scholarly journals Dissipativity and Error Feedback Controller Design of Time-Delay Genetic Regulatory Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yonggang Ma ◽  
Junmei Liu ◽  
Jiao Ai
Keyword(s):  
Time Delay ◽  
Regulatory Networks ◽  
Controller Design ◽  
Estimation Error ◽  
Rapid Development ◽  
Genetic Regulation ◽  
Genetic Regulatory Networks ◽  
Error Feedback ◽  
Attraction Set ◽  
Parameter Dependent

Genetic regulatory networks (GRNs) play an important role in the development and evolution of the biological system. With the rapid development of DNA technology, further research on GRNs becomes possible. In this paper, we discuss a class of time-delay genetic regulatory networks with external inputs. Firstly, under some reasonable assumptions, using matrix measures, matrix norm inequalities, and Halanay inequalities, we give the global dissipative properties of the solution of the time-delay genetic regulation networks and estimate the parameter-dependent global attraction set. Secondly, an error feedback control system is designed for the time-delay genetic control networks. Furthermore, we prove that the estimation error of the model is asymptotically stable. Finally, two examples are used to illustrate the validity of the theoretical results.

scholarly journals State Observer Design for Delayed Genetic Regulatory Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Li-Ping Tian ◽  
Zhi-Jun Wang ◽  
Amin Mohammadbagheri ◽  
Fang-Xiang Wu
Keyword(s):  
Regulatory Network ◽  
Regulatory Networks ◽  
Estimation Error ◽  
State Observer ◽  
Genetic Regulatory Networks ◽  
Genetic Regulatory Network ◽  
Observer Design ◽  
Linear Matrix ◽  
Globally Asymptotically Stable ◽  
Internal States

Genetic regulatory networks are dynamic systems which describe the interactions among gene products (mRNAs and proteins). The internal states of a genetic regulatory network consist of the concentrations of mRNA and proteins involved in it, which are very helpful in understanding its dynamic behaviors. However, because of some limitations such as experiment techniques, not all internal states of genetic regulatory network can be effectively measured. Therefore it becomes an important issue to estimate the unmeasured states via the available measurements. In this study, we design a state observer to estimate the states of genetic regulatory networks with time delays from available measurements. Furthermore, based on linear matrix inequality (LMI) approach, a criterion is established to guarantee that the dynamic of estimation error is globally asymptotically stable. A gene repressillatory network is employed to illustrate the effectiveness of our design approach.

scholarly journals On convergence for hybrid models of gene regulatory networks under polytopic uncertainties: a Lyapunov approach

2021 ◽  
Vol 83 (6-7) ◽  
Author(s):  
Mirko Pasquini ◽  
David Angeli
Keyword(s):  
Lyapunov Function ◽  
Regulatory Networks ◽  
Sliding Mode ◽  
Uncertain System ◽  
Hybrid Models ◽  
Genetic Regulatory Networks ◽  
Linear Matrix ◽  
Affine Model ◽  
Polytopic Uncertainties ◽  
Parameter Dependent

AbstractHybrid models of genetic regulatory networks allow for a simpler analysis with respect to fully detailed quantitative models, still maintaining the main dynamical features of interest. In this paper we consider a piecewise affine model of a genetic regulatory network, in which the parameters describing the production function are affected by polytopic uncertainties. In the first part of the paper, after recalling how the problem of finding a Lyapunov function is solved in the nominal case, we present the considered polytopic uncertain system and then, after describing how to deal with sliding mode solutions, we prove a result of existence of a parameter dependent Lyapunov function subject to the solution of a feasibility linear matrix inequalities problem. In the second part of the paper, based on the previously described Lyapunov function, we are able to determine a set of domains where the system is guaranteed to converge, with the exception of a zero measure set of times, independently from the uncertainty realization. Finally a three nodes network example shows the validity of the results.

Discrete Networks as a Suitable Approach for the Analysis of Genetic Regulation

2009 ◽  
pp. 530-540
Author(s):  
Elizabeth Santiago-Cortés
Keyword(s):  
Transcription Factors ◽  
Dynamical Systems ◽  
Regulatory Networks ◽  
Dynamical Behavior ◽  
Genetic Regulation ◽  
Genetic Regulatory Networks ◽  
Theoretical Studies ◽  
Biological Interpretation ◽  
Complex Dynamical Behavior ◽  
Discrete Networks

Biological systems are composed of multiple interacting elements; in particular, genetic regulatory networks are formed by genes and their interactions mediated by transcription factors. The establishment of such networks is critical to guarantee the reliability of transcriptional performance in any organism. The study of genetic regulatory networks as dynamical systems is a helpful methodology to understand the transcriptional behavior of the genome. From a number of theoretical studies, it is known that networks present a complex dynamical behavior that includes stability, redundancy, homeostasis, and multistationarity. In this chapter we present some particular biological processes modeled as discrete networks to show that the theoretical properties of networks have a clear biological interpretation.

Exponential state estimation for discrete-time switched genetic regulatory networks with random delays

2014 ◽  
Vol 92 (9) ◽  
pp. 976-986 ◽  
Author(s):  
K. Mathiyalagan ◽  
R. Sakthivel ◽  
Hongye Su
Keyword(s):  
State Estimation ◽  
Discrete Time ◽  
Time Delays ◽  
Regulatory Networks ◽  
Estimation Error ◽  
Average Dwell Time ◽  
Genetic Regulatory Networks ◽  
Linear Matrix ◽  
State Estimator ◽  
Exponentially Stable

This paper is concerned with the problem of state estimator design for a class of discrete-time switched genetic regulatory networks (GRNs) with random time delays. The involved time delays are assumed to be randomly time-varying and are modeled by introducing Bernoulli distributed sequences. By using a piecewise Lyapunov–Krasovskii functional together with the linear matrix inequality (LMI) approach, we design a delay-distributed dependent state estimator such that the estimation error system is globally exponentially stable. Further, a class of switching signals specified by the average dwell time is identified to guarantee the exponential state estimation. All the conditions are established in the framework of LMIs, which can easily be solved by using standard numerical software. If a set of LMIs are feasible, then the desired state estimator can be obtained. Finally, a numerical example with simulation result is provided for the GRN model to illustrate the applicability and usefulness of the obtained theory.

scholarly journals Kalman Filtering for Genetic Regulatory Networks with Missing Values

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Qiongbin Lin ◽  
Qiuhua Liu ◽  
Tianyue Lai ◽  
Wu Wang
Keyword(s):  
Kalman Filtering ◽  
Time Delays ◽  
Regulatory Networks ◽  
Missing Values ◽  
Genetic Regulation ◽  
Genetic Regulatory Networks ◽  
Measurement Noise ◽  
Process Noise ◽  
Missing Value ◽  
Measurement Equations

The filter problem with missing value for genetic regulation networks (GRNs) is addressed, in which the noises exist in both the state dynamics and measurement equations; furthermore, the correlation between process noise and measurement noise is also taken into consideration. In order to deal with the filter problem, a class of discrete-time GRNs with missing value, noise correlation, and time delays is established. Then a new observation model is proposed to decrease the adverse effect caused by the missing value and to decouple the correlation between process noise and measurement noise in theory. Finally, a Kalman filtering is used to estimate the states of GRNs. Meanwhile, a typical example is provided to verify the effectiveness of the proposed method, and it turns out to be the case that the concentrations of mRNA and protein could be estimated accurately.

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