Asynchronous Dissipative State Estimation for Stochastic Complex Networks With Quantized Jumping Coupling and Uncertain Measurements

Recursive Filtering Under Probabilistic Encoding-Decoding Schemes: Handling Randomly Occurring Measurement Outliers

This article focuses on the recursive filtering problem for networked time-varying systems with randomly occurring measurement outliers (ROMOs), where the so-called ROMOs denote a set of large-amplitude perturbations on measurements. A new model is presented to describe the dynamical behaviors of ROMOs by using a set of independent and identically distributed stochastic scalars. A probabilistic encoding-decoding scheme is exploited to convert the measurement signal into the digital format. For the purpose of preserving the filtering process from the performance degradation induced by measurement outliers, a novel recursive filtering algorithm is developed by using the active detection-based method where the "problematic" measurements (i.e., the measurements contaminated by outliers) are removed from the filtering process. A recursive calculation approach is proposed to derive the time-varying filter parameter via minimizing such the upper bound on the filtering error covariance. The uniform boundedness of the resultant time-varying upper bound is analyzed for the filtering error covariance by using the stochastic analysis technique. Two numerical examples are presented to verify the effectiveness and correctness of our developed filter design approach.

Hybrid Adjusting Variables-Dependent Event-Based Finite-Time State Estimation for Two-Time-Scale Markov Jump Complex Networks

This article investigates the problem of dynamic event-triggered finite-time H∞ state estimation for a class of discrete-time nonlinear two-time-scale Markov jump complex networks. A hybrid adjusting variables-dependent dynamic event-triggered mechanism (DETM) is proposed to regulate the releases of measurement outputs of a node to a remote state estimator. Such a DETM contains both an additive dynamically adjusting variable (DAV) and a multiplicative adaptively adjusting variable. The aim is to design a DETM-based mode-dependent state estimator, which guarantees that the resultant error dynamics is stochastically finite-time bounded with H∞ performance. By constructing a mode-dependent Lyapunov function with multiple DAVs and a singular perturbation parameter associated with time scales, a matrix-inequalities-based sufficient condition is derived, the feasible solutions of which facilitate the design of the parameters of the state estimator. The validity of the designed state estimator and the superiority of the devised DETM are verified by two examples. It is verified that the devised DETM is capable of saving network resources and simultaneously improving the estimation performance.

Distributed Extended State Estimation for Complex Networks With Nonlinear Uncertainty

This article studies the distributed state estimation issue for complex networks with nonlinear uncertainty. The extended state approach is used to deal with the nonlinear uncertainty. The distributed state predictor is designed based on the extended state system model, and the distributed state estimator is designed by using the measurement of the corresponding node. The prediction error and the estimation error are derived. The prediction error covariance (PEC) is obtained in terms of the recursive Riccati equation, and the upper bound of the PEC is minimized by designing an optimal estimator gain. With the vectorization approach, a sufficient condition concerning stability of the upper bound is developed. Finally, a numerical example is presented to illustrate the effectiveness of the designed extended state estimator.

Event-Triggered Recursive State Estimation for Stochastic Complex Dynamical Networks Under Hybrid Attacks

In this article, the event-based recursive state estimation problem is investigated for a class of stochastic complex dynamical networks under cyberattacks. A hybrid cyberattack model is introduced to take into account both the randomly occurring deception attack and the randomly occurring denial-of-service attack. For the sake of reducing the transmission rate and mitigating the network burden, the event-triggered mechanism is employed under which the measurement output is transmitted to the estimator only when a preset condition is satisfied. An upper bound on the estimation error covariance on each node is first derived through solving two coupled Riccati-like difference equations. Then, the desired estimator gain matrix is recursively acquired that minimizes such an upper bound. Using the stochastic analysis theory, the estimation error is proven to be stochastically bounded with probability 1. Finally, an illustrative example is provided to verify the effectiveness of the developed estimator design method.

