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

An Impulsive Approach to State Estimation for Multirate Singularly Perturbed Complex Networks Under Bit Rate Constraints

In this article, the problem of ultimately bounded state estimation is investigated for discrete-time multirate singularly perturbed complex networks under the bit rate constraints, where the sensor sampling period is allowed to differ from the updating period of the networks. The facilitation of communication between sensors and the remote estimator through wireless networks, which are subject to bit rate constraints, involves the use of a coding-decoding mechanism. For efficient estimation in the presence of periodic measurements, a specialized impulsive estimation method is developed, which aims to carry out impulsive corrections precisely at the instants when the measurement signal is received by the estimator. By employing the iteration analysis method under the impulsive mechanism, a sufficient condition is established that ensures the exponential boundedness of the estimation error dynamics. Furthermore, an optimization algorithm is introduced for addressing the challenges related to bit rate allocation and the design of desired estimator gains. Within the presented theoretical framework, the correlation between estimation performance and bit rate allocation is elucidated. Finally, a simulation example is provided to demonstrate the validity of the proposed estimation 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.

Identifying the switching topology of dynamical networks based on adaptive synchronization

This paper proposes an approach for identifying unknown switching topology in a complex dynamical network. The setup is divided into two components: a primary drive network and a specialized response network equipped with switched topology observers. Each class of observers is dedicated to tracking a specific topology structure. The updating law for these observers is dynamically adjusted based on the operational status of the corresponding topology in the drive network-active if engaged and dormant if not. The sufficient conditions for successful identification are obtained by employing adaptive synchronization control and the Lyapunov function method. In particular, this paper abandons the generally used assumption of linear independence and adopts an easily verifiable condition for accurate identification. The result shows that the proposed identification method is applicable for any finite switching periods. By employing the chaotic Lü system and the Lorenz system as the local dynamics of the networks, numerical examples demonstrate the effectiveness of the proposed topology identification method.

Partial-Node-Based State Estimation for Delayed Complex Networks Under Intermittent Measurement Outliers: A Multiple-Order-Holder Approach

This article is concerned with the partial-node-based (PNB) state estimation problem for delayed complex networks (DCNs) subject to intermittent measurement outliers (IMOs). In order to describe the intermittent nature of outliers, several sequences of shifted gate functions are adopted to model the occurrence moments and the disappearing moments of IMOs. Two outlier-related indices, namely, minimum and maximum interval lengths, are employed to parameterize the "occurrence frequency" of IMOs. The norm of the addressed outlier is allowed to be greater than a certain fixed threshold, and this distinguishes the outlier from the extensively studied norm-bounded noise. By adopting the input-output models of the considered complex network, a novel multiple-order-holder (MOH) approach is developed to resist the effects of IMOs by dedicatedly designing a weighted average of certain non-IMO measurements, and then, a PNB state estimator is constructed based on the outputs of the MOHs. Sufficient conditions are proposed to ensure the exponentially ultimate boundedness (EUB) of the resultant estimation error, and the estimator gain matrices are subsequently obtained by solving a constrained optimization problem. Finally, two simulation examples are provided to demonstrate the effectiveness of our developed outlier-resistant PNB state estimation scheme.

A new event-triggered distributed state estimation approach for one-sided Lipschitz nonlinear discrete-time systems and its application to wireless sensor networks

This article proposes the design of a distributed state estimator for a class of one-sided Lipschitz nonlinear systems over wireless sensor networks. The suggested estimation scheme utilizes the one-sided Lipschitz constraint in conjunction with quadratic inner-boundedness, which makes it applicable to a broader class of nonlinear systems. The proposed estimator design is evaluated under a conventional event-triggered mechanism both in the absence and presence of external perturbations. Furthermore, a novel event-triggering condition is introduced that ensures error convergence to the origin in the absence of external perturbations. It is further established that the inclusion of new triggering condition reduces the estimation error upper bounds in the presence of external disturbances and noises. Sufficient conditions for boundedness of estimation errors are derived for each case, and matrix inequalities are developed for the calculation of estimator gains. Finally, a numerical example is considered to illustrate the efficacy of the proposed 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.

