Alain Rapaport

Interval observers for uncertain biological systems

We present a technique for the dynamic estimation of bounds on unmeasured variables (or parameters) of an uncertain dynamical system. Our approach is purely deterministic and relies on interval observers: from (possibly time varying) intervals on the uncertainty and measurements, we compute guaranteed intervals for the unmeasured variables. This method is applicable for a class of non-linear systems met in several biological modellings: two examples are shown, one model of a three stages structured population, and one of biological water treatment.

Software sensors for highly uncertain WWTPs: a new approach based on interval observers

This paper presents the practical implementation of a new robust interval observer on a 1 m3 continuous fixed bed anaerobic reactor used for the treatment of industrial wine distillery wastewater. This interval observer is able to generate guaranteed intervals for the unmeasured variables (i.e. acidogenic and methanogenic bacteria, alkalinity and chemical oxygen demand) from few on-line measurements (i.e. input liquid flow rate, CO2 gaseous flow rate, volatile fatty acids and total inorganic carbon). The main advantage of this approach is its independance with respect to disturbances and uncertainty in the initial conditions, in the kinetics and, last but not least, in the process inputs.

Parallelotopic and practical observers for non-linear uncertain systems

For a class of dynamical systems, with uncertain non-linear terms considered as unknown inputs, we give suffcient 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 arbitrarily small neighbourhood of the origin. Under the hypothesis that bounds are available for the uncertain terms, we build parallelotopic observers providing time-varying bounds for the state variables, even when the system is not observable for unknown inputs. These results are illustrated with a biological model of a structured population.

Priming effect and microbial diversity in ecosystem functioning and response to global change: a modeling approach using the SYMPHONY model.

Integration of the priming effect (PE) in ecosystem models is crucial to better predict the consequences of global change on ecosystem carbon (C) dynamics and its feedbacks on climate. Over the last decade, many attempts have been made to model PE in soil. However, PE has not yet been incorporated into any ecosystem models. Here, we build plant/soil models to explore how PE and microbial diversity influence soil/plant interactions and ecosystem C and nitrogen (N) dynamics in response to global change (elevated CO2 and atmospheric N depositions). Our results show that plant persistence, soil organic matter (SOM) accumulation, and low N leaching in undisturbed ecosystems relies on a fine adjustment of microbial N mineralization to plant N uptake. This adjustment can be modeled in the SYMPHONY model by considering the destruction of SOM through PE, and the interactions between two microbial functional groups: SOM decomposers and SOM builders. After estimation of parameters, SYMPHONY provided realistic predictions on forage production, soil C storage and N leaching for a permanent grassland. Consistent with recent observations, SYMPHONY predicted a CO2 -induced modification of soil microbial communities leading to an intensification of SOM mineralization and a decrease in the soil C stock. SYMPHONY also indicated that atmospheric N deposition may promote SOM accumulation via changes in the structure and metabolic activities of microbial communities. Collectively, these results suggest that the PE and functional role of microbial diversity may be incorporated in ecosystem models with a few additional parameters, improving accuracy of predictions.

Robust regulation of a class of partially observed nonlinear continuous bioreactors

We propose a design of robust dynamic output feedback for the global partial stabilization of a class of continuous stirred bioreactors. Our approachis robust withrespect to exogenous disturbances and functional uncertainties of the kinetics, considered as bounded unknown inputs. The method is based on a design of dynamic guaranteed bounds on the unmeasured variables, conditioned to past measurements and given bounds on the initial condition. This approach is suitable to systems which are not detectable for unknown inputs. The flexibility in the design of the parameters allows the consideration of saturation constraints on the control variable. # 2002 Elsevier Science Ltd. All rights reserved.

