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

Finite-Time H∞ State Estimation for PDT-Switched Genetic Regulatory Networks With Randomly Occurring Uncertainties

This article is concerned with the problem of finite-time H_∞ state estimation for switched genetic regulatory networks with randomly occurring uncertainties. The persistent dwell-time switching rule, as a more versatile class of switching rules, is considered in this paper. Besides, several random variables that obey the Bernoulli distribution are used to represent randomly occurring uncertainties. The overriding purpose of this article is to design an estimator to ensure that the estimation error system is stochastically finite-time bounded and satisfies the H_∞ performance. Based on this, sufficient conditions for the explicit form of the estimator gains can be obtained by the Lyapunov method. Finally, a numerical example is given to verify the correctness and feasibility of the proposed method.

Sampled-Data State Estimation of Reaction Diffusion Genetic Regulatory Networks via Space-Dividing Approaches

A novel state estimator is designed for genetic regulatory networks with reaction-diffusion terms in this study. First, the diffusion space (where mRNA and protein exist) is divided into several parts and only a point, a line, or a plane, etc., is measured in every subspace to reduce the measurement cost effectively. Then, samplers and network-induced time delay are considered to meet the network transmission requirement. A new criterion to ensure that the estimation error converges to zero is established by using the Lyapunov functional combined with Wirtinger's inequality, reciprocally convex approach, and Halanay's inequality; furthermore, the estimator's parameters are derived by solving linear matrix inequalities. Finally, two simulation examples (including one-dimensional and two-dimensional spaces) are presented to demonstrate the developed scheme's applicability.

A Novel Sigmoid-Function-Based Adaptive Weighted Particle Swarm Optimizer

In this paper, a novel particle swarm optimization (PSO) algorithm is put forward where a sigmoid-function-based weighting strategy is developed to adaptively adjust the acceleration coefficients. The newly proposed adaptive weighting strategy takes into account both the distances from the particle to the global best position and from the particle to its personal best position, thereby having the distinguishing feature of enhancing the convergence rate. Inspired by the activation function of neural networks, the new strategy is employed to update the acceleration coefficients by using the sigmoid function. The search capability of the developed adaptive weighting PSO (AWPSO) algorithm is comprehensively evaluated via eight well-known benchmark functions including both the unimodal and multimodal cases. The experimental results demonstrate that the designed AWPSO algorithm substantially improves the convergence rate of the particle swarm optimizer and also outperforms some currently popular PSO algorithms.

A Scalable Algorithm for Event-Triggered State Estimation With Unknown Parameters and Switching Topologies Over Sensor Networks

An event-triggered distributed state estimation problem is investigated for a class of discrete-time nonlinear stochastic systems with unknown parameters over sensor networks (SNs) subject to switched topologies. An event-triggered communication strategy is employed to govern the information broadcast and reduce the unnecessary resource consumption. Based on the adopted communication strategy, a distributed state estimator is designed to estimate the plant states and also identify the unknown parameters. In the framework of input-to-state stability, sufficient conditions with an average dwell time are established to ensure the boundedness of estimation errors in mean-square sense. In addition, the gains of the designed estimators are dependent on the solution of a set of matrix inequalities whose dimensions are unrelated to the scale of underlying SNs, thereby fulfill the scalability requirement. Finally, an illustrative simulation is utilized to verify the feasibility of the proposed design scheme.

Neural-Network-Based Consensus Control for Multiagent Systems With Input Constraints: The Event-Triggered Case

In this paper, the neural-network (NN)-based consensus control problem is investigated for a class of discrete-time nonlinear multiagent systems (MASs) with a leader subject to input constraints. Relative measurements related to local tracking errors are collected via some smart sensors. A local nonquadratic cost function is first introduced to evaluate the control performance with input constraints. Then, in view of the relative measurements, an NN-based observer under the event-triggered mechanism is designed to reconstruct the dynamics of the local tracking errors, where the adopted event-triggered condition has a time-dependent threshold and the weight of NNs is updated via a new adaptive tuning law catering to the employed event-triggered mechanism. Furthermore, an ideal control policy is developed for the addressed consensus control problem while minimizing the prescribed local nonquadratic cost function. Moreover, an actor-critic NN scheme with online learning is employed to realize the obtained control policy, where the critic NN is a three-layer structure with powerful approximation capability. Through extensive mathematical analysis, the consensus condition is established for the underlying MAS, and the boundedness of the estimated errors is proven for actor and critic NN weights. In addition, the effect from the adopted event-triggered mechanism on the local cost is thoroughly discussed, and the upper bound of the corresponding increment is derived in comparison with time-triggered cases. Finally, a simulation example is utilized to illustrate the usefulness of the proposed controller design scheme.

