Eric Bullinger

A note on stability, robustness and performance of output feedback nonlinear model predictive control

In recent years, nonlinear model predictive control (NMPC) schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in the framework of nonlinear predictive control. This paper combines stabilizing instantaneous state feedback NMPC schemes with high-gain observers to achieve output feedback stabilization. For a uniformly observable MIMO system class it is shown that the resulting closed loop is asymptotically stable. Furthermore, the output feedback NMPC scheme recovers the performance of the state feedback in the sense that the region of attraction and the trajectories of the state feedback scheme can be recovered to any degree of accuracy for large enough observer gains, thus leading to semi-regional results. Additionally, it is shown that the output feedback controller is robust with respect to static sector bounded nonlinear input uncertainties.

An adaptive high-gain observer for nonlinear systems

In this paper we present a high-gain observer for a general class of nonlinear SISO systems for which the high-gain parameter is determined on-line in an adaptive fashion. The adaptation scheme is simple and universal in the sense that it is independent of the system the observer is designed for. We prove that the observer output error becomes smaller than a user specified bound for large times and that the adaptation converges. The assumptions required for the adaptive high-gain observer are the same as for the nonadaptive high-gain observer, namely that the system is uniformly observable for any u(t).

Adaptive λ-tracking for nonlinear higher relative degree systems

This paper proposes a relatively simple adaptive controller for nonlinear systems with higher relative degree. The controller achieves @l-tracking for a large class of nonlinear systems, i.e. it asymptotically stabilizes the system up to an error of at most @l which is chosen by the user. Only little information on the system is needed in the sense that no model needs to be known for the controller design, but only structural information like the relative degree and a lower bound on the positive high-frequency gain. The zero-dynamics does not need to be asymptotically stable, boundedness is sufficient. The controller consists of a high-gain observer, a high-gain observer-state feedback and a common adaptation of both high-gain parameters. The adaptation increases the gains of the observer and the state-feedback whenever the control objective, namely that the tracking error is of magnitude not larger than @l, is not attained. It is proved that the controllers adaptation converges and the control objective is achieved at least asymptotically.

The role of control and system theory in systems biology

The use of new technology and mathematics to study the systems of nature is one of the most significant scientific trends of the century. Driven by the need for more precise scientific understanding, advances in automated measurement are providing rich new sources of biological and physiological data. These data provide information to create mathematical models of increasing sophistication and realism—models that can emulate biological and physiological systems with sufficient accuracy to advance our understanding of living systems and disease mechanisms. New measurement and modelling methods set the stage for control and systems theory to play their role in seeking out the mechanisms and principles that regulate life. It is of inestimable importance for the future of control as a discipline that this role is performed in the correct manner. If we handle the area wisely then living systems will present a seemingly boundless range of important new problems—just as physical and engineering systems have done in previous centuries. But there is a crucial difficulty. Faced with a bewildering array of choices in an unfamiliar area, how does a researcher select a worthwhile and fruitful problem? This article is an attempt to help by offering a control-oriented guide to the labyrinthine world of biology/physiology and its control research opportunities.

Heterogeneity reduces sensitivity of cell death for TNF-stimuli.

BackgroundApoptosis is a form of programmed cell death essential for the maintenance of homeostasis and the removal of potentially damaged cells in multicellular organisms. By binding its cognate membrane receptor, TNF receptor type 1 (TNF-R1), the proinflammatory cytokine Tumor Necrosis Factor (TNF) activates pro-apoptotic signaling via caspase activation, but at the same time also stimulates nuclear factor κB (NF-κB)-mediated survival pathways. Differential dose-response relationships of these two major TNF signaling pathways have been described experimentally and using mathematical modeling. However, the quantitative analysis of the complex interplay between pro- and anti-apoptotic signaling pathways is an open question as it is challenging for several reasons: the overall signaling network is complex, various time scales are present, and cells respond quantitatively and qualitatively in a heterogeneous manner.ResultsThis study analyzes the complex interplay of the crosstalk of TNF-R1 induced pro- and anti-apoptotic signaling pathways based on an experimentally validated mathematical model. The mathematical model describes the temporal responses on both the single cell level as well as the level of a heterogeneous cell population, as observed in the respective quantitative experiments using TNF-R1 stimuli of different strengths and durations. Global sensitivity of the heterogeneous population was quantified by measuring the average gradient of time of death versus each population parameter. This global sensitivity analysis uncovers the concentrations of Caspase-8 and Caspase-3, and their respective inhibitors BAR and XIAP, as key elements for deciding the cells fate. A simulated knockout of the NF-κB-mediated anti-apoptotic signaling reveals the importance of this pathway for delaying the time of death, reducing the death rate in the case of pulse stimulation and significantly increasing cell-to-cell variability.ConclusionsCell ensemble modeling of a heterogeneous cell population including a global sensitivity analysis presented here allowed us to illuminate the role of the different elements and parameters on apoptotic signaling. The receptors serve to transmit the external stimulus; procaspases and their inhibitors control the switching from life to death, while NF-κB enhances the heterogeneity of the cell population. The global sensitivity analysis of the cell population model further revealed an unexpected impact of heterogeneity, i.e. the reduction of parametric sensitivity.