H∞Bipartite Synchronization of Double-Layer Markov Switched Cooperation-Competition Neural Networks: A Distributed Dynamic Event-Triggered Mechanism

In this article, the H_∞ bipartite synchronization issue is studied for a class of discrete-time coupled switched neural networks with antagonistic interactions via a distributed dynamic event-triggered control scheme. Essentially different from most current literature, the topology switching of the investigated signed graph is governed by a double-layer switching signal, which integrates a flexible deterministic switching regularity, the persistent dwell-time switching, into a Markov chain to represent the variation of transition probability. Considering the coexistence of cooperative and antagonistic interactions among nodes, the bipartite synchronization of which the dynamics of nodes converge to values with the same modulus but the opposite signs is explored. A distributed control strategy based on the dynamic event-triggered mechanism is utilized to achieve this goal. Under this circumstance, the information update of the controller presents an aperiodic manner, and the frequency of data transmission can be reduced extensively. Thereafter, by constructing a novel Lyapunov function depending on both the switching signal and the internal dynamic nonnegative variable of the triggering mechanism, the exponential stability of bipartite synchronization error systems in the mean-square sense is analyzed. Finally, two simulation examples are provided to illustrate the effectiveness of the derived results.

Compensation-Based Output Feedback Control for Fuzzy Markov Jump Systems With Random Packet Losses

This article is concerned with the problem of compensation-based output feedback control for Takagi-Sugeno fuzzy Markov jump systems subject to packet losses. The phenomenon of packet losses is assumed to randomly occur in the feedback channel, which is modeled by a Bernoulli process. Employing the single exponential smoothing method as a compensation scheme, the missing measurements are predicted to help offset the impact of packet losses on system performance. Then, an asynchronous output feedback controller is designed by the hidden Markov model. Based on the mode-dependent Lyapunov function, some novel sufficient conditions on the controller existence are derived such that the closed-loop system is stochastically stable with strict dissipativity. Besides, an algorithm for determining the optimal smoothing parameter is proposed. Finally, the validity and advantages of the design approach are manifested by some simulation results.

A Probabilistically Quantized Learning Control Framework for Networked Linear Systems

In this article, we consider quantized learning control for linear networked systems with additive channel noise. Our objective is to achieve high tracking performance while reducing the communication burden on the communication network. To address this problem, we propose an integrated framework consisting of two modules: a probabilistic quantizer and a learning scheme. The employed probabilistic quantizer is developed by employing a Bernoulli distribution driven by the quantization errors. Three learning control schemes are studied, namely, a constant gain, a decreasing gain sequence satisfying certain conditions, and an optimal gain sequence that is recursively generated based on a performance index. We show that the control with a constant gain can only ensure the input error sequence to converge to a bounded sphere in a mean-square sense, where the radius of this sphere is proportional to the constant gain. On the contrary, we show that the control that employs any of the two proposed gain sequences drives the input error to zero in the mean-square sense. In addition, we show that the convergence rate associated with the constant gain is exponential, whereas the rate associated with the proposed gain sequences is not faster than a specific exponential trend. Illustrative simulations are provided to demonstrate the convergence rate properties and steady-state tracking performance associated with each gain, and their robustness against modeling uncertainties.

Recursive Minimum-Variance Filter Design for State-Saturated Complex Networks With Uncertain Coupling Strengths Subject to Deception Attacks

In this article, the recursive filtering problem is investigated for state-saturated complex networks (CNs) subject to uncertain coupling strengths (UCSs) and deception attacks. The measurement signals transmitted via the communication network may suffer from deception attacks, which are governed by Bernoulli-distributed random variables. The purpose of the problem under consideration is to design a minimum-variance filter for CNs with deception attacks, state saturations, and UCSs such that upper bounds on the resulting error covariances are guaranteed. Then, the expected filter gains are acquired via minimizing the traces of such upper bounds, and sufficient conditions are established to ensure the exponential mean-square boundedness of the filtering errors. Finally, two simulation examples (including a practical application) are exploited to validate the effectiveness of our designed approach.

