estimation methods. These methods enable the calculation of the optimal parameter estimates, as well as the evaluation of the parameter and prediction uncertainties. The proposed tools allow for novel insights in population dynamics, in particular the model-based characterization of population heterogeneity and cellular subgroups. This is illustrated for two different application examples: pro- and anti-apoptotic signaling, which is interesting in the context of cancer therapy, and immune cell proliferation.
Open Access
Nonlinear model predictive control : a sampled data feedback perspective
(2005) Findeisen, Rolf; Allgöwer, Frank (Prof. Dr.-Ing.)
This work considers theoretical and implementational aspects of sampled-data open-loop nonlinear model predictive control (NMPC) of continuous time systems. Sampled-data open-loop NMPC refers to NMPC schemes, in which the optimal control problem is only solved at discrete recalculation instants, and where the resulting optimal input signal is applied open-loop in between. Various aspects and open questions in sampled-data open-loop NMPC are considered in this work. Specifically, methods for efficient implementations of NMPC are presented, and results with respect to theoretical questions such as nominal stability, compensation of computational and measurement delays, inherent robustness, and the output-feedback problem for sampled-data open-loop NMPC are derived. Most of the derived results are not limited to NMPC. They are rather applicable to a general class of sampled-data open-loop feedback control schemes.
Open Access
Nonlinearity assessment and linear control of nonlinear systems
(2006) Schweickhardt, Tobias; Allgöwer, Frank (Prof. Dr.-Ing.)
Linear control may be favorable over nonlinear control because linear design techniques greatly facilitate the controller design process and because linear controllers impose lower requirements on the implementation of the control law as compared to nonlinear controllers. It is therefore a tempting idea to use linear models and linear controller design methods also for nonlinear systems. However, the assumption of linear dynamics generally implies a modelling error that has to be taken into account in the controller design process. In this work, a methodology is presented that allows to quantify the degree of nonlinearity of a system’s dynamic behaviour, to derive an optimal linear model, and that allows using this or any other linear model to design a linear controller for the nonlinear system that guarantees stability also for the nonlinear closed loop. A key component of the underlying concept is to consider the nonlinear behaviour only on a designated operating regime. This way, only nonlinear behaviour is taken into account, that also matters for the practical operation of the nonlinear plant. The presented methodology uses an input-output approach, and the operating regime is characterized by the set of admissible input signals. For special system classes, the nonlinearity measure and best linear model can be determined with given formulas, while optimization techniques are used for general system classes. The results for controller design are built on concepts from robust control. The nonlinear plant it therefore devided into a nominal linear model and a nonlinear error term. The given stability conditions then allow to design a linear controller for the saturated nominal linear model such that the closed loop remains stable if the nonlinear error term is present.
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.
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.
Open Access
Planning and control for robotic tasks with a human-in-the-loop
(2014) Masone, Carlo; Allgöwer, Frank (Prof. Dr.-Ing.)
The design of robotic tasks with a joint interaction with a human user (human-in-the-loop) is currently a highly popular topic in robotics research. One of the main reasons of interest is the possibility of combining the skills of both humans and robots to successfully perform complex tasks. In particular: - Robots are extremely capable at autonomously executing specific and repetitive tasks, with great speed and precision, and they can operate in environments that are dangerous for a human operator. - With respect to robots, humans possess far superior cognitive capabilities and world awareness which allow them to tackle applications that involve unstructured environments or require taking difficult and quick decisions. The co-participation of humans and robots to a task can also arise from other reasons, such as an implicit constraint of the task itself (wearable robots, motion simulators) or safety regulations that require a human to supervise the activity of robotic workers. In view of these considerations, shared control (between human and robot) is a promising (and, in some fields, consolidated) approach to address a number of robotics applications. However, there are several open questions and challenges regarding the design of shared control architectures, such as choosing the role of the human in the task, devising suitable command interfaces and feedback algorithms that increase the situation awareness of the operator, and coping with the unpredictable signals or decisions from the human user. In this doctoral thesis it is presented a study of some novel robotic tasks involving human-robot interaction. The original shared control architectures developed for these tasks illustrate several novel solutions to the aforementioned questions. Furthermore, the tasks considered in the thesis span various possibilities for the typical characteristics of shared control architectures in robotics, i.e.: - the role of the human operator in the shared task and his/her interaction with the robot(s); - the typology and number of robots that participate to the shared task; - the feedback returned to the human operator.
Open Access
Robust fault detection and isolation of nonlinear systems with augmented state models
(2009) Aßfalg, Jochen; Allgöwer, Frank (Prof. Dr.-Ing.)
Model-based fault detection and isolation (FDI) is one of the most important fields in system theory and automation. Roughly speaking, FDI aims at finding and backtracking discrepancies between a system's observed behavior (described by its measurements) and its expected behavior (described by its model). Whenever the model used is uncertain, which means that it does not match the real process accurately, the FDI problem becomes particularly challenging. In practical applications, uncertain system representations are not unusual and thus, incorrect fault detection and false diagnosis can only be prevented, if employed FDI algorithms are robust against model uncertainties. This thesis presents novel modeling, analysis, and synthesis concepts for the robust FDI of nonlinear systems in a discrete-time representation. In the modeling section, a new formalism for the representation of nonlinear systems subject to faults is introduced. The presented model allows the description of a particularly wide class of faulty systems and moves the problems of fault diagnosis and state estimation close together, which would otherwise be different. By exploiting this relationship, novel conditions for linear and nonlinear fault-detectability and -isolability analysis are provided. The proposed conditions are based on well-known observability definitions and can thus be verified by means of established methods from the field of observability analysis. On the basis of the proposed model, the nominal and the Gaussian noisy fault diagnosis problem are expressed as an optimal hybrid state estimation problem. The use of sub-optimal solutions is discussed and illustrated by means of a practical example. In order to cope with uncertain problem formulations including plant-model-mismatch and unanticipated faults, the suggested modeling formalism is modified. Disturbances, modeling uncertainties, and measurement noise are characterized using unknown-but-bounded exogenous inputs. The unknown-but-bounded uncertainty representation proves to be exceptionally practicable, since no specific and difficult assumptions about the uncertainties have to be met a priori. On the other hand, unforeseen plant operations that are not captured by the model, e.g. unanticipated faults and unexpectedly large disturbances, are lumped in an unknown mode of operation. Based on the resulting uncertain model, a robust FDI algorithm is developed that is capable of diagnosing permanent and intermittent faults and furthermore is able to detect unknown modes of operation. Robust fault-detection and -isolation conditions are derived, by which the suggested algorithm is guaranteed to determine a meaningful and unique result. The fault diagnosis methods proposed in this thesis are expressed as algorithms that can be directly implemented and processed in a reasonable time. Several detailed examples, including the three-tank benchmark with unknown-but-bounded modeling uncertainties, demonstrate the properties and the applicability of the proposed methods.
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.
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.