Biogeography of soil microbial communities: a review and a description of the ongoing french national initiative

Microbial biogeography is the study of the distribution of microbial diversity on large scales of space and time. This science aims at understanding biodiversity regulation and its link with ecosystem biological functioning, goods and services such as maintenance of productivity, of soil and atmospheric quality, and of soil health. Although the initial concept dates from the early 20th century (Beijerinck (1913) De infusies en de ontdekking der backterien, in: Jaarboek van de Knoniklijke Akademie van Wetenschappen, Muller, Amsterdam), only recently have an increasing number of studies have investigated the biogeographical patterns of soil microbial diversity. A such delay is due to the constraints of the microbial models, the need to develop relevant molecular and bioinformatic tools to assess microbial diversity, and the non-availability of an adequate sampling strategy. Consequently, the conclusions from microbial ecology studies have rarely been generally applicable and even the fundamental power-laws differ because the taxa-area relationship and the influence of global and distal parameters on the spatial distribution of microbial communities have not been examined. In this article we define and discuss the scientific, technical and operational limits and outcomes resulting from soil microbial biogeography together with the technical and logistical feasibility. The main results are that microbial communities are not stochastically distributed on a wide scale and that biogeographical patterns are more influenced by local parameters such as soil type and land use than by distal ones, e.g. climate and geomorphology, contrary to plants and animals. We then present the European soil biological survey network, focusing on the French national initiative and the „ECOMIC-RMQS” project. The objective of the ECOMIC-RMQS project is to characterise the density and diversity of bacterial communities in all soils in the RMQS library in order to assess, for the first time, not only microbial biogeography across the whole of France but also the impact of land use on soil biodiversity (Réseau de Mesures de la Qualité des Sols = French Soil Quality Monitoring Network, 2200 soils covering all the French territory with a systematic grid of sampling). The scientific, technical and logistical outputs are examined with a view to the future prospects needed to develop this scientific domain and its applications in sustainable land use.

Minimal Time Sequential Batch Reactors with Bounded and Impulse Controls for One or More Species

We consider the optimal control problem of feeding in minimal time a tank where several species compete for a single resource, with the objective being to reach a given level of the resource. We allow controls to be bounded measurable functions of time plus possible impulses. For the one-species case, we show that the immediate one-impulse strategy (filling the whole reactor with one single impulse at the initial time) is optimal when the growth function is monotonic. For nonmonotonic growth functions with one maximum, we show that a particular singular arc strategy (precisely defined in section 3) is optimal. These results extend and improve former ones obtained for the class of measurable controls only. For the two-species case with monotonic growth functions, we give conditions under which the immediate one-impulse strategy is optimal. We also give optimality conditions for the singular arc strategy (at a level that depends on the initial condition) to be optimal. The possibility for the immediate one-impulse strategy to be nonoptimal while both growth functions are monotonic is a surprising result and is illustrated with the help of numerical simulations.

Brief paper: Output tracking of continuous bioreactors through recirculation and by-pass

In this paper, we propose to regulate the output of an auto-catalytic bioprocess (a biological process associated with a growth of a micro-organism) by means of a recirculation loop and by-pass. We give conditions on the volume of the reactor and the kinetic function for which it is possible to stabilize the output concentration under a constant or disturbed unmeasured input flow. Furthermore, we obtain convergence of the output variable in finite time with a Lipschitz continuous feedback.

Minimal Time Control of Fed-Batch Processes With Growth Functions Having Several Maxima

We address the issue of minimal time optimal control of fed-batch reactor in presence of complex non monotonic kinetics. Several extremal paths with singular arcs can be locally optimal. We show how a regularization technique can help determining the optimal synthesis, based on a numerical approach.

A Robust Asymptotic Observer for Chemical and Biochemical Reactors

Abstract A simple state observer is proposed for a class of lumped nonlinear time-varying systems useful in chemical and biochemical engineering. It is shown that this asymptotic nonlinear observer is stable in the presence of time-varying elements and robust in the face of initial conditions uncertainty and a total lack of knowledge on the nonlinearities of the system. Experimental results are presented using a model of an anaerobic digestion process for the treatment of industrial wastewater from a wine distillery and tested using real data obtained from a 1 m continuous fixed bed pilot bioreactor.