Event-triggered H∞/passive synchronization for Markov jumping reaction-diffusion neural networks under deception attacks

The issue of H_∞/passive master-slave synchronization for Markov jumping neural networks with reaction-diffusion terms is investigated in this paper via an event-triggered control scheme under deception attacks. To lighten the burden of limited communication bandwidth as well as ensure the control performance, an event-triggered transmission scheme is developed. Meanwhile, the randomly occurring deception attacks, which received from the event generator are assumed to modify the sign of the control signal, are taken into account. Furthermore, sufficient conditions ensuring the prescribed H_∞/passive performance level of the neural networks, are deduced beyond Lyapunov stability theory, and the controller gains are derived dealing with the matrix convex optimization problem. At last, the availability of the approach proposed is demonstrated via a numerical example.

Adaptive event-based robust passive fault tolerant control for nonlinear lateral stability of autonomous electric vehicles with asynchronous constraints

This work solves the robust passive fault-tolerant control problem for autonomous electric vehicles based on an adaptive event triggered mechanism. Firstly, given the system uncertainties from the tire dynamics and the longitudinal speed, the T-S fuzzy model method is used to approximate the vehicle lateral dynamics. Secondly, taking the communication constraints caused by band-limited networks into account, an adaptive event-triggered scheme is introduced in the process of the control design. Moreover, the asynchronous constraint of the weight function between the controller and system is considered. Thirdly, considering that the actuator faults are inevitably encountered in the control system, a robust passive fault-tolerant control method is proposed to improve vehicle performances. Finally, simulations are carried out to illustrate the effectiveness and robustness of the proposed approach.

Quantized control for extended dissipative synchronization of chaotic neural networks: A discretized LKF method

This work focuses on the extended dissipative synchronization problem for chaotic neural networks with time delay under quantized control. The discretized Lyapunov-Krasovskii functional method, in combination with the free-weighting matrix approach, is employed to obtain an analysis result of the extended dissipativity with low conservatism. Then, with the help of several decoupling methods, a computationally tractable design approach is proposed for the needed quantized controller. Finally, two examples are provided to illustrate the usefulness of the present analysis and design methods, respectively.

Finite-Time Pinning Synchronization Control for T-S Fuzzy Discrete Complex Networks with Time-Varying Delays via Adaptive Event-Triggered Approach

This paper is concerned with the adaptive event-triggered finite-time pinning synchronization control problem for T-S fuzzy discrete complex networks (TSFDCNs) with time-varying delays. In order to accurately describe discrete dynamical behaviors, we build a general model of discrete complex networks via T-S fuzzy rules, which extends a continuous-time model in existing results. Based on an adaptive threshold and measurement errors, a discrete adaptive event-triggered approach (AETA) is introduced to govern signal transmission. With the hope of improving the resource utilization and reducing the update frequency, an event-based fuzzy pinning feedback control strategy is designed to control a small fraction of network nodes. Furthermore, by new Lyapunov–Krasovskii functionals and the finite-time analysis method, sufficient criteria are provided to guarantee the finite-time bounded stability of the closed-loop error system. Under an optimization condition and linear matrix inequality (LMI) constraints, the desired controller parameters with respect to minimum finite time are derived. Finally, several numerical examples are conducted to show the effectiveness of obtained theoretical results. For the same system, the average triggering rate of AETA is significantly lower than existing event-triggered mechanisms and the convergence rate of synchronization errors is also superior to other control strategies.

Estimating the state of epidemics spreading with graph neural networks

When an epidemic spreads into a population, it is often impractical or impossible to continuously monitor all subjects involved. As an alternative, we propose using algorithmic solutions that can infer the state of the whole population from a limited number of measures. We analyze the capability of deep neural networks to solve this challenging task. We base our proposed architecture on Graph Convolutional Neural Networks. As such, it can reason on the effect of the underlying social network structure, which is recognized as the main component in spreading an epidemic. The proposed architecture can reconstruct the entire state with accuracy above 70%, as proven by two scenarios modeled on the CoVid-19 pandemic. The first is a generic homogeneous population, and the second is a toy model of the Boston metropolitan area. Note that no retraining of the architecture is necessary when changing the model.

