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2019 | Buch

Backgrounds Kapitel lesen Erstes Kapitel lesen

Analysis and Design of Delayed Genetic Regulatory Networks

verfasst von: Prof. Xian Zhang, Yantao Wang, Prof. Ligang Wu

Verlag: Springer International Publishing

Buchreihe : Studies in Systems, Decision and Control

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book offers an essential introduction to the latest advances in delayed genetic regulatory networks (GRNs) and presents cutting-edge work on the analysis and design of delayed GRNs in which the system parameters are subject to uncertain, stochastic and/or parameter-varying changes. Specifically, the types examined include delayed switching GRNs, delayed stochastic GRNs, delayed reaction–diffusion GRNs, delayed discrete-time GRNs, etc. In addition, the solvability of stability analysis, control and estimation problems involving delayed GRNs are addressed in terms of linear matrix inequality or M-matrix tests.

The book offers a comprehensive reference guide for researchers and practitioners working in system sciences and applied mathematics, and a valuable source of information for senior undergraduates and graduates in these areas. Further, it addresses a gap in the literature by providing a unified and concise framework for the analysis and design of delayed GRNs.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Backgrounds
Abstract
In this chapter we will briefly introduce some background knowledge related to Genetic Regulatory Networks (GRNs).
Xian Zhang, Yantao Wang, Ligang Wu

Analysis of Delayed GRNs

Frontmatter
Chapter 2. Stability Analysis for GRNs with Mixed Delays
Abstract
The chapter will propose an \({\text {M}}\)-matrix-based approach to establish globally asymptotic stability criteria for the nonnegative equilibrium point of GRNs with mixed (i.e., discrete and distributed) delays.
Xian Zhang, Yantao Wang, Ligang Wu
Chapter 3. Stability Analysis of Delayed GRNs
Abstract
The chapter first proves an inequality concerning with double integrals by partitioning the integral domain into two parts and exchanging the order of double integrals over a sub-domain. Then it is mathematically proven that the proposed integral inequality is less conservative than Lemma 1.​14(ii). Thereby, for a class of GRNs with time-varying delays, a pair of delay-range-dependent and delay-rate-dependent asymptotic stability criteria are investigated by constructing an appropriate LKF and applying reciprocally convex techniques. The obtained stability criteria are given in the form of LMIs, which can be easily checked by the Toolbox YALMIP of MATLAB. Furthermore, it is theoretically proven that a stability criterion proposed in this chapter is less conservative than [25, Corollary 3.1]. Finally, numerical examples and their simulation results show that the stability criteria proposed in this chapter may be less conservative than ones in [13, 21, 25, 28, 30]
Xian Zhang, Yantao Wang, Ligang Wu
Chapter 4. Stability Analysis for Delayed Switching GRNs
Abstract
This chapter is concerned with analyzing the global exponential stability of delayed switching GRNs.
Xian Zhang, Yantao Wang, Ligang Wu
Chapter 5. Stability Analysis for Delayed Stochastic GRNs
Abstract
In this chapter we will establish a robust asymptotic mean square stability criterion for delayed stochastic GRNs with parameter uncertainties.
Xian Zhang, Yantao Wang, Ligang Wu
Chapter 6. Stability Analysis for Delayed Reaction-Diffusion GRNs
Abstract
This chapter addresses the problems of asymptotic stability analysis and finite-time stability analysis for delayed reaction-diffusion GRNs, respectively.
Xian Zhang, Yantao Wang, Ligang Wu

Design of Delayed GRNs

Frontmatter
Chapter 7. State Estimation for Delayed GRNs
Abstract
Usually, not all states information (that is, mRNA and protein concentrations) of GRNs are measurable, we have to estimate unmeasured state information by making use of the effective network outputs.
Xian Zhang, Yantao Wang, Ligang Wu
Chapter 8. Guaranteed Cost Control for Delayed GRNs
Abstract
This chapter addresses the problem of state feedback guaranteed cost control for uncertain GRNs with interval time-varying delays. The involved norm-bounded uncertainties are first transformed into external disturbances, and then an LKF approach combined with the convex technique and cone complementarity linearization technique is proposed to investigate a sufficient condition for the existence of expected controllers. Thereby, we design a state feedback guaranteed cost controller which guarantees the resultant closed-loop system is robustly asymptotically stable and its linear quadratic performance has an upper bound. A numerical example is provided to show the effectiveness of the proposed method.
Xian Zhang, Yantao Wang, Ligang Wu
Chapter 9. State Estimation for Delayed Reaction-Diffusion GRNs
Abstract
This chapter addresses the problem of state estimation for delayed reaction-diffusion GRNs under Dirichlet boundary conditions.
Xian Zhang, Yantao Wang, Ligang Wu
Chapter 10. State Estimation for Delayed Stochastic GRNs
Abstract
This chapter addresses the problem of robust \(H_\infty \) filter for a class of uncertain stochastic GRNs with mixed delays. The uncertain stochastic GRNs under consideration are extended to involve Itô-type stochastic disturbance, norm-bounded uncertainties, time-varying discrete delays and distributed delays. By constructing an appropriate LKF and using reciprocal convex technique, LMIs-based sufficient conditions were presented to guarantee that the filtering error systems are robustly asymptotically mean square stable with pre-specified disturbance attenuation level. Furthermore, two numerical examples are given to illustrate the effectiveness of the proposed approach.
Xian Zhang, Yantao Wang, Ligang Wu
Chapter 11. State Estimation for Delayed Discrete-Time GRNs
Abstract
This chapter is concerned with the problem of \(H_\infty \) state estimation for a class of discrete-time GRNs with random delay and external disturbance. The random delay is described by a Markovian chain. The aim is to estimate the concentrations of mRNAs and proteins by designing \(H_\infty \) filter based on available measurement outputs. By using the LKF method, a sufficient LMI condition is first established to ensure the filtering error system to be stochastically stable with a prescribed \(H_\infty \) disturbance attenuation level. The condition is dependent on the transition probability matrix of the random delay. Then, the filter gains are represented via a feasible solution of the LMIs. Moreover, an optimization problem with LMIs constraints is established to design an \(H_\infty \) filter which ensures an optimal \(H_\infty \) disturbance attenuation level. The effectiveness of the proposed approach is illustrated by a numerical example.
Xian Zhang, Yantao Wang, Ligang Wu
Metadaten
Titel
Analysis and Design of Delayed Genetic Regulatory Networks
verfasst von
Prof. Xian Zhang
Yantao Wang
Prof. Ligang Wu
Copyright-Jahr
2019
Electronic ISBN
978-3-030-17098-1
Print ISBN
978-3-030-17097-4
DOI
https://doi.org/10.1007/978-3-030-17098-1

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