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

Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

A Pseudospectral Observer for Nonlinear Systems

The article of record as published may be located at http://dx.doi.org/10.2514/6.2005-5845Proceedings of AIAA Guidance, Navigation, and Control Conference ; Paper no. AIAA-2005-5845, San Francisco, California, Aug. 15-18, 2005We present a method for designing an observer for nonlinear systems based on Pseudospectral discretization and a moving horizon strategy. The observer has a low computational burden, fast convergence rate and an ability to handle measurement noise. Our observer can also be applied to nonlinear systems governed by deferential-algebraic equations (DAE) which is very did_cult to deal with by other designs like the unscented Kalman filter. The performance of the proposed observer is demonstrated by numerical experiments on a time-varying chaotic nonlinear system with unknown parameters and also a nonlinear circuit with singularity-induced bifurcation.NAApproved for public release; distribution is unlimited