H∞ filtering for discrete-time genetic regulatory networks with random delays

A Recursive Approach to Quantized H∞ State Estimation for Genetic Regulatory Networks Under Stochastic Communication Protocols

This paper deals with the finite-horizon quantized H_∞ state estimation problem for a class of discrete time-varying genetic regulatory networks with quantization effects under stochastic communication protocols (SCPs). To better reflect the data-driven flavor of today's biological research, the network measurements (typically gigabytes in size by high-throughput sequencing technologies) are transmitted to a remote state estimator via two independent communication networks of limited bandwidths. To lighten the communication loads and avoid undesired data collisions, the measurement outputs are quantized and then transmitted under two SCPs introduced to schedule the large-scale data transmissions. The purpose of this paper is to design a time-varying state estimator such that the error dynamics of the state estimation satisfies a prescribed H_∞ performance requirement over a finite horizon in the presence of nonlinearities, quantization effects, and SCPs. By utilizing the completing-the-square technique, sufficient conditions are derived to ensure the H_∞ estimation performance and the parameters of the state estimator are designed by solving coupled backward recursive Riccati difference equations. A numerical example is given to illustrate the effectiveness of the design scheme of the proposed state estimator.

State Estimation for Discrete Time-Delayed Genetic Regulatory Networks With Stochastic Noises Under the Round-Robin Protocols

This paper investigates the problem of state estimation for discrete time-delayed genetic regulatory networks with stochastic process noises and bounded exogenous disturbances under the Round-Robin (RR) protocols. The network measurement outputs obtained by two groups of sensors are transmitted to two remote sub-estimators via two independent communication channels, respectively. To lighten the communication loads of the networks and reduce the occurrence rate of data collisions, two RR protocols are utilized to orchestrate the transmission orders of sensor nodes in two groups, respectively. The error dynamics of the state estimation is governed by a switched system with periodic switching parameters. By constructing a transmission-order-dependent Lyapunov-like functional and utilizing the up-to-date discrete Wirtinger-based inequality together with the reciprocally convex approach, sufficient conditions are established to guarantee the exponentially ultimate boundedness of the estimation error dynamics in mean square with a prescribed upper bound on the decay rate. An asymptotic upper bound of the outputs of the estimation errors in mean square is derived and the estimator parameters are then obtained by minimizing such an upper bound subject to linear matrix inequality constraints. The repressilator model is utilized to illustrate the effectiveness of the designed estimator.

Kalman Filtering for Genetic Regulatory Networks with Missing Values

The filter problem with missing value for genetic regulation networks (GRNs) is addressed, in which the noises exist in both the state dynamics and measurement equations; furthermore, the correlation between process noise and measurement noise is also taken into consideration. In order to deal with the filter problem, a class of discrete-time GRNs with missing value, noise correlation, and time delays is established. Then a new observation model is proposed to decrease the adverse effect caused by the missing value and to decouple the correlation between process noise and measurement noise in theory. Finally, a Kalman filtering is used to estimate the states of GRNs. Meanwhile, a typical example is provided to verify the effectiveness of the proposed method, and it turns out to be the case that the concentrations of mRNA and protein could be estimated accurately.

Exponential H∞ filtering for discrete-time switched neural networks with random delays

This paper addresses the exponential H∞ filtering problem for a class of discrete-time switched neural networks with random time-varying delays. The involved delays are assumed to be randomly time-varying which are characterized by introducing a Bernoulli stochastic variable. Effects of both variation range and distribution probability of the time delays are considered. The nonlinear activation functions are assumed to satisfy the sector conditions. Our aim is to estimate the state by designing a full order filter such that the filter error system is globally exponentially stable with an expected decay rate and a H∞ performance attenuation level. The filter is designed by using a piecewise Lyapunov-Krasovskii functional together with linear matrix inequality (LMI) approach and average dwell time method. First, a set of sufficient LMI conditions are established to guarantee the exponential mean-square stability of the augmented system and then the parameters of full-order filter are expressed in terms of solutions to a set of LMI conditions. The proposed LMI conditions can be easily solved by using standard software packages. Finally, numerical examples by means of practical problems are provided to illustrate the effectiveness of the proposed filter design.

Exponential state estimation of Markovian jumping genetic regulatory networks with mode-dependent probabilistic time-varying delays

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.

Robust H(∞) observer-based controller for stochastic genetic regulatory networks

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.