Cell invasion in the spheroid sprouting assay: a spatial organisation analysis adaptable to cell behaviour.

The endothelial cell spheroid assay provides a suitable in vitro model to study (lymph) angiogenesis and test pro- and anti-(lymph) angiogenic factors or drugs. Usually, the extent of cell invasion, observed through optical microscopy, is measured. The present study proposes the spatial distribution of migrated cells as a new descriptor of the (lymph) angiogenic response. The utility of this novel method rests with its capacity to locally characterise spheroid structure, allowing not only the investigation of single and collective cell invasion but also the evolution of the spheroid core itself. Moreover, the proposed method can be applied to 2D-projected spheroid images obtained by optical microscopy, as well as to 3D images acquired by confocal microscopy. To validate the proposed methodology, endothelial cell invasion was evaluated under different experimental conditions. The results were compared with widely used global parameters. The comparison shows that our method prevents local spheroid modifications from being overlooked and leading to the possible misinterpretation of results.

Results Towards Identifiability Properties of Biochemical Reaction Networks

In this paper we consider the question of parameter identifiability for biochemical reaction networks, as typically encountered in systems biology. Specifically, we are interested in deriving conditions on the biochemical reaction network and on the measured outputs that guarantee identifiability of the parameters. Taking the specific system structure of biochemical reaction networks into account, we derive sufficient conditions for local parameter identifiability based on a suitable system expansion which does not any more directly depend on the parameters. Rather, as shown, the problem of identifiability can be recast as the question of observability of the (parameter free) expanded system. The conditions derived are exemplified considering a simple example

An approach for dividing models of biological reaction networks into functional units

Biological reaction networks consist of many substances and reactions between them. Like many other biological systems, they have a modular structure. Therefore, a division of a biological reaction network into smaller units highly facilitates its investigation. The authors propose an algorithm to divide an ordinary differential equation (ODE) model of a biological reaction network hierarchically into functional units. For every compound, an activity function dependent on concentration or concentration change rate is defined. After performing suitable simulations, distances between the compounds are computed by comparing the activities along the trajectories of the simulation. The distance information is used to generate a dendrogram revealing the internal structure of the reaction network. The algorithm identifies functional units in two models of different networks: catabolite repression in Escherichia coli and epidermal growth factor (EGF) signal transduction in mammalian cells.

Adaptive /spl lambda/-tracking for nonlinear systems with higher relative degree

Previous results for adaptive /spl lambda/-tracker have focused on nonlinear systems with relative degree one or on linear systems with higher relative degree. We extend the adaptive /spl lambda/-tracker to /spl lambda/-stabilize nonlinear system with higher relative degree. Only little structural information about the system to be controlled is needed. /spl lambda/-stability and convergence of the adaptation is proven for tracking a large class of reference trajectories. The design of the controller is very simple and intuitive, only few parameters have to be tuned.

Functional morphology of Tethya species (Porifera) 2. Three-dimensional morphometrics on spicules and skeleton superstructures of T-minuta

The biomechanics of body contraction in Porifera is almost unknown, although sponge contraction has been observed already in ancient times. Some members of the genus Tethya represent the most contractile poriferan species. All of them show a highly ordered skeleton layout. Based on three main spicule types, functional units are assembled, termed skeleton superstructures here. Using synchrotron radiation based x-ray microtomography and quantitative image analysis with specially developed particle and structure recognition algorithms allowed us to perform spatial allocation and 3D-morphometric characterizations of single spicules and skeleton superstructures in T. minuta. We found and analyzed three skeleton superstructures in the investigated specimen: (1) 85 megasclere bundles, (2) a megaster sphere, composed by 16,646 oxyasters and (3) a pinacoderm–tylaster layer composed by micrasters. All three skeleton superstructures represent composite materials of siliceous spicules and extracellular matrix. From structure recognition we developed an abstracted mathematical model of the bundles and the sphere. In addition, we analyzed the megaster network interrelation topology and found a baso-apical linear symmetry axis for the megaster density inside the sphere. Based on our results, we propose a hypothetical biomechanical contraction model for T. minuta and T. wilhelma, in which the skeleton superstructures restrain physical stress generated by contraction in the tissue. While skeletal structures within the genus Tethya have been explained using R. Buckminster Fullers principle of tensegrity by other authors, we prefer material science based biomechanical approaches, to understand skeletal superstructures by referring to their composite material properties.