Recursive state estimation for a class of nonlinear uncertain coupled complex networks subject to random link failures and packet disorders

This paper is concerned with the recursive state estimation (RSE) problem under minimum mean-square error sense for a class of nonlinear complex networks (CNs) with uncertain inner coupling, random link failures and packet disorders. Firstly, a set of random variables obeying the Bernoulli distribution is adopted to characterize whether there are connections between different network units, i.e., there is no random link failure when the random variable is equal to 1, otherwise the random link failure occurs. In addition, the inner coupling strength is assumed to be varying within a given interval and the phenomenon of packet disorders caused by the random transmission delay (RTD) is also taken into account. In our study, the nonlinearity satisfies the continuously differentiable condition, which can be linearized by resorting to the Taylor expansion. The focus of the addressed RSE problem is on the design of an RSE approach in the mean-square error sense such that, for all uncertain inner coupling, random link failures and packet disorders, a suboptimal upper bound of the state estimation error covariance is obtained and minimized by parameterizing the state estimator gain with explicit expression form. Furthermore, a sufficient condition with respect to the uniform boundedness of state estimation error in mean-square sense is elaborated. Finally, a numerical experiment is introduced to demonstrate the validity of the presented RSE approach.

Event-Triggered Filtering for Delayed Markov Jump Nonlinear Systems with Unknown Probabilities

This paper focuses on the problem of event-triggered H∞ asynchronous filtering for Markov jump nonlinear systems with varying delay and unknown probabilities. An event-triggered scheduling scheme is adopted to decrease the transmission rate of measured outputs. The devised filter is mode dependent and asynchronous with the original system, which is represented by a hidden Markov model (HMM). Both the probability information involved in the original system and the filter are assumed to be only partly available. Under this framework, via employing the Lyapunov–Krasovskii functional and matrix inequality transformation techniques, a sufficient condition is given and the filter is further devised to ensure that the resulting filtering error dynamic system is stochastically stable with a desired H∞ disturbance attenuation performance. Lastly, the validity of the presented filter design scheme is verified through a numerical example.

A Partial-Node-Based Approach to State Estimation for Complex Networks With Sensor Saturations Under Random Access Protocol

In this article, the robust finite-horizon state estimation problem is investigated for a class of time-varying complex networks (CNs) under the random access protocol (RAP) through available measurements from only a part of network nodes. The underlying CNs are subject to randomly occurring uncertainties, randomly occurring multiple delays, as well as sensor saturations. Several sequences of random variables are employed to characterize the random occurrences of parameter uncertainties and multiple delays. The RAP is adopted to orchestrate the data transmission at each time step based on a Markov chain. The aim of the addressed problem is to design a series of robust state estimators that make use of the available measurements from partial network nodes to estimate the network states, under the RAP and over a finite horizon, such that the estimation error dynamics achieves the prescribed H_∞ performance requirement. Sufficient conditions are provided for the existence of such time-varying partial-node-based H_∞ state estimators via stochastic analysis and matrix operations. The desired estimators are parameterized by solving certain recursive linear matrix inequalities. The effectiveness of the proposed state estimation algorithm is demonstrated via a simulation example.

Synchronization of Stochastic Complex Dynamical Networks Subject to Consecutive Packet Dropouts

This paper studies the modeling and synchronization problems for stochastic complex dynamical networks subject to consecutive packet dropouts. Different from some existing research results, both probability characteristic and upper bound of consecutive packet dropouts are involved in the proposed approach of controller design. First, an error dynamical network with stochastic and bounded delay is established by step-delay method, where the randomness of the bounded delay can be verified later by the probability theory method. A new modeling method is introduced to reflect the probability characteristic of consecutive packet dropouts. Based on the proposed model, some sufficient conditions are proposed under which the error dynamical network is globally exponentially synchronized in the mean square sense. Subsequently, a probability-distribution-dependent controller design procedure is then proposed. Finally, two numerical examples with simulations are provided to validate the analytical results and demonstrate the less conservatism of the proposed model method.

Adaptive Synchronization of Fractional-Order Output-Coupling Neural Networks via Quantized Output Control

This article focuses on the adaptive synchronization for a class of fractional-order coupled neural networks (FCNNs) with output coupling. The model is new for output coupling item in the FCNNs that treat FCNNs with state coupling as its particular case. Novel adaptive output controllers with logarithm quantization are designed to cope with the stability of the fractional-order error systems for the first attempt, which is also an effective way to synchronize fractional-order complex networks. Based on fractional-order Lyapunov functionals and linear matrix inequalities (LMIs) method, sufficient conditions rather than algebraic conditions are built to realize the synchronization of FCNNs with output coupling. A numerical simulation is put forward to substantiate the applicability of our results.

