On delayed genetic regulatory networks with polytopic uncertainties: Robust stability analysis

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we investigate the robust asymptotic stability problem of genetic regulatory networks with time-varying delays and polytopic parameter uncertainties. Both cases of differentiable and nondifferentiable time-delays are considered, and the convex polytopic description is utilized to characterize the genetic network model uncertainties. By using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the uncertain delayed genetic networks are established in the form of LMIs, which can be readily verified by using standard numerical software. An important feature of the results reported here is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using up-to-date techniques for achieving delay dependence. Another feature of the results lies in that a novel Lyapunov functional dependent on the uncertain parameters is utilized, which renders the results to be potentially less conservative than those obtained via a fixed Lyapunov functional for the entire uncertainty domain. A genetic network example is employed to illustrate the applicability and usefulness of the developed theoretical results

Synchronization of stochastic genetic oscillator networks with time delays and Markovian jumping parameters

The official published version of the article can be found at the link below.Genetic oscillator networks (GONs) are inherently coupled complex systems where the nodes indicate the biochemicals and the couplings represent the biochemical interactions. This paper is concerned with the synchronization problem of a general class of stochastic GONs with time delays and Markovian jumping parameters, where the GONs are subject to both the stochastic disturbances and the Markovian parameter switching. The regulatory functions of the addressed GONs are described by the sector-like nonlinear functions. By applying up-to-date ‘delay-fractioning’ approach for achieving delay-dependent conditions, we construct novel matrix functional to derive the synchronization criteria for the GONs that are formulated in terms of linear matrix inequalities (LMIs). Note that LMIs are easily solvable by the Matlab toolbox. A simulation example is used to demonstrate the synchronization phenomena within biological organisms of a given GON and therefore shows the applicability of the obtained results.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the UK under Grants BB/C506264/1 and 100/EGM17735, the Royal Society of the UK, the National Natural Science Foundation of China under Grant 60804028, the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China, the International Science and Technology Cooperation Project of China under Grant 2009DFA32050, and the Alexander von Humboldt Foundation of Germany

Robust synchronization of a class of coupled delayed networks with multiple stochastic disturbances: The continuous-time case

In this paper, the robust synchronization problem is investigated for a new class of continuous-time complex networks that involve parameter uncertainties, time-varying delays, constant and delayed couplings, as well as multiple stochastic disturbances. The norm-bounded uncertainties exist in all the network parameters after decoupling, and the stochastic disturbances are assumed to be Brownian motions that act on the constant coupling term, the delayed coupling term as well as the overall network dynamics. Such multiple stochastic disturbances could reflect more realistic dynamical behaviors of the coupled complex network presented within a noisy environment. By using a combination of the Lyapunov functional method, the robust analysis tool, the stochastic analysis techniques and the properties of Kronecker product, we derive several delay-dependent sufficient conditions that ensure the coupled complex network to be globally robustly synchronized in the mean square for all admissible parameter uncertainties. The criteria obtained in this paper are in the form of linear matrix inequalities (LMIs) whose solution can be easily calculated by using the standard numerical software. The main results are shown to be general enough to cover many existing ones reported in the literature. Simulation examples are presented to demonstrate the feasibility and applicability of the proposed results

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Time delay arising in a genetic regulatory network may cause the instability. This paper is concerned with the stability analysis of genetic regulatory networks with interval time-varying delays. Firstly, a relaxed double integral inequality, named as Wirtinger-type double integral inequality (WTDII), is established to estimate the double integral term appearing in the derivative of Lyapunov-Krasovskii functional with a triple integral term. And it is proved theoretically that the proposed WTDII is tighter than the widely used Jensen-based double inequality and the recently developed Wiringter-based double inequality. Then, by applying the WTDII to the stability analysis of a delayed genetic regulatory network, together with the usage of useful information of regulatory functions, several delay-range- and delay-rate-dependent (or delay-rate-independent) criteria are derived in terms of linear matrix inequalities. Finally, an example is carried out to verify the effectiveness of the proposed method and also to show the advantages of the established stability criteria through the comparison with some literature

Finite-Time Stability Analysis of Switched Genetic Regulatory Networks

This paper investigates the finite-time stability problem of switching genetic regulatory networks (GRNs) with interval time-varying delays and unbounded continuous distributed delays. Based on the piecewise Lyapunov-Krasovskii functional and the average dwell time method, some new finite-time stability criteria are obtained in the form of linear matrix inequalities (LMIs), which are easy to be confirmed by the Matlab toolbox. The finite-time stability is taken into account in switching genetic regulatory networks for the first time and the average dwell time of the switching signal is obtained. Two numerical examples are presented to illustrate the effectiveness of our results

An advanced delay-dependent approach of impulsive genetic regulatory networks besides the distributed delays, parameter uncertainties and time-varying delays

In this typescript, we concerned the problem of delay-dependent approach of impulsive genetic regulatory networks besides the distributed delays, parameter uncertainties and time-varying delays. An advanced Lyapunov–Krasovskii functional are defined, which is in triple integral form. Combining the Lyapunov–Krasovskii functional with convex combination method and free-weighting matrix approach the stability conditions are derived with the help of linear matrix inequalities (LMIs). Some available software collections are used to solve the conditions. Lastly, two numerical examples and their simulations are conferred to indicate the feasibility of the theoretical concepts

Robust synchronization for 2-D discrete-time coupled dynamical networks

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini–Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008 and 61174136, the International Science and Technology Cooperation Project of China under Grant No. 2009DFA32050, the Natural Science Foundation of Jiangsu Province of China under Grant BK2011598, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Parameters identification of unknown delayed genetic regulatory networks by a switching particle swarm optimization algorithm

The official published version can be found at the link below.This paper presents a novel particle swarm optimization (PSO) algorithm based on Markov chains and competitive penalized method. Such an algorithm is developed to solve global optimization problems with applications in identifying unknown parameters of a class of genetic regulatory networks (GRNs). By using an evolutionary factor, a new switching PSO (SPSO) algorithm is first proposed and analyzed, where the velocity updating equation jumps from one mode to another according to a Markov chain, and acceleration coefficients are dependent on mode switching. Furthermore, a leader competitive penalized multi-learning approach (LCPMLA) is introduced to improve the global search ability and refine the convergent solutions. The LCPMLA can automatically choose search strategy using a learning and penalizing mechanism. The presented SPSO algorithm is compared with some well-known PSO algorithms in the experiments. It is shown that the SPSO algorithm has faster local convergence speed, higher accuracy and algorithm reliability, resulting in better balance between the global and local searching of the algorithm, and thus generating good performance. Finally, we utilize the presented SPSO algorithm to identify not only the unknown parameters but also the coupling topology and time-delay of a class of GRNs.This research was partially supported by the National Natural Science Foundation of PR China (Grant No. 60874113), the Research Fund for the Doctoral Program of Higher Education (Grant No. 200802550007), the Key Creative Project of Shanghai Education Community (Grant No. 09ZZ66), the Key Foundation Project of Shanghai (Grant No. 09JC1400700), the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant No. GR/S27658/01, the International Science and Technology Cooperation Project of China under Grant No. 2009DFA32050, an International Joint Project sponsored by the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: A survey

This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany