On output feedback nonlinear model predictive control using high gain observers for a class of systems

In recent years, nonlinear model predictive control 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 connection to nonlinear predictive control. Most of the existing approaches for output feedback nonlinear model predictive control do only guarantee local stability. Here we consider the combination of stabilizing instantaneous NMPC schemes with high gain observers. For a special MIMO system class we show that the closed loop is asymptotically stable, and that 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 are recovered for a high gain observer with large enough gain and thus leading to semi-global/non-local results

Steady state and (bi-) stability evaluation of simple protease signalling networks

Signal transduction networks are complex, as are their mathematical models. Gaining a deeper understanding requires a system analysis. Important aspects are the number, location and stability of steady states. In particular, bistability has been recognised as an important feature to achieve molecular switching. This paper compares different model structures and analysis methods particularly useful for bistability analysis. The biological applications include proteolytic cascades as, for example, encountered in the apoptotic signalling pathway or in the blood clotting system. We compare three model structures containing zero-order, inhibitor and cooperative ultrasensitive reactions, all known to achieve bistability. The combination of phase plane and bifurcation analysis provides an illustrative and comprehensive understanding of how bistability can be achieved and indicates how robust this behaviour is. Experimentally, some so-called “inactive” components were shown to have a residual activity. This has been mostly ignored in mathematical models. Our analysis reveals that bistability is only mildly affected in the case of zero-order or inhibitor ultrasensitivity. However, the case where bistability is achieved by cooperative ultrasensitivity is severely affected by this perturbation

Generalization of navigation memory in honeybees

Flying insects like the honeybee learn multiple features of the environment for efficient navigation. Here we introduce a novel paradigm in the natural habitat, and ask whether the memory of such features is generalized to novel test conditions. Foraging bees from colonies located in 5 different home areas were tested in a common area for their search flights. The home areas differed in the arrangements of rising natural objects or their lack, and in the existence or lack of elongated ground structures. The test area resembled partly or not at all the layout of landmarks in the respective home areas. In particular, the test area lacked rising objects. The search flights were tracked with harmonic radar and quantified by multiples procedures, extracting their differences on an individual basis. Random search as the only guide for searching was excluded by two model calculations. The frequencies of directions of flight sectors differed from both model calculations and between the home areas in a graded fashion. Densities of search flight fixes were used to create heat maps and classified by a partial least squares regression analysis. Classification was performed with a support vector machine in order to account for optimal hyperplanes. A rank order of well separated clusters was found that partly resemble the graded differences between the ground structures of the home areas and the test area. The guiding effect of elongated ground structures was quantified with respect to the sequence, angle and distance from these ground structures. We conclude that foragers generalize their specific landscape memory in a graded way to the landscape features in the test area, and argue that both the existence and absences of landmarks are taken into account. The conclusion is discussed in the context of the learning and generalization process in an insect, the honeybee, with an emphasis on exploratory learning in the context of navigation

AN ECONOMIC ANALYSIS OF GENETIC INFORMATION: LEPTIN GENOTYPING IN FED CATTLE

The use of genetic knowledge is widespread in crop production but is just recently being utilized in livestock production. This study investigates the economic value to feedlots of a polymorphism in the bovine leptin gene. Previous studies indicate that this polymorphism is associated with fat deposition. Since fed cattle are often priced on a grid that considers both yield and quality grades, fat deposition is an important factor in the value and profitability of fed cattle. Using data from 590 crossbred steers and heifers, we estimate growth curves for relevant biological traits, both with and without genotypic information. Using the resulting functions, we then simulate carcass traits to various days-on-feed and compute the associated profit under three price grids. Maximum profits are determined in an unconstrained profit maximization model and in a model that constrains cattle to be marketed in 45-head "potloads." Results indicate that leptin genotypic knowledge has little impact on optimal days-on-feed but may play a role in valuing feeder cattle. The differences in value of cattle varied by as much as $37 per head between genotypes.genetics, leptin genotype, beef cattle, value of information, Livestock Production/Industries,

Review of "Stochastic Modelling for Systems Biology" by Darren Wilkinson

"Stochastic Modelling for Systems Biology" by Darren Wilkinson introduces the peculiarities of stochastic modelling in biology. This book is particularly suited to as a textbook or for self-study, and for readers with a theoretical background

Piecewise constant high-gain adaptive λ-[lambda]-tracking for higher relative degree linear systems

In this paper we present an adaptive high-gain observer-based controller for linear, minimum-phase systems with known relative degree larger than one and known sign of the high-frequency gain. The adaptation scheme does not use any identification mechanism and is universal in the sense that it is independent of the system the controller is designed for. We prove that for any bounded and sufficiently smooth reference signal the modulus of the tracking error becomes smaller than an arbitrary small but fixed error bound X if t tends to infinity. All states of the nonlinear closed-loop system remain bounded

A simple adaptive observer for nonlinear systems

In this note we present a high-gain observer for nonlinear uniformly observable SISO systems for which the high-gain parameter is determined adaptively on-line. The adaptation scheme is simple and universal in the sense that it is independent of the system the observer is designed for. Unlike in an earlier approach, the gain is adapted continuously in the present paper. This further simplifies the adaptation law and also leads to lower values of the high-gain parameter. We prove that the observer output error becomes smaller than a User specified bound for large times and that the adaptation converges

Heterogeneity reduces sensitivity of cell death for TNF-Stimuli

Background Apoptosis 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 kappaB (NF-kappaB)-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. Results This 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 cell's fate. A simulated knockout of the NF-kappaB-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. Conclusions Cell 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-kappaB 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

Approximations and their consequences for dynamic modelling of signal transduction pathways

Signal transduction is the process by which the cell converts one kind of signal or stimulus into another. This involves a sequence of biochemical reactions, carried out by proteins. The dynamic response of complex cell signalling networks can be modelled and simulated in the framework of chemical kinetics. The mathematical formulation of chemical kinetics results in a system of coupled differential equations. Simplifications can arise through assumptions and approximations. The paper provides a critical discussion of frequently employed approximations in dynamic modelling of signal transduction pathways. We discuss the requirements for conservation laws, steady state approximations, and the neglect of components. We show how these approximations simplify the mathematical treatment of biochemical networks but we also demonstrate differences between the complete system and its approximations with respect to the transient and steady state behavior