Event-triggered H ∞ state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays

In this paper, the event-triggered H ∞ state estimation problem is investigated for a class of discrete-time stochastic genetic regulatory networks with both Markovian jumping parameters and time-varying delays. The jumping parameters are governed by a homogeneous Markovian chain and the time-varying delays under consideration occur in both the feedback regulatory process and transcription process. The aim of this paper is to estimate the concentrations of mRNA and protein in such genetic regulatory networks by using the available measurement outputs. In order to reduce the information communication burden, the event-triggered mechanism is adopted and the measurement outputs are only transmitted to the estimator when a certain triggered condition is met. By constructing an appropriate Lyapunov functional, some sufficient conditions are derived under which the estimation error dynamics is stochastically stable and the H ∞ performance constraint is satisfied. Based on the analysis results, the desired H ∞ estimator parameters are designed in terms of the solution to a set of matrix inequalities that can be easily solved by the Matlab toolboxes. Finally, a simulation example is provided to illustrate the effectiveness of the proposed event-triggered state estimation scheme.

[1]  Huijun Gao,et al.  Event-Based $H_{\infty}$ Filter Design for a Class of Nonlinear Time-Varying Systems With Fading Channels and Multiplicative Noises , 2015, IEEE Transactions on Signal Processing.

[2]  Zidong Wang,et al.  Envelope-constrained H∞ filtering with fading measurements and randomly occurring nonlinearities: The finite horizon case , 2015, Autom..

[3]  Zhi Chen,et al.  Optimal phase searching of PTS using modified genetic algorithm for PAPR reduction in OFDM systems , 2014, Science China Information Sciences.

[4]  Mario Lefebvre,et al.  Analytical solutions to LQG homing problems in one dimension , 2014 .

[5]  Yeung Sam Hung,et al.  Stability analysis of uncertain genetic sum regulatory networks , 2008, Autom..

[6]  Jun Hu,et al.  State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays , 2014, Int. J. Gen. Syst..

[7]  Zidong Wang,et al.  State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates , 2009 .

[8]  Jun Hu,et al.  A recursive approach to non-fragile filtering for networked systems with stochastic uncertainties and incomplete measurements , 2015, J. Frankl. Inst..

[9]  K. Aihara,et al.  Stability of genetic regulatory networks with time delay , 2002 .

[10]  Huajing Fang,et al.  Robust non-fragile H∞ state estimation for discrete-time genetic regulatory networks with Markov jump delays and uncertain transition probabilities , 2015, Neurocomputing.

[11]  Fan Wu,et al.  Optimal resource allocation for transmission diversity in multi-radio access networks: a coevolutionary genetic algorithm approach , 2012, Science China Information Sciences.

[12]  P. Balasubramaniam,et al.  Robust asymptotic stability of fuzzy Markovian jumping genetic regulatory networks with time-varying delays by delay decomposition approach , 2011 .

[13]  Kazuyuki Aihara,et al.  Modeling genetic switches with positive feedback loops. , 2003, Journal of theoretical biology.

[14]  Zidong Wang,et al.  Robust filtering for stochastic genetic regulatory networks with time-varying delay. , 2009, Mathematical biosciences.

[15]  Yonghui Sun,et al.  Stochastic stability of Markovian switching genetic regulatory networks , 2009 .

[16]  Dong,et al.  Asymptotic Stability of Markovian Jumping Genetic Regulatory Networks with Random Delays , 2013 .

[17]  Jinde Cao,et al.  Asymptotic and robust stability of genetic regulatory networks with time-varying delays , 2008, Neurocomputing.

[18]  Saleh Yousefi,et al.  Genetic algorithm approach for QoS-based tree topology construction in IEEE 802.16 mesh networks , 2012, Science China Information Sciences.

[19]  Zidong Wang,et al.  H∞ state estimation with fading measurements, randomly varying nonlinearities and probabilistic distributed delays , 2015 .

[20]  James Lam,et al.  Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[21]  James Lam,et al.  Filtering for Nonlinear Genetic Regulatory Networks With Stochastic Disturbances , 2008, IEEE Transactions on Automatic Control.

[22]  Jinde Cao,et al.  Stability analysis for stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays , 2010, Neurocomputing.

[23]  James Lam,et al.  Robust state estimation for stochastic genetic regulatory networks , 2010, Int. J. Syst. Sci..

[24]  D. A. Baxter,et al.  Mathematical Modeling of Gene Networks , 2000, Neuron.

[25]  Edwin E. Yaz,et al.  Robust and resilient state-dependent control of discrete-time nonlinear systems with general performance criteria , 2014 .

[26]  Shuai Liu,et al.  Probability-guaranteed set-membership filtering for systems with incomplete measurements , 2015, Autom..

[27]  Hamid Reza Momeni,et al.  H∞ mode-independent filter design for Markovian jump genetic regulatory networks with time-varying delays , 2012, Neurocomputing.

[28]  E. Davidson,et al.  Modeling transcriptional regulatory networks. , 2002, BioEssays : news and reviews in molecular, cellular and developmental biology.

[29]  Qi Li,et al.  Event-triggered synchronization control for complex networks with uncertain inner coupling , 2015, Int. J. Gen. Syst..

[30]  Wenwu Yu,et al.  Estimating Uncertain Delayed Genetic Regulatory Networks: An Adaptive Filtering Approach , 2009, IEEE Transactions on Automatic Control.

[31]  Huijun Gao,et al.  Finite-horizon reliable control with randomly occurring uncertainties and nonlinearities subject to output quantization , 2015, Autom..

[32]  Zidong Wang,et al.  Sampled‐data H∞ filtering for stochastic genetic regulatory networks , 2011 .

[33]  Dong Yue,et al.  Event-based H∞ filtering for networked system with communication delay , 2012, Signal Process..

[34]  Gang Feng,et al.  Distributed event-triggered control of multi-agent systems with combinational measurements , 2013, Autom..

[35]  Fuad E. Alsaadi,et al.  Nonfragile $H_{\infty}$ Fuzzy Filtering With Randomly Occurring Gain Variations and Channel Fadings , 2016, IEEE Transactions on Fuzzy Systems.

[36]  Donghua Zhou,et al.  Event-Based Recursive Distributed Filtering Over Wireless Sensor Networks , 2015, IEEE Transactions on Automatic Control.

[37]  James Lam,et al.  Finite-Horizon ${\cal H}_{\infty}$ Control for Discrete Time-Varying Systems With Randomly Occurring Nonlinearities and Fading Measurements , 2015, IEEE Transactions on Automatic Control.

[38]  Huijun Gao,et al.  Finite-horizon estimation of randomly occurring faults for a class of nonlinear time-varying systems , 2014, Autom..