Interval observers design for hybrid and biological systems

International audienceThis work deals with interval observer design techniques. In the firstpart, the problem of interval observer design is studied for a classof linear hybrid systems. Several observers are proposed orientedon different conditions of positivity and stability for estimation errordynamics. Efficiency of the proposed approach is demonstrated bycomputer experiments for academic and bouncing ball systems. Notethat interval observer design techniques for linear hybrid systemshave been developed for the first time in the present work. The secondpart is devoted to the interval estimation of sequestred infected erythrocytesin plasmodium falciparum malaria patients. An advantageof the interval approaches in this case is that they give a bound ofthe errors at any time, which can be controlled in order to ensurethe positivity of the state estimates of the system. Thus, intervalestimation is very close to the reality in this case and has not beendeveloped before the present work. An interval observer in orderto estimate the sequestered parasite population is proposed in thisreport. Its efficiency is demonstrated by computer simulations

Gender Perception From Gait: A Comparison Between Biological, Biomimetic and Non-biomimetic Learning Paradigms

This paper explores in parallel the underlying mechanisms in human perception of biological motion and the best approaches for automatic classification of gait. The experiments tested three different learning paradigms, namely, biological, biomimetic, and non-biomimetic models for gender identification from human gait. Psychophysical experiments with twenty-one observers were conducted along with computational experiments without applying any gender specific modifications to the models or the stimuli. Results demonstrate the utilization of a generic memory based learning system in humans for gait perception, thus reducing ambiguity between two opposing learning systems proposed for biological motion perception. Results also support the biomimetic nature of memory based artificial neural networks (ANN) in their ability to emulate biological neural networks, as opposed to non-biomimetic models. In addition, the comparison between biological and computational learning approaches establishes a memory based biomimetic model as the best candidate for a generic artificial gait classifier (83% accuracy, p < 0.001), compared to human observers (66%, p < 0.005) or non-biomimetic models (83%, p < 0.001) while adhering to human-like sensitivity to gender identification, promising potential for application of the model in any given non-gender based gait perception objective with superhuman performance

Practical and Polytopic Observers for Nonlinear Uncertain Systems

For a class of dynamical systems, with uncertain nonlinear terms considered as «unknown inputs», we give sufficient conditions for observability. We show also that there does not exist any exact observer independent of the unknown inputs. Under the additional assumption that the uncertainty is bounded, we build practical observers whose error converges exponentially towards an arbitrary small neighborhood of the origin. For the general case, when the system might be not observable with unknown inputs, we build polytopic observers providing time-varying bounds (depending on the uncertainty bounds) on the state variables. We illustrate these results on a biological model of a structured population

Modeling and Estimation of Biological Plants

Estimating the state of a dynamic system is an essential task for achieving important objectives such as process monitoring, identification, and control. Unlike linear systems, no systematic method exists for the design of observers for nonlinear systems. Although many researchers have devoted their attention to these issues for more than 30 years, there are still many open questions. We envisage that estimation plays a crucial role in biology because of the possibility of creating new avenues for biological studies and for the development of diagnostic, management, and treatment tools. To this end, this thesis aims to address two types of nonlinear estimation techniques, namely, the high-gain observer and the moving-horizon estimator with application to three different biological plants. After recalling basic definitions of stability and observability of dynamical systems and giving a bird's-eye survey of the available state estimation techniques, we are interested in the high-gain observers. These observers may be used when the system dynamics can be expressed in specific a coordinate under the so-called observability canonical form with the possibility to assign the rate of convergence arbitrarily by acting on a single parameter called the high-gain parameter. Despite the evident benefits of this class of observers, their use in real applications is questionable due to some drawbacks: numerical problems, the peaking phenomenon, and high sensitivity to measurement noise. The first part of the thesis aims to enrich the theory of high-gain observers with novel techniques to overcome or attenuate these challenging performance issues that arise when implementing such observers. The validity and applicability of our proposed techniques have been shown firstly on a simple one-gene regulatory network, and secondly on an SI epidemic model. The second part of the thesis studies the problem of state estimation using the moving horizon approach. The main advantage of MHE is that information about the system can be explicitly considered in the form of constraints and hence improve the estimates. In this work, we focus on estimation for nonlinear plants that can be rewritten in the form of quasi-linear parameter-varying systems with bounded unknown parameters. Moving-horizon estimators are proposed to estimate the state of such systems according to two different formulations, i.e., "optimistic" and "pessimistic". In the former case, we perform estimation by minimizing the least-squares moving-horizon cost with respect to both state variables and parameters simultaneously. In the latter, we minimize such a cost with respect to the state variables after picking up the maximum of the parameters. Under suitable assumptions, the stability of the estimation error given by the exponential boundedness is proved in both scenarios. Finally, the validity of our obtained results has been demonstrated through three different examples from biological and biomedical fields, namely, an example of one gene regulatory network, a two-stage SI epidemic model, and Amnioserosa cell's mechanical behavior during Dorsal closure