Observer-Based Fuzzy Output-Feedback Control for Discrete-Time Strict-Feedback Nonlinear Systems With Stochastic Noises

This paper focuses on the observer-based output-feedback control (OBOFC) problem for a class of discrete-time strict-feedback nonlinear systems (DTSFNSs) with both multiplicative process noises and additive measurement noises. A state observer is first designed to estimate immeasurable system states, and then a novel observer-based backstepping control framework is proposed for DTSFNSs with known model information. To be specific, virtual control laws and the actual control law are derived using a variable substitution method that gets rid of the repeated accumulation of measurement noises in the recursive process. Furthermore, for technical derivation, the multiplicative noise is successively bounded by state estimation errors and controlled errors. Stability conditions are obtained to guarantee the exponential mean-square boundedness of the closed-loop system. Moreover, the nonlinear modeling uncertainties are taken into account to better reflect engineering practices. In virtue of the universal approximation property of fuzzy-logic systems, a fuzzy observer and the corresponding fuzzy output-feedback controller are simultaneously constructed to derive the stability criteria by using novel weight updated laws. Simulation studies are performed to test the validity of the proposed OBOFC scheme.

Robust Partial-Nodes-Based State Estimation for Complex Networks Under Deception Attacks

In this paper, the partial-nodes-based state estimators (PNBSEs) are designed for a class of uncertain complex networks subject to finite-distributed delays, stochastic disturbances, as well as randomly occurring deception attacks (RODAs). In consideration of the likely unavailability of the output signals in harsh environments from certain network nodes, only partial measurements are utilized to accomplish the state estimation task for the addressed complex network with norm-bounded uncertainties in both the network parameters and the inner couplings. The RODAs are taken into account to reflect the compromised data transmissions in cyber security. We aim to derive the gain parameters of the estimators such that the overall estimation error dynamics satisfies the specified security constraint in the simultaneous presence of stochastic disturbances and deception signals. Through intensive stochastic analysis, sufficient conditions are obtained to guarantee the desired security performance for the PNBSEs, based on which the estimator gains are acquired by solving certain matrix inequalities with nonlinear constraints. A simulation study is carried out to testify the security performance of the presented state estimation method.

Stubborn State Estimation for Delayed Neural Networks Using Saturating Output Errors

This paper is concerned with the stubborn state estimation of delayed neural networks that subject to a general class of disturbances in measurements, including outliers and impulsive disturbances as its special cases. This class of disturbances may be unbounded, irregular, and assorted; therefore, they can hardly be suppressed by existing identification-based estimation approaches. In this paper, a stubborn state estimator is constructed by intentionally devising a saturation scheme on the injection of output estimation error. The embedded saturation can effectively resist the influences from these measurement disturbances by saturating them. Moreover, the saturation threshold in the designed scheme is not constant but governed by a dynamic equation with parameters to be designed. Benefiting from this adaptiveness, the estimator obtains more freedom in dealing with various disturbances. By combining a novel Lyapunov functional, the generalized sector condition and two latest integral inequalities, a delay-dependent criterion is derived in a less conservative way to check whether the estimation error system with this dynamic saturation is globally stable. A sufficient condition with two tuning scalars is further provided to codesign the gain of the state estimator and the evolution law of the saturation threshold. Finally, two numerical examples are used to illustrate the stubbornness of this state estimator in the presence of measurement outliers or impulsive disturbances.

Distributed Set-Membership Filtering for Multirate Systems Under the Round-Robin Scheduling Over Sensor Networks

In this paper, the distributed set-membership filtering problem is dealt with for a class of time-varying multirate systems in sensor networks with the communication protocol. For relieving the communication burden, the round-Robin (RR) protocol is exploited to orchestrate the transmission order, under which each sensor node only broadcasts partial information to both the corresponding local filter and its neighboring nodes. In order to meet the practical transmission requirements as well as reduce communication cost, the multirate strategy is proposed to govern the sampling/update rate of the plant, the sensors, and the filters. By means of the lifting technique, the augmented filtering error system is established with a unified sampling rate. The main purpose of the addressed filtering problem is to design a set of distributed filters such that, in the simultaneous presence of the RR transmission protocol, the multirate mechanism, and the bounded noises, there exists a certain ellipsoid that includes all possible error states at each time instant. Then, the desired distributed filter gains are obtained by minimizing such an ellipsoid in the sense of the minimum trace of the weighted matrix. The proposed resource-efficient filtering algorithm is of a recursive form, thereby facilitating the online implementation. A numerical simulation example is given to demonstrate the effectiveness of the proposed protocol-based distributed filter design method.