l₂-l∞ State Estimation for Persistent Dwell-Time Switched Coupled Networks Subject to Round-Robin Protocol

This article is concerned with the issue of l₂ - l_∞ state estimation for nonlinear coupled networks, where the variation of coupling mode is governed by a set of switching signals satisfying a persistent dwell-time property. To solve the problem of data collisions in a constrained communication network, the round-robin protocol, as an important scheduling strategy for orchestrating the transmission order of sensor nodes, is introduced. Redundant channels with signal quantization are used to improve the reliability of data transmission. The main purpose is to determine an estimator that can guarantee the exponential stability in mean square sense and an l₂ - l_∞ performance level of the estimation error system. Based on the Lyapunov method, sufficient conditions for the addressed problem are established. The desired estimator gains can be obtained by addressing a convex optimization case. The correctness and availability of the developed approach are finally explained via two illustrative examples.

Finite-Horizon H∞ State Estimation for Stochastic Coupled Networks With Random Inner Couplings Using Round-Robin Protocol

This article is concerned with the problem of finite-horizon H_∞ state estimation for time-varying coupled stochastic networks through the round-robin scheduling protocol. The inner coupling strengths of the considered coupled networks are governed by a random sequence with known expectations and variances. For the sake of mitigating the occurrence probability of the network-induced phenomena, the communication network is equipped with the round-robin protocol that schedules the signal transmissions of the sensors' measurement outputs. By using some dedicated approximation techniques, an uncertain auxiliary system with stochastic parameters is established where the multiplicative noises enter the coefficient matrix of the augmented disturbances. With the established auxiliary system, the desired finite-horizon H_∞ state estimator is acquired by solving coupled backward Riccati equations, and the corresponding recursive estimator design algorithm is presented that is suitable for online application. The effectiveness of the proposed estimator design method is validated via a numerical example.

Resilient asynchronous state estimation of Markov switching neural networks: A hierarchical structure approach

This paper deals with the issue of resilient asynchronous state estimation of discrete-time Markov switching neural networks. Randomly occurring signal quantization and packet dropout are involved in the imperfect measured output. The asynchronous switching phenomena appear among Markov switching neural networks, quantizer modes and filter modes, which are modeled by a hierarchical structure approach. By resorting to the hierarchical structure approach and Lyapunov functional technique, sufficient conditions are achieved, and asynchronous resilient filters are derived such that filtering error dynamic is stochastically stable. Finally, two examples are included to verify the validity of the proposed method.

An Event-Triggering Approach to Recursive Filtering for Complex Networks With State Saturations and Random Coupling Strengths

In this article, the recursive filtering problem is investigated for a class of time-varying complex networks with state saturations and random coupling strengths under an event-triggering transmission mechanism. The coupled strengths among nodes are characterized by a set of random variables obeying the uniform distribution. The event-triggering scheme is employed to mitigate the network data transmission burden. The purpose of the problem addressed is to design a recursive filter such that in the presence of the state saturations, event-triggering communication mechanism, and random coupling strengths, certain locally optimized upper bound is guaranteed on the filtering error covariance. By using the stochastic analysis technique, an upper bound on the filtering error covariance is first derived via the solution to a set of matrix difference equations. Next, the obtained upper bound is minimized by properly parameterizing the filter parameters. Subsequently, the boundedness issue of the filtering error covariance is studied. Finally, two numerical simulation examples are provided to illustrate the effectiveness of the proposed algorithm.

State-Saturated Recursive Filter Design for Stochastic Time-Varying Nonlinear Complex Networks Under Deception Attacks

This article tackles the recursive filtering problem for a class of stochastic nonlinear time-varying complex networks (CNs) suffering from both the state saturations and the deception attacks. The nonlinear inner coupling and the state saturations are taken into account to characterize the nonlinear nature of CNs. From the defender's perspective, the randomly occurring deception attack is governed by a set of Bernoulli binary distributed white sequence with a given probability. The objective of the addressed problem is to design a state-saturated recursive filter such that, in the simultaneous presence of the state saturations and the randomly occurring deception attacks, a certain upper bound is guaranteed on the filtering error covariance, and such an upper bound is then minimized at each time instant. By employing the induction method, an upper bound on the filtering error variance is first constructed in terms of the solutions to a set of matrix difference equations. Subsequently, the filter parameters are appropriately designed to minimize such an upper bound. Finally, a numerical simulation example is provided to demonstrate the feasibility and usefulness of the proposed filtering scheme.