Nonlinear observer design and synchronization analysis for classical models of neural oscillators

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 37-38).This thesis explores four nonlinear classical models of neural oscillators, the Hodgkin- Huxley model, the Fitzhugh-Nagumo model, the Morris-Lecar model, and the Hindmarsh-Rose model. Analysis techniques for nonlinear systems were used to develop a set of observers and perform synchronization analysis on the aforementioned neural systems. By using matrix analysis techniques, a study of biological background and motivation, and MATLAB simulation with mathematical computation, it was possible to do a preliminary contraction and nonlinear control systems structural study of these classical neural oscillator models. Neural oscillation and signaling models are based fundamentally on the biological function of the neuron, with behavior mediated through the channeling of ions across a cell membrane. The variable assumed to be measured for this study is the voltage or membrane potential, which could be measured empirically through the use of a neuronal force-clamp system. All other variables were estimated by using the partial state and full state observers developed here. Preliminary observer rate convergence analysis was done for the Fitzhugh-Nagumo system, and preliminary synchronization analysis was done for both the Fitzhugh-Nagumo and the Hodgkin- Huxley systems. It was found that by using a variety of techniques and mathematical matrix analyses methods (e.g. diagonal dominance or other norms), it was possible to develop a case-by-case nonlinear control systems approach to each particular system as a biomathematical entity.by Ranjeetha Bharath.S.B

Parameter estimation in kinetic reaction models using nonlinear observers facilitated by model extensions

An essential part of mathematical modelling is the accurate and reliable estimation of model parameters. In biology, the required parameters are particularly difficult to measure due to either shortcomings of the measurement technology or a lack of direct measurements. In both cases, parameters must be estimated from indirect measurements, usually in the form of time-series data. Here, we present a novel approach for parameter estimation that is particularly tailored to biological models consisting of nonlinear ordinary differential equations. By assuming specific types of nonlinearities common in biology, resulting from generalised mass action, Hill kinetics and products thereof, we can take a three step approach: (1) transform the identification into an observer problem using a suitable model extension that decouples the estimation of non-measured states from the parameters; (2) reconstruct all extended states using suitable nonlinear observers; (3) estimate the parameters using the reconstructed states. The actual estimation of the parameters is based on the intrinsic dependencies of the extended states arising from the definitions of the extended variables. An important advantage of the proposed method is that it allows to identify suitable measurements and/or model structures for which the parameters can be estimated. Furthermore, the proposed identification approach is generally applicable to models of metabolic networks, signal transduction and gene regulation

High-gain nonlinear observer for simple genetic regulation process

High-gain nonlinear observers occur in the nonlinear automatic control theory and are in standard usage in chemical engineering processes. We apply such a type of analysis in the context of a very simple one-gene regulation circuit. In general, an observer combines an analytical differential-equation-based model with partial measurement of the system in order to estimate the non-measured state variables. We use one of the simplest observers, that of Gauthier et al., which is a copy of the original system plus a correction term which is easy to calculate. For the illustration of this procedure, we employ a biological model, recently adapted from Goodwin's old book by De Jong, in which one plays with the dynamics of the concentrations of the messenger RNA coding for a given protein, the protein itself, and a single metabolite. Using the observer instead of the metabolite, it is possible to rebuild the non-measured concentrations of the mRNA and the proteinComment: 9 pages, one figur