ℓ1-gain filter design of discrete-time positive neural networks with mixed delays

This paper mainly focuses on the filter design with ℓ₁-gain disturbance attenuation performance for a class of discrete-time positive neural networks. Discrete and distributed time-varying delays occurring in neuron transmission are taken into account. Especially, the probabilistic distribution of distributed delays is described by a Bernoulli random process in the system model. First, criteria on the positiveness and the unique equilibrium of discrete-time neural networks are presented. Second, through linear Lyapunov method, sufficient conditions for globally asymptotic stability with ℓ₁-gain disturbance attenuation performance of positive neural networks are proposed. Third, using the results obtained above, criteria on ℓ₁-gain stability of the established filtering error system are presented, based on which a linear programming (LP) approach is put forward to design the desired positive filter. Finally, two examples of applications to water distribution network and genetic regulatory network are given to demonstrate the effectiveness and applicability of the derived results.

Observer-Based Consensus Control for Discrete-Time Multiagent Systems With Coding-Decoding Communication Protocol

In this paper, the consensus control problem is investigated for a class of discrete-time networked multiagent systems (MASs) with the coding-decoding communication protocol (CDCP). Under a directed communication topology, an observer-based control scheme is proposed for each agent by utilizing the relative measurement outputs between the agent itself and its neighboring ones. The signal delivery is in a digital manner, which means that only the sequence of finite coded signals is sent from the observer to the controller. To be specific, the observed data is encoded to certain codewords by a designed coder via the CDCP, and the received codewords are then decoded by the corresponding decoder at the controller side. The purpose of the addressed problem is to design an observer-based controller such that the close-loop MAS achieves the expected consensus performance. First, with the help of the input-to-state stability theory, a theoretical framework for the detectability is established for analyzing and designing the CDCP. Then, under such a communication protocol, some sufficient conditions for the existence of the proposed observer-based controller are derived to guarantee the asymptotic consensus of the MASs. In addition, the controller parameter is explicitly determined in terms of the solution to certain matrix inequalities associated with the information of the communication topology. Finally, a simulation example is given to demonstrate the effectiveness of the developed control strategy.

H∞ State Estimation for Discrete-Time Nonlinear Singularly Perturbed Complex Networks Under the Round-Robin Protocol

This paper investigates the H_∞ state estimation problem for a class of discrete-time nonlinear singularly perturbed complex networks (SPCNs) under the Round-Robin (RR) protocol. A discrete-time nonlinear SPCN model is first devised on two time scales with their discrepancies reflected by a singular perturbation parameter (SPP). The network measurement outputs are transmitted via a communication network where the data transmissions are scheduled by the RR protocol with hope to avoid the undesired data collision. The error dynamics of the state estimation is governed by a switched system with a periodic switching parameter. A novel Lyapunov function is constructed that is dependent on both the transmission order and the SPP. By establishing a key lemma specifically tackling the SPP, sufficient conditions are obtained such that, for any SPP less than or equal to a predefined upper bound, the error dynamics of the state estimation is asymptotically stable and satisfies a prescribed H_∞ performance requirement. Furthermore, the explicit parameterization of the desired state estimator is given by means of the solution to a set of matrix inequalities, and the upper bound of the SPP is then evaluated in the feasibility of these matrix inequalities. Moreover, the corresponding results for linear discrete-time SPCNs are derived as corollaries. A numerical example is given to illustrate the effectiveness of the proposed state estimator design scheme.

Stability Analysis of Genetic Regulatory Networks With General Random Disturbances

This paper establishes the stability criteria for genetic regulatory networks with random disturbances. We assume the nonlinear feedback regulation function to satisfy the sector-like condition and the random perturbation to have a finite second-order moment. First, under the globally Lipschitz condition, the existence and uniqueness of solution to random genetic regulatory networks are considered by exploiting an iterative approximation method. Then, by feat of the random analysis method and matrix technique, sufficient conditions are given to guarantee the noise-to-state stability in mean and globally asymptotic stability in probability, respectively. At last, two simulation examples are exploited in order to verify the validity of the proposed theory.