Variance-Constrained Recursive State Estimation for Time-Varying Complex Networks With Quantized Measurements and Uncertain Inner Coupling

In this paper, a new recursive state estimation problem is discussed for a class of discrete time-varying stochastic complex networks with uncertain inner coupling and signal quantization under the error-variance constraints. The coupling strengths are allowed to be varying within certain intervals, and the measurement signals are subject to the quantization effects before being transmitted to the remote estimator. The focus of the conducted topic is on the design of a variance-constrained state estimation algorithm with the aim to ensure a locally minimized upper bound on the estimation error covariance at every sampling instant. Furthermore, the boundedness of the resulting estimation error is analyzed, and a sufficient criterion is established to ensure the desired exponential boundedness of the state estimation error in the mean square sense. Finally, some simulations are proposed with comparisons to illustrate the validity of the newly developed variance-constrained estimation method.

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.

Hidden Markov Model-Based Nonfragile State Estimation of Switched Neural Network With Probabilistic Quantized Outputs

This paper focuses on the state estimator design problem for a switched neural network (SNN) with probabilistic quantized outputs, where the switching process is governed by a sojourn probability. It is assumed that both packet dropouts and signal quantization exist in communication channels. Asynchronous estimator and quantification function are described by two different hidden Markov model between the SNNs and its estimator. To deal with the small uncertain of estimators in a random way, a probabilistic nonfragile state estimator is introduced, where uncertain information is described by the interval type of gain variation. A sufficient condition on mean square stable of the estimation error system is obtained and then the desired estimator is designed. Finally, a simulation result is provided to verify the effectiveness of the proposed design method.

Set-Membership Estimation for Complex Networks Subject to Linear and Nonlinear Bounded Attacks

This paper is concerned with the set-membership estimation problem for complex networks subject to unknown but bounded attacks. Adversaries are assumed to exist in the nonsecure communication channels from the nodes to the estimators. The transmitted measurements may be modified by an attack function with added noise that is determined by the adversary but unknown to the estimators. A novel set-membership estimation model against unknown but bounded attacks is presented. Two sufficient conditions are derived to guarantee the existence of the set-membership estimators for the cases that the attack functions are linear and nonlinear, respectively. Two strategies for the design of the set-membership estimator gains are presented. The effectiveness of the proposed estimator design method is verified by two simulation examples.

Neural Network Controller Design for a Class of Nonlinear Delayed Systems With Time-Varying Full-State Constraints

This paper proposes an adaptive neural control method for a class of nonlinear time-varying delayed systems with time-varying full-state constraints. To address the problems of the time-varying full-state constraints and time-varying delays in a unified framework, an adaptive neural control method is investigated for the first time. The problems of time delay and constraint are the main factors of limiting the system performance severely and even cause system instability. The effect of unknown time-varying delays is eliminated by using appropriate Lyapunov-Krasovskii functionals. In addition, the constant constraint is the only special case of time-varying constraint which leads to more complex and difficult tasks. To guarantee the full state always within the time-varying constrained interval, the time-varying asymmetric barrier Lyapunov function is employed. Finally, two simulation examples are given to confirm the effectiveness of the presented control scheme.

Prescribed Performance Model-Free Adaptive Integral Sliding Mode Control for Discrete-Time Nonlinear Systems

This paper studies the data-driven prescribed performance control (PPC) problem for a class of discrete-time nonlinear systems in the presence of tracking error constraints. By using the equivalent dynamic linearization technique and constructing a novel transformed error strategy, an adaptive integral sliding mode controller is designed such that the tracking error converges to a predefined neighborhood. Meanwhile, the presented control scheme can effectively ensure that the convergence rate is less than a predefined value and maximum overshoot is not smaller than a preselected constant. In addition, better tracking performance can be achieved by regulating the design parameters appropriately, which is more preferable in the practical application. Contrary to the existing PPC results, the new proposed control law does not use either the plant structure or any knowledge of system dynamics. The efficiency of the proposed control approach is shown with two simulated examples.

