Sampled-data synchronization control of dynamical networks with stochastic sampling

Copyright @ 2012 IEEEThis technical note is concerned with the sampled-data synchronization control problem for a class of dynamical networks. The sampling period considered here is assumed to be time-varying that switches between two different values in a random way with given probability. The addressed synchronization control problem is first formulated as an exponentially mean-square stabilization problem for a new class of dynamical networks that involve both the multiple probabilistic interval delays (MPIDs) and the sector-bounded nonlinearities (SBNs). Then, a novel Lyapunov functional is constructed to obtain sufficient conditions under which the dynamical network is exponentially mean-square stable. Both Gronwall's inequality and Jenson integral inequality are utilized to substantially simplify the derivation of the main results. Subsequently, a set of sampled-data synchronization controllers is designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical simulation example is employed to show the effectiveness of the proposed sampled-data synchronization control scheme.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Natural Science Foundation of China under Grants 61028008, 60974030, 61134009 and 61104125, the National 973 Program of China under Grant 2009CB320600, 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

Filtering for Discrete-Time Genetic Regulatory Networks with Random Delay Described by a Markovian Chain

This paper is concerned with the ∞ filtering problem for a class of discretetime genetic regulatory networks with random delay and external disturbance. The aim is to design ∞ filter to estimate the true concentrations of mRNAs and proteins based on available measurement data. By introducing an appropriate Lyapunov function, a sufficient condition is derived in terms of linear matrix inequalities (LMIs) which makes the filtering error system stochastically stable with a prescribed ∞ disturbance attenuation level. The filter gains are given by solving the LMIs. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach; that is, our approach is available for a smaller ∞ disturbance attenuation level than one in

On the transient and steady-state estimates of interval genetic regulatory networks

This paper is concerned with the transient and steady-state estimates of a class of genetic regulatory networks (GRNs). Some sufficient conditions, which do not only present the transient estimate but also provide the estimates of decay rate and decay coefficient of the GRN with interval parameter uncertainties (interval GRN), are established by means of linear matrix inequality (LMI) and Lyapunov-Krasovskii functional. Moreover, the steady-state estimate of the proposed GRN model is also investigated. Furthermore, it is well known that gene regulation is an intrinsically noisy process due to intracellular and extracellular noise perturbations and environmental fluctuations. Then, by utilizing stochastic differential equation theory, the obtained results are extended to the case with noise perturbations due to natural random fluctuations. All the conditions are expressed within the framework of LMIs, which can easily be computed by using standard numerical software. A three-gene network is provided to illustrate the effectiveness of the theoretical results