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

Partial-Neurons-Based Proportional-Integral Observer Design for Artificial Neural Networks: A Multiple Description Encoding Scheme

This article is concerned with a new partial-neurons-based proportional-integral observer (PIO) design problem for a class of artificial neural networks (ANNs) subject to bounded disturbances. For the purpose of improving the reliability of the data transmission, the multiple description encoding mechanisms are exploited to encode the measurement data into two identically important descriptions, and the encoded data are then transmitted to the decoders via two individual communication channels susceptible to packet dropouts, where Bernoulli-distributed stochastic variables are utilized to characterize the random occurrence of the packet dropouts. An explicit relationship is discovered that quantifies the influences of the packet dropouts on the decoding accuracy, and a sufficient condition is provided to assess the boundedness of the estimation error dynamics. Furthermore, the desired PIO parameters are calculated by solving two optimization problems based on two metrics (i.e., the smallest ultimate bound and the fastest decay rate) characterizing the estimation performance. Finally, the applicability and advantage of the proposed PIO design strategy are verified by means of an illustrative example.

Sampled-Data Synchronization of Stochastic Markovian Jump Neural Networks With Time-Varying Delay

In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method.

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.

Nonfragile H∞ State Estimation for Recurrent Neural Networks With Time-Varying Delays: On Proportional-Integral Observer Design

In this article, a novel proportional-integral observer (PIO) design approach is proposed for the nonfragile H_∞ state estimation problem for a class of discrete-time recurrent neural networks with time-varying delays. The developed PIO is equipped with more design freedom leading to better steady-state accuracy compared with the conventional Luenberger observer. The phenomena of randomly occurring gain variations, which are characterized by the Bernoulli distributed random variables with certain probabilities, are taken into consideration in the implementation of the addressed PIO. Attention is focused on the design of a nonfragile PIO such that the error dynamics of the state estimation is exponentially stable in a mean-square sense, and the prescribed H_∞ performance index is also achieved. Sufficient conditions for the existence of the desired PIO are established by virtue of the Lyapunov-Krasovskii functional approach and the matrix inequality technique. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed PIO design scheme.

Finite-/Fixed-Time Synchronization of Delayed Coupled Discontinuous Neural Networks With Unified Control Schemes

In this article, it addresses the problem of finite-/fixed-time synchronization of delayed coupled discontinuous neural networks in the unified framework. To achieve the finite-/fixed-time synchronization and precise estimations of setting time, two novel different kinds of controllers are established, in which one is switching. Then, based on the finite-/fixed-time theorem and Lyapunov function theory, some useful criteria are obtained to select suitable controllers' parameters, which can guarantee error systems converge in the finite time/fixed time with respect to coupled neural networks. Moreover, corresponding estimations of the setting time are also provided. Finally, two numerical examples are introduced to show the effectiveness of the proposed control protocols.

Outlier-Resistant Remote State Estimation for Recurrent Neural Networks With Mixed Time-Delays

In this brief, a new outlier-resistant state estimation (SE) problem is addressed for a class of recurrent neural networks (RNNs) with mixed time-delays. The mixed time delays comprise both discrete and distributed delays that occur frequently in signal transmissions among artificial neurons. Measurement outputs are sometimes subject to abnormal disturbances (resulting probably from sensor aging/outages/faults/failures and unpredictable environmental changes) leading to measurement outliers that would deteriorate the estimation performance if directly taken into the innovation in the estimator design. We propose to use a certain confidence-dependent saturation function to mitigate the side effects from the measurement outliers on the estimation error dynamics (EEDs). Through using a combination of Lyapunov-Krasovskii functional and inequality manipulations, a delay-dependent criterion is established for the existence of the outlier-resistant state estimator ensuring that the corresponding EED achieves the asymptotic stability with a prescribed H_∞ performance index. Then, the explicit characterization of the estimator gain is obtained by solving a convex optimization problem. Finally, numerical simulation is carried out to demonstrate the usefulness of the derived theoretical results.

Energy-to-Peak State Estimation for Switched Neutral-Type Neural Networks With Sector Condition via Sampled-Data Information

In this article, the energy-to-peak state estimation problem is investigated for a class of switched neutral neural networks subject to the external perturbations with bounded energy. Both the values of the measurement outputs and switching signal of the subsystems are only available for the controllers at the discrete sampling instants. Unlike the results for nonswitched neural networks, the coexistence of the switching and sampling actions directly causes the asynchronous phenomena between the indexes of subsystems and their corresponding controllers. To address this situation, the piecewise time-dependent Lyapunov-Krasovskii functional and slow switching mechanism are introduced. Under the developed theorem conditions, we prove that the designed state estimator exponentially tracks the true value of the neural state with the accessible sampled-data information. Also, the influence of the exogenous perturbations on the peak value of the estimation error is constrained at a prescribed level. Finally, a neutral cellular neural network with switching parameters is employed to substantiate the effectiveness and applicability of the theoretical results.

Synchronization for Quantized Semi-Markov Switching Neural Networks in a Finite Time

Finite-time synchronization (FTS) is discussed for delayed semi-Markov switching neural networks (S-MSNNs) with quantized measurement, in which a logarithmic quantizer is employed. The stochastic phenomena of structural and parametrical changes are modeled by a semi-Markov process whose transition rates are time-varying to depend on the sojourn time. Practical systems subject to unpredictable structural changes, such as quadruple-tank process systems, are described by delayed S-MSNNs. A key issue under the consideration is how to design a feedback controller to guarantee the FTS between the master system and the slave system. For this purpose, by using the weak infinitesimal operator, sufficient conditions are constructed to realize FTS of the resulting error system over a finite-time interval. Then, the solvability conditions for the desired finite-time controller can be determined under a linear matrix inequality framework. Finally, the theoretical findings are illustrated by the quadruple-tank process model.

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.

Synchronization of Nonidentical Neural Networks With Unknown Parameters and Diffusion Effects via Robust Adaptive Control Techniques

This paper considers the self-synchronization and tracking synchronization issues for a class of nonidentically coupled neural networks model with unknown parameters and diffusion effects. Using the special structure of neural networks with global Lipschitz activation function, nonidentical terms are treated as external disturbances, which can then be compensated via robust adaptive control techniques. For the case where no common reference trajectory is given in advance, a distributed adaptive controller is proposed to drive the synchronization error to an adjustable bounded area. For the case where a reference trajectory is predesigned, two distributed adaptive controllers are proposed, respectively, to address the tracking synchronization problem with bounded and unbounded reference trajectories, different decomposition methods are given to extract the heterogeneous characteristics. To avoid the appearance of global information, such as the spectrum of the coupling matrix, corresponding adaptive designs on coupling strengths are also provided for both cases. Moreover, the upper bounds of the final synchronization errors can be gradually adjusted according to the parameters of the adaptive designs. Finally, numerical examples are given to test the effectiveness of the control algorithms.

Dynamic event-based state estimation for delayed artificial neural networks with multiplicative noises: A gain-scheduled approach

This study is concerned with the state estimation issue for a kind of delayed artificial neural networks with multiplicative noises. The occurrence of the time delay is in a random way that is modeled by a Bernoulli distributed stochastic variable whose occurrence probability is time-varying and confined within a given interval. A gain-scheduled approach is proposed for the estimator design to accommodate the time-varying nature of the occurrence probability. For the sake of utilizing the communication resource as efficiently as possible, a dynamic event triggering mechanism is put forward to orchestrate the data delivery from the sensor to the estimator. Sufficient conditions are established to ensure that, in the simultaneous presence of the external noises, the randomly occurring time delays with time-varying occurrence probability as well as the dynamic event triggering communication protocol, the estimation error is exponentially ultimately bounded in the mean square. Moreover, the estimator gain matrices are explicitly calculated in terms of the solution to certain easy-to-solve matrix inequalities. Simulation examples are provided to show the validity of the proposed state estimation method.

H∞ and l2-l∞ state estimation for delayed memristive neural networks on finite horizon: The Round-Robin protocol

In this paper, a protocol-based finite-horizon H_∞ and l₂-l_∞ estimation approach is put forward to solve the state estimation problem for discrete-time memristive neural networks (MNNs) subject to time-varying delays and energy-bounded disturbances. The Round-Robin protocol is utilized to mitigate unnecessary network congestion occurring in the sensor-to-estimator communication channel. For the delayed MNNs, our aim is to devise an estimator that not only ensures a prescribed disturbance attenuation level over a finite time-horizon, but also keeps the peak value of the estimation error within a given range. By resorting to the Lyapunov-Krasovskii functional method, the delay-dependent criteria are formulated that guarantee the existence of the desired estimator. Subsequently, the estimator gains are obtained via figuring out a bank of convex optimization problems. The validity of our estimator is finally shown via a numerical example.