Finite-Horizon l2-l∞ Synchronization for Time-Varying Markovian Jump Neural Networks Under Mixed-Type Attacks: Observer-Based Case

This paper studies the synchronization issue of time-varying Markovian jump neural networks (NNs). The denial-of-service (DoS) attack is considered in the communication channel connecting master NNs and slave NNs. An observer is designed based on the measurements of master NNs transmitted over this unreliable channel to estimate their states. The deception attack is used to destroy the controller by changing the sign of the control signal. Then, the mixed-type attacks are expressed uniformly, and a synchronization error system is established using this function. A finite-horizon l₂-l_∞ performance is proposed, and sufficient conditions are derived to ensure that the synchronization error system satisfies this performance. The controllers are then obtained by a recursive linear matrix inequality algorithm. At last, a simulation result to show the feasibility of the developed results is given.

Nonfragile Dissipative Synchronization for Markovian Memristive Neural Networks: A Gain-Scheduled Control Scheme

In this paper, the dissipative synchronization control problem for Markovian jump memristive neural networks (MNNs) is addressed with fully considering the time-varying delays and the fragility problem in the process of implementing the gain-scheduled controller. A Markov jump model is introduced to describe the stochastic changing among the connection of MNNs and it makes the networks under consideration suitable for some actual circumstances. By utilizing some improved integral inequalities and constructing a proper Lyapunov-Krasovskii functional, several delay-dependent synchronization criteria with less conservatism are established to ensure the dynamic error system is strictly stochastically dissipative. Based on these criteria, the procedure of designing the desired nonfragile gain-scheduled controller is established, which can well handle the fragility problem in the process of implementing the controller. Finally, an illustrated example is employed to explain that the developed method is efficient and available.

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.

Nonfragile State Estimation of Quantized Complex Networks With Switching Topologies

This paper considers the nonfragile $H_\infty $ estimation problem for a class of complex networks with switching topologies and quantization effects. The network architecture is assumed to be dynamic and evolves with time according to a random process subject to a sojourn probability. The coupled signal is to be quantized before transmission due to power and bandwidth constraints, and the quantization errors are transformed into sector-bounded uncertainties. The concept of nonfragility is introduced by inserting randomly occurred uncertainties into the estimator parameters to cope with the unavoidable small gain variations emerging from the implementations of estimators. Both the quantizers and the estimators have several operation modes depending on the switching signal of the underlying network structure. A sufficient condition is provided via a linear matrix inequality approach to ensure the estimation error dynamic to be stochastically stable in the absence of external disturbances, and the $H_\infty $ performance with a prescribed index is also satisfied. Finally, a numerical example is presented to clarify the validity of the proposed method.

Connectivity-Preserving Consensus Tracking of Uncertain Nonlinear Strict-Feedback Multiagent Systems: An Error Transformation Approach

This brief addresses a distributed connectivity-preserving adaptive consensus tracking problem of uncertain nonlinear strict-feedback multiagent systems with limited communication ranges. Compared with existing consensus results for uncertain nonlinear lower triangular multiagent systems, the main contribution of this brief is to present an error-transformation-based design methodology to preserve initial connectivity patterns in the consensus tracking field, namely, both connectivity preservation and consensus tracking problems are considered for uncertain nonlinear lower triangular multiagent systems. A dynamic surface design based on nonlinearly transformed errors and neural network function approximators is established to construct the local controller of each follower. In addition, a technical lemma is derived to analyze the stability of the proposed connectivity-preserving consensus scheme in the Lyapunov sense.

Variance-Constrained State Estimation for Complex Networks With Randomly Varying Topologies

This paper investigates the variance-constrained state estimation problem for a class of nonlinear time-varying complex networks with randomly varying topologies, stochastic inner coupling, and measurement quantization. A Kronecker delta function and Markovian jumping parameters are utilized to describe the random changes of network topologies. A Gaussian random variable is introduced to model the stochastic disturbances in the inner coupling of complex networks. As a kind of incomplete measurements, measurement quantization is taken into consideration so as to account for the signal distortion phenomenon in the transmission process. Stochastic nonlinearities with known statistical characteristics are utilized to describe the stochastic evolution of the complex networks. We aim to design a finite-horizon estimator, such that in the simultaneous presence of quantized measurements and stochastic inner coupling, the prescribed variance constraints on the estimation error and the desired performance requirements are guaranteed over a finite horizon. Sufficient conditions are established by means of a series of recursive linear matrix inequalities, and subsequently, the estimator gain parameters are derived. A simulation example is presented to illustrate the effectiveness and applicability of the proposed estimator design algorithm.

