1
|
Mohammadian M, Sufi Karimi H. Decentralized PI Controller Design for Robust Perfect Adaptation in Noisy Time-Delayed Genetic Regulatory Networks. Neural Process Lett 2023. [DOI: 10.1007/s11063-023-11162-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
|
2
|
State estimator design for genetic regulatory networks with leakage and discrete heterogeneous delays: A nonlinear model transformation approach. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.03.022] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
|
3
|
Liu C, Wang X, Xue Y. Global exponential stability analysis of discrete-time genetic regulatory networks with time-varying discrete delays and unbounded distributed delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.09.047] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
|
4
|
Wu Z, Wang Z, Zhou T. Global stability analysis of fractional-order gene regulatory networks with time delay. INT J BIOMATH 2019. [DOI: 10.1142/s1793524519500670] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Fractional-order gene regulatory networks with time delay (DFGRNs) have proven that they are more suitable to model gene regulation mechanism than integer-order. In this paper, a novel DFGRN is proposed. The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions. On this basis, the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN, and the stability conditions are dependent on the fractional-order [Formula: see text]. Finally, numerical simulations show that the obtained results are reasonable.
Collapse
Affiliation(s)
- Zhaohua Wu
- College of Information Science and Technology, Hunan Agricultural University, Changsha, Hunan 410128, P. R. China
- College of Plant Protection, Hunan Agricultural University, Changsha, Hunan 410128, P. R. China
- Hunan Engineering Research Center for Information Technology in Agriculture, Hunan Agricultural University, Changsha, Hunan 410128, P. R. China
| | - Zhiming Wang
- College of Information Science and Technology, Hunan Agricultural University, Changsha, Hunan 410128, P. R. China
- College of Plant Protection, Hunan Agricultural University, Changsha, Hunan 410128, P. R. China
- Hunan Engineering Research Center for Information Technology in Agriculture, Hunan Agricultural University, Changsha, Hunan 410128, P. R. China
| | - Tiejun Zhou
- College of Information Science and Technology, Hunan Agricultural University, Changsha, Hunan 410128, P. R. China
| |
Collapse
|
5
|
Secondary delay-partition approach to finite-time stability analysis of delayed genetic regulatory networks with reaction–diffusion terms. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.06.018] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
|
6
|
Wu A, Liu L, Huang T, Zeng Z. Mittag-Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments. Neural Netw 2017; 85:118-127. [DOI: 10.1016/j.neunet.2016.10.002] [Citation(s) in RCA: 77] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2016] [Revised: 09/30/2016] [Accepted: 10/09/2016] [Indexed: 11/24/2022]
|
7
|
Wu A, Zeng Z. Global Mittag-Leffler Stabilization of Fractional-Order Memristive Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2017; 28:206-217. [PMID: 28055914 DOI: 10.1109/tnnls.2015.2506738] [Citation(s) in RCA: 50] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
According to conventional memristive neural network theories, neurodynamic properties are powerful tools for solving many problems in the areas of brain-like associative learning, dynamic information storage or retrieval, etc. However, as have often been noted in most fractional-order systems, system analysis approaches for integral-order systems could not be directly extended and applied to deal with fractional-order systems, and consequently, it raises difficult issues in analyzing and controlling the fractional-order memristive neural networks. By using the set-valued maps and fractional-order differential inclusions, then aided by a newly proposed fractional derivative inequality, this paper investigates the global Mittag-Leffler stabilization for a class of fractional-order memristive neural networks. Two types of control rules (i.e., state feedback stabilizing control and output feedback stabilizing control) are designed for the stabilization of fractional-order memristive neural networks, while a list of stabilization criteria is established. Finally, two numerical examples are given to show the effectiveness and characteristics of the obtained theoretical results.
Collapse
|
8
|
Moradi H, Majd VJ. Robust control of uncertain nonlinear switched genetic regulatory networks with time delays: A redesign approach. Math Biosci 2016; 275:10-7. [PMID: 26924600 DOI: 10.1016/j.mbs.2016.02.006] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2014] [Revised: 02/10/2016] [Accepted: 02/17/2016] [Indexed: 10/22/2022]
Abstract
In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based control law that was designed for the unperturbed GRNs with time delays. The switched GRNs are switched from one mode to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law and the transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The redesigned control law forces the GRN to always remain on the sliding surface and the dissipativity is maintained from the initial time in the presence of the norm-bounded perturbations. The global stability of the perturbed GRNs is maintained if the unperturbed model is globally dissipative. The designed control law for the perturbed GRNs guarantees robust exponential or asymptotic stability of the closed-loop network depending on the type of stability of the unperturbed model. The results are applied to a nonlinear switched GRN, and its convergence to the origin is verified by simulation.
Collapse
Affiliation(s)
- Hojjatullah Moradi
- Intelligent Control Systems Laboratory, School of Electrical and Computer Engineering, Tarbiat Modares University, P.O. Box 14115-194, Tehran, Iran
| | - Vahid Johari Majd
- Intelligent Control Systems Laboratory, School of Electrical and Computer Engineering, Tarbiat Modares University, P.O. Box 14115-194, Tehran, Iran.
| |
Collapse
|
9
|
Wang W, Wang Y, Nguang SK, Zhong S, Liu F. Delay partition method for the robust stability of uncertain genetic regulatory networks with time-varying delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.08.045] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
10
|
Zhang X, Wu L, Cui S. An Improved Integral Inequality to Stability Analysis of Genetic Regulatory Networks With Interval Time-Varying Delays. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2015; 12:398-409. [PMID: 26357226 DOI: 10.1109/tcbb.2014.2351815] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
This paper focuses on stability analysis for a class of genetic regulatory networks with interval time-varying delays. An improved integral inequality concerning on double-integral items is first established. Then, we use the improved integral inequality to deal with the resultant double-integral items in the derivative of the involved Lyapunov-Krasovskii functional. As a result, a delay-range-dependent and delay-rate-dependent asymptotical stability criterion is established for genetic regulatory networks with differential time-varying delays. Furthermore, it is theoretically proven that the stability criterion proposed here is less conservative than the corresponding one in [Neurocomputing, 2012, 93: 19-26]. Based on the obtained result, another stability criterion is given under the case that the information of the derivatives of delays is unknown. Finally, the effectiveness of the approach proposed in this paper is illustrated by a pair of numerical examples which give the comparisons of stability criteria proposed in this paper and some literature.
Collapse
|
11
|
Rakkiyappan R, Chandrasekar A, Rihan FA, Lakshmanan S. Exponential state estimation of Markovian jumping genetic regulatory networks with mode-dependent probabilistic time-varying delays. Math Biosci 2014; 251:30-53. [PMID: 24565574 DOI: 10.1016/j.mbs.2014.02.008] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2013] [Revised: 11/19/2013] [Accepted: 02/12/2014] [Indexed: 12/01/2022]
Abstract
In this paper, we investigate a problem of exponential state estimation for Markovian jumping genetic regulatory networks with mode-dependent probabilistic time-varying delays. A new type of mode-dependent probabilistic leakage time-varying delay is considered. Given the probability distribution of the time-delays, stochastic variables that satisfying Bernoulli random binary distribution are formulated to produce a new system which includes the information of the probability distribution. Under these circumstances, the state estimator is designed to estimate the true concentration of the mRNA and the protein of the GRNs. Based on Lyapunov-Krasovskii functional that includes new triple integral terms and decomposed integral intervals, delay-distribution-dependent exponential stability criteria are obtained in terms of linear matrix inequalities. Finally, a numerical example is provided to show the usefulness and effectiveness of the obtained results.
Collapse
Affiliation(s)
- R Rakkiyappan
- Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamilnadu, India.
| | - A Chandrasekar
- Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamilnadu, India
| | - F A Rihan
- Department of Mathematical Sciences, College of Science, UAE University, Al Ain 15551, United Arab Emirates
| | - S Lakshmanan
- Department of Mathematical Sciences, College of Science, UAE University, Al Ain 15551, United Arab Emirates
| |
Collapse
|
12
|
Shokouhi-Nejad H, Rikhtehgar-Ghiasi A. Robust H(∞) observer-based controller for stochastic genetic regulatory networks. Math Biosci 2014; 250:41-53. [PMID: 24530345 DOI: 10.1016/j.mbs.2014.02.003] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2013] [Revised: 11/22/2013] [Accepted: 02/05/2014] [Indexed: 10/25/2022]
Abstract
This study is considered with the robust H∞ observer based controller problem for a nonlinear genetic regulatory network (GRN) includes noise and disturbances, delays, and parameter uncertainties. The nonlinear functions describing the feedback regulation are assumed to satisfy the sector-like conditions; the parameter uncertainties are time-varying and unknown but are norm-bounded, and the delays are time-varying. We aim to design robust observer based controller to stabilize the stochastic GRN such that, for all admissible uncertainties, nonlinearities, stochastic perturbations and time varying delays, the dynamics of the GRN and observer are guaranteed to be robustly asymptotically stable in the mean square sense while achieving the prescribed H∞ disturbance attenuation level. Based on the Lyapunov method and the stochastic analysis technique, it is shown that if a set of linear matrix inequalities (LMIs) are feasible, the desired observer based controller does exist. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical results.
Collapse
|