Local Identification of Piecewise Deterministic Models of Genetic Networks

We address the identification of genetic networks under stationary conditions. A stochastic hybrid description of the genetic interactions is considered and an approximation of it in stationary conditions is derived. Contrary to traditional structure identification methods based on fitting deterministic models to several perturbed equilibria of the system, we set up an identification strategy which exploits randomness as an inherent perturbation of the system. Estimation of the dynamics of the system from sampled data under stability constraints is then formulated as a convex optimization problem. Numerical results are shown on an artificial genetic network model. While our methods are conceived for the identification of interaction networks, they can as well be applied in the study of general piecewise deterministic systems with randomly switching inputs.

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