Output Feedback Control and Stabilization for Multiplicative Noise Systems With Intermittent Observations

This paper mainly focuses on the optimal output feedback control and stabilization problems for discrete-time multiplicative noise system with intermittent observations. The main contributions of this paper can be concluded as follows. First, different from the previous literatures, this paper overcomes the barrier of the celebrated separation principle for stochastic control problems of multiplicative noise systems. Based on the measurement process, the optimal estimation is presented, and by using dynamic programming principle, the optimal output feedback controller is designed with feedback gain based on the given coupled Riccati equations. Second, the necessary and sufficient stabilization conditions for multiplicative noise system with intermittent observation in the mean square sense are developed for the first time. Finally, the novel results developed in this paper can be applied to solve the output feedback control and stabilization problems for general networked control system of user datagram protocol network case. The range of packet losses rate and the allowable maximum packet losses rate are presented explicitly.

Asynchronous State Estimation for Discrete-Time Switched Complex Networks With Communication Constraints

This paper is concerned with the asynchronous state estimation for a class of discrete-time switched complex networks with communication constraints. An asynchronous estimator is designed to overcome the difficulty that each node cannot access to the topology/coupling information. Also, the event-based communication, signal quantization, and the random packet dropout problems are studied due to the limited communication resource. With the help of switched system theory and by resorting to some stochastic system analysis method, a sufficient condition is proposed to guarantee the exponential stability of estimation error system in the mean-square sense and a prescribed performance level is also ensured. The characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem. Finally, the effectiveness of the proposed design approach is demonstrated by a simulation example.

Robust Estimation for Neural Networks With Randomly Occurring Distributed Delays and Markovian Jump Coupling

This paper studies the issue of robust state estimation for coupled neural networks with parameter uncertainty and randomly occurring distributed delays, where the polytopic model is employed to describe the parameter uncertainty. A set of Bernoulli processes with different stochastic properties are introduced to model the randomly occurrences of the distributed delays. Novel state estimators based on the local coupling structure are proposed to make full use of the coupling information. The augmented estimation error system is obtained based on the Kronecker product. A new Lyapunov function, which depends both on the polytopic uncertainty and the coupling information, is introduced to reduce the conservatism. Sufficient conditions, which guarantee the stochastic stability and the performance of the augmented estimation error system, are established. Then, the estimator gains are further obtained on the basis of these conditions. Finally, a numerical example is used to prove the effectiveness of the results.

Variance-Constrained State Estimation for Nonlinearly Coupled Complex Networks

This paper studies the state estimation problem for nonlinearly coupled complex networks. A variance-constrained state estimator is developed by using the structure of the extended Kalman filter, where the gain matrix is determined by optimizing an upper bound matrix for the estimation error covariance despite the linearization errors and coupling terms. Compared with the existing estimators for linearly coupled complex networks, a distinct feature of the proposed estimator is that the gain matrix can be derived separately for each node by solving two Riccati-like difference equations. By using the stochastic analysis techniques, sufficient conditions are established which guarantees the state estimation error is bounded in mean square. A numerical example is provided to show the effectiveness and applicability of the proposed estimator.

Finite-Time Distributed State Estimation Over Sensor Networks With Round-Robin Protocol and Fading Channels

This paper considers finite-time distributed state estimation for discrete-time nonlinear systems over sensor networks. The Round-Robin protocol is introduced to overcome the channel capacity constraint among sensor nodes, and the multiplicative noise is employed to model the channel fading. In order to improve the performance of the estimator under the situation, where the transmission resources are limited, fading channels with different stochastic properties are used in each round by allocating the resources. Sufficient conditions of the average stochastic finite-time boundedness and the average stochastic finite-time stability for the estimation error system are derived on the basis of the periodic system analysis method and Lyapunov approach, respectively. According to the linear matrix inequality approach, the estimator gains are designed. Finally, the effectiveness of the developed results are illustrated by a numerical example.