H∞ filtering for nonlinearly coupled complex networks subjected to unknown varying delays and multiple fading measurements

In this paper, the robust filtering problem for uncertain complex networks with time-varying state delay and stochastic nonlinear coupling based on H_∞ performance criterion is studied. The random connections of coupling nodes are represented by utilizing independent random variables and the multiple fading measurements phenomenon is characterized by introducing diagonal matrices with independent stochastic elements. Moreover, the probabilistic time-varying delays in the measurement outputs are described by white sequences with the Bernoulli distributions. Furthermore, All system's matrices are supposed to have uncertainty and a quadratic bound is assumed for nonlinear part of the network. This bound can be obtained by solving a sum of squares (SOS) optimization problem. By applying the Lyapunov theory, we design a robust filter for each node of the network so that the filtering error system is asymptomatically stable and the H_∞ performances are met. Then, the parameters of the filters are achieved by solving a linear matrix inequality (LMI) feasibility problem. Finally, the applicability and performance of the proposed H_∞ filtering approach are demonstrated via a practical 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.

A survey on attack detection, estimation and control of industrial cyber-physical systems

Cyber-physical systems (CPSs) are complex systems that involve technologies such as control, communication, and computing. Nowadays, CPSs have a wide range of applications in smart cities, smart grids, smart manufacturing and intelligent transportation. However, with integration of industrial control systems with modern communication technologies, CPSs would be inevitably exposed to increasing security threats, which could lead to severe degradation of the system performance and even destruction of CPSs. This paper presents a survey on recent advances on security issues of industrial cyber-physical systems (ICPSs). We specifically discuss two typical kinds of attacks, i.e., Denial-of-Service (DoS) attack and Deception attack, and present recent results in terms of attack detection, estimation, and control of ICPSs. Classifications of current studies are analyzed and summarized based on different system modeling and analysis methods. In addition, advantages and disadvantage of various methodologies are also discussed. Finally, the paper concludes with some potential future research directions on secure ICPSs.

Adaptive control of a class of strict feedback nonlinear systems under replay attacks

The adaptive control of a class of strict-feedback nonlinear system under replay attack is investigated in this paper. Durations of each attack and the resting time after each attack are analyzed and their explicit bounds are presented to ensure closed-loop stability. Two scenarios are considered. In the first scenario, it is shown that if the duration of each attack is less than a given constant, asymptotical convergence of system output is still preserved. The second scenario shows that if the resting time of each attack meets certain condition after each arbitrarily long duration of attack, closed-loop boundedness is still preserved. This shows that the system controlled under our proposed adaptive controller will not be broken down even in the presence of replay attacks. Simulation results are given to illustrate the effectiveness of the control schemes.

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.

Adaptive bounded neural network control for coordinated path-following of networked underactuated autonomous surface vehicles under time-varying state-dependent cyber-attack

This paper is concerned with the problem of coordinated path-following for networked underactuated autonomous surface vehicles in the presence of time-varying state-dependent cyber-attack. An adaptive bounded neural network controller is proposed to mitigate the malicious effect of the cyber-attack. At first, an individual path-following control law is designed for each vehicle by fusing a back-stepping technique, a line-of-sight guidance principle and a predictor-based neural network method. Second, a path update law is developed based on a synchronization approach together with an adaptive control method. The salient features of the proposed controller are presented as follows. First, an adaptive corrective signal is incorporated into the path update law design such that a desired formation can be achieved regardless of the time-varying state-dependent cyber-attack. Second, by using a saturation function and a projection operator, the proposed controller is bounded and the bound is known as a priori. It is proven that the closed-loop system is input-to-state practical stable in the face of time-varying state-dependent cyber-attack. Simulation results show the effectiveness of the proposed adaptive bounded neural network controller for coordinated path-following of networked underactuated autonomous surface vehicles subject to the cyber-attack.

