Analysis And Control Of Genetic Regulatory Networks

Gene expression and regulation processes are the core problem of molecular bi-ology. Genetic regulatory networks (GRNs) are the fundamental problem in studyingsystems biology and synthetic biology. A lot of experiments show that the nonlinearinteractions, time delay, positive and negative regulation and inherently stochastic na-ture of gene regulatory networks. This thesis focuses on the problem of robust stabilityanalysis and robust control for time-delayed genetic regulatory networks under noisesbased on Lyapunov stability theory, It(o|∧)'s formula, Schur lemma, stochastic analysis ap-proach, and Linear Matrix Inequality approach. The main works of this thesis are asfollows:Gene regulation is inherently a stochastic process due to intrinsic and extrinsicnoiseswhichcausethefluctuationsanduncertaintiesofkineticparameters. Ontheotherhand, time delays are usually inevitable due to different biochemical reactions in GRNswhich are also affected by noises. Therefore, in this paper, we propose a GRN modelthat is subject to additive and multiplicative noises as well as time-varying delays. Thetime-varying delay is assumed to belong to an interval and no restriction on the deriva-tiveofthetime-varyingdelayisneeded,whichallowsthedelaytobeafasttime-varyingfunction. Robust stochastic stability of such GRNs with disturbance attenuation is ana-lyzedbyapplyingthestochasticanalysisapproach, inequalityandfree-weighingmatrixtechnique。Based on the Lyapunov method, new stability conditions are derived in theform of linear matrix inequalities that are dependent on the upper and lower bounds oftime delays.Next,A feedback gene controller design scheme is proposed to guarantee that theGRN is mean-square asymptotically stable with noise attenuation, where the structureof the controllers can be specified according to engineering requirements. Suffcientdelay-dependent conditions for the existence of state feedback controllers are proposed,which guarantee mean-square asymptotic stability and a prescribed H_∞performancelevel of the resulting closed-loop systems. Based on H_∞control theory, the designproblem is transformed to a convex optimization problem and the analytical solution tothe control design problem is given, which helps to provide some theoretical foundationto experimental design in synthetic biology. The control scheme is employed in a three-gene network to illustrate the applicability and usefulness of the design.At last, a compact summary of this paper is given by combining the advances of the previous researches in this field and our work.