Viability, Invariance and Reachability for Controlled Piecewise Deterministic Markov Processes Associated to Gene Networks

Details Viability, Invariance and Reachability for Controlled Piecewise Deterministic Markov Processes Associated to Gene Networks Viability, Invariance and Reachability for Controlled Piecewise Deterministic Markov Processes Associated to Gene Networks

2010-02-10

arxiv.org/abs/1002.2242v1

ESAIM: Control, Optimisation and Calculus of Variations (2011), online first DOI:10.1051/cocv/2010103

Mathematics

Optimization and Control

submitted

Scientific paper

10.1051/cocv/2010103

We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general On/Off systems, Cook's model for haploinssuficiency, and a stochastic model for bacteriophage lambda.

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