Robust estimation for hybrid models of genetic networks

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.