In this paper we consider state estimation problems with Boolean measurements for a classical negative loop genetic network governed by a piecewise affine (PWA) model. In the first part, an observer is proposed for the case where full state Boolean measurements are available. In particular sliding modes may occur and this leads to finite time convergence for the observer. In the second part we discuss state estimation with partial state Boolean measurements. A naive approach based on algebraic computation is proposed to solve the initial condition inverse problem. In the third part the observer is used to identify some unknown but fixed parameters of the model. We also investigate the robustness of the observer for a parametric uncertain model, and show that the error bound is proportional to the magnitude of the uncertainty.

 Determination of the observability/detectability properties of a nonlinear system is fundamental to assess the possibility of constructing observers and their expected properties as convergence assignability. For linear systems this task can be solved by well-known techniques, for the unperturbed and also the case with perturbations. However, for nonlinear systems this study is usually a very hard task, in particular when perturbations are present. In this paper a general method to study these properties will be described, and its capabilities and feasibility will be assessed by means of a few case studies related to the culture of phytoplankton in the chemostat.

 In dynamic bioprocess models parameters often appear in a nonlinear way. When designing optimal experiments to calibrate these models, the Fisher Information Matrix explicitly depends on the current parameter estimates. Hence, it is advisable to take this parametric uncertainty into account in the design procedure in order to obtain an experiment which is robust with respect to changes in the parameters. The current paper applies computationally efficient approximate robustifcation strategies based on a worst case scenario. Both methods exploit linearisation techniques to avoid the hard to solve max-min optimisation problems. The methods will be illustrated on a predictive microbiology case study.

 In silico experimentation has opened new ways to analyze biological systems behavior under different conditions. The incorporation of an outer optimization loop may help to find the right operation conditions to achieve specific goals (maximization of a given product concentration, minimization of process energy/time, etc.). Mathematically, this is stated as a dynamic optimization problem being particularly challenging when the system is described by nonlinear sets of partial differential equations as well as when constraints are considered. These issues impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques.

In this work, the control vector parametrization approach is combined with reduced order methods and suitable hybrid global optimization methods to overcome such difficulties. The capabilities of this strategy are illustrated considering the solution of two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model. The presented methodology can be used for the efficient dynamic optimization of generic distributed biological systems.

 We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how to use a continuation method to reconstruct the whole graph of the growth function. Two variants, in continuous and discrete time, are presented. The case of two species in competition is also examined.

 In this paper we consider a well studied model of Glycolysis in yeast cells, leading from Glucose to the end product Ethanol, via a minimal nine steps mechanism. We first linearize each step in the pathway around a given set point and we then assemble the (originally nonlinear) system as a linear system subject to various polytopic uncertainties. We study the effect of the negative feedback-loop that is internally exerted on the system. We then probe the sensitivity of the system to variations in certain variables in order to asses the possible optimality of the system in the $H_2,; H_infty$ and the $L_2 - L_infty,;L_infty -L_infty$ senses.