Critic-only adaptive dynamic programming algorithms' applications to the secure control of cyber-physical systems

Industrial cyber-physical systems generally suffer from the malicious attacks and unmatched perturbation, and thus the security issue is always the core research topic in the related fields. This paper proposes a novel intelligent secure control scheme, which integrates optimal control theory, zero-sum game theory, reinforcement learning and neural networks. First, the secure control problem of the compromised system is converted into the zero-sum game issue of the nominal auxiliary system, and then both policy-iteration-based and value-iteration-based adaptive dynamic programming methods are introduced to solve the Hamilton-Jacobi-Isaacs equations. The proposed secure control scheme can mitigate the effects of actuator attacks and unmatched perturbation, and stabilize the compromised cyber-physical systems by tuning the system performance parameters, which is proved through the Lyapunov stability theory. Finally, the proposed approach is applied to the Quanser helicopter to verify the effectiveness.

Non-fragile dissipative filtering of cyber-physical systems with random sensor delays

This paper considers the problem of non-fragile state estimation under dissipative constraint for a class of nonlinear cyber-physical systems (CPSs) with sensor delays. The dynamics of the considered CPSs is characterized by the well-known T-S fuzzy model and system measurements are valued by wireless sensors. The communication link between the filter and the plant is described by a relatively practical model and sensor delays occurred in signal transmissions are taken into consideration. A stochastic variable which yields the standard Bernoulli distribution is exploited to model sensor delays encountered by the sensor measurements. With the help of a basis-dependent Lyapunov function and predefined performance constraint, sufficient conditions are then developed to establish the stochastic stability as well as strict dissipativity for the resultant filtering error system. The existence of the corresponding filter is guaranteed and the expression of desired filter parameters are shown explicitly. In the end, the established theoretical results are validated by a tunnel diode circuit example and corresponding simulations are also provided.

Nonlinear model of cascade failure in weighted complex networks considering overloaded edges

Considering the elasticity of the real networks, the components in the network have a redundant capacity against the load, such as power grids, traffic networks and so on. Moreover, the interaction strength between nodes is often different. This paper proposes a novel nonlinear model of cascade failure in weighted complex networks considering overloaded edges to describe the redundant capacity for edges and capture the interaction strength of nodes. We fill this gap by studying a nonlinear weighted model of cascade failure with overloaded edges over synthetic and real weighted networks. The cascading failure model is constructed for the first time according to the overload coefficient, capacity parameter, weight coefficient, and distribution coefficient. Then through theoretical analysis, the conditions for stopping failure cascades are obtained, and the analysis shows the superiority of the constructed model. Finally, the cascading invulnerability is simulated in several typical network models and the US power grid. The results show that the model is a feasible and reasonable change of weight parameters, capacity coefficient, distribution coefficient, and overload coefficient can significantly improve the destructiveness of complex networks against cascade failure. Our methodology provides an efficacious reference for the control and prevention of cascading failures in many real networks.

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.

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.

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.

Finite-Time Passivity-Based Stability Criteria for Delayed Discrete-Time Neural Networks via New Weighted Summation Inequalities

In this paper, we study the problem of finite-time stability and passivity criteria for discrete-time neural networks (DNNs) with variable delays. The main objective is how to effectively evaluate the finite-time passivity conditions for NNs. To achieve this, some new weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of a novel Lyapunov-Krasovskii functional, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed results.

Nonfragile H∞ output feedback control of linear systems with an event-triggered scheme against unreliable communication links

This paper studies the event-triggered H_∞ static output feedback control of linear systems with unreliable communication. The unreliable phenomenon between the event-triggering unit and the controller is described by a stochastic variable with Bernoulli random binary distribution. To cast the considered problem in the robust control framework, the event-triggering scheme is presented by a time-delay form. A vertex structure separation strategy is utilized to handle control gain with interval variations, which could alleviate computation burden heavily. Resorting to a division of control gain from Lyapunov variable, a new method for the non-fragile H_∞ controller synthesis is established in the framework of linear matrix inequalities. Simulations are executed to show the validity of the proposed approach.