Robust \(H_\infty\) feedback control for uncertain stochastic delayed genetic regulatory networks with additive and multiplicative noise. (English) Zbl 1207.93099
Summary: Noises are ubiquitous in Genetic Regulatory Networks (GRNs). Gene regulation is inherently a stochastic process because of intrinsic and extrinsic noises that cause kinetic parameter variations and basal rate disturbance. Time delays are usually inevitable due to different biochemical reactions in such GRNs. In this paper, a delayed stochastic model with additive and multiplicative noises is utilized to describe stochastic GRNs. A feedback gene controller design scheme is proposed to guarantee that the GRN is mean-square asymptotically stable with noise attenuation, where the structure of the controllers can be specified according to engineering requirements. By applying control theory and mathematical tools, the analytical solution to the control design problem is given, which helps to provide some insight into synthetic biology and systems biology. The control scheme is employed in a three-gene network to illustrate the applicability and usefulness of the design.
MSC:
| 93E03 | Stochastic systems in control theory (general) |
| 93B36 | \(H^\infty\)-control |
| 93B52 | Feedback control |
| 93D20 | Asymptotic stability in control theory |
Keywords:
genetic regulatory networks (GRNs); robust \(H_{\infty }\) feedback control; noise attenuation; time delayReferences:
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