Distributed Robust Filtering for Wireless Sensor Networks with Markov Switching Topologies and Deception Attacks

This paper is concerned with the distributed full- and reduced-order l2-l∞ state estimation issue for a class of discrete time-invariant systems subjected to both randomly occurring switching topologies and deception attacks over wireless sensor networks. Firstly, a switching topology model is proposed which uses homogeneous Markov chain to reflect the change of filtering networks communication modes. Then, the sector-bound deception attacks among the communication channels are taken into consideration, which could better characterize the filtering network communication security. Additionally, a random variable obeying the Bernoulli distribution is used to describe the phenomenon of the randomly occurring deception attacks. Furthermore, through an adjustable parameter E, we can obtain full- and reduced-order l2-l∞ state estimator over sensor networks, respectively. Sufficient conditions are established for the solvability of the addressed switching topology-dependent distributed filtering design in terms of certain convex optimization problem. The purpose of solving the problem is to design a distributed full- and reduced-order filter such that, in the presence of deception attacks, stochastic external interference and switching topologies, the resulting filtering dynamic system is exponentially mean-square stable with prescribed l2-l∞ performance index. Finally, a simulation example is provided to show the effectiveness and flexibility of the designed approach.

l2-l∞ state estimation for delayed artificial neural networks under high-rate communication channels with Round-Robin protocol

In this paper, the l₂-l_∞ state estimation problem is addressed for a class of delayed artificial neural networks under high-rate communication channels with Round-Robin (RR) protocol. To estimate the state of the artificial neural networks, numerous sensors are deployed to measure the artificial neural networks. The sensors communicate with the remote state estimator through a shared high-rate communication channel. In the high-rate communication channel, the RR protocol is utilized to schedule the transmission sequence of the numerous sensors. The aim of this paper is to design an estimator such that, under the high-rate communication channel and the RR protocol, the exponential stability of the estimation error dynamics as well as the l₂-l_∞ performance constraint are ensured. First, sufficient conditions are given which guarantee the existence of the desired l₂-l_∞ state estimator. Then, the estimator gains are obtained by solving two sets of matrix inequalities. Finally, numerical examples are provided to verify the effectiveness of the developed l₂-l_∞ state estimation scheme.

Synchronization of Multiple Reaction-Diffusion Neural Networks With Heterogeneous and Unbounded Time-Varying Delays

The synchronization problem of multiple/coupled reaction-diffusion neural networks with time-varying delays is investigated. Differing from the existing considerations, state delays among distinct neurons and coupling delays among different subnetworks are included in the proposed model, the assumptions posed on the arisen delays are very weak, time-varying, heterogeneous, even unbounded delays are permitted. To overcome the difficulties from this kind of delay as well as diffusion effects, a comparison-based approach is applied to this model and a series of algebraic criteria are successfully obtained to verify the global asymptotical synchronization. By specifying the existing delays, some M -matrix-based criteria are derived to justify the power-rate synchronization and exponential synchronization. In addition, new criterion on synchronization of general connected neural networks without diffusion effects is also given. Finally, two simulation examples are given to verify the effectiveness of the obtained theoretical results and provide a comparison with the existing criterion.

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.

Multiple ψ -Type Stability of Cohen-Grossberg Neural Networks With Both Time-Varying Discrete Delays and Distributed Delays

In this paper, multiple ψ -type stability of Cohen-Grossberg neural networks (CGNNs) with both time-varying discrete delays and distributed delays is investigated. By utilizing ψ -type functions combined with a new ψ -type integral inequality for treating distributed delay terms, some sufficient conditions are obtained to ensure that multiple equilibrium points are ψ -type stable for CGNNs with discrete and distributed delays, where the distributed delays include bounded and unbounded delays. These conditions of CGNNs with different output functions are less restrictive. More specifically, the algebraic criteria of the generalized model are applicable to several well-known neural network models by taking special parameters, and multiple different output functions are introduced to replace some of the same output functions, which improves the diversity of output results for the design of neural networks. In addition, the estimation of relative convergence rate of ψ -type stability is determined by the parameters of CGNNs and the selection of ψ -type functions. As a result, the existing results on multistability and monostability can be improved and extended. Finally, some numerical simulations are presented to illustrate the effectiveness of the obtained results.

Protocol-based state estimation for delayed Markovian jumping neural networks

This paper is concerned with the state estimation problem for a class of Markovian jumping neural networks (MJNNs) with sensor nonlinearities, mode-dependent time delays and stochastic disturbances subject to the Round-Robin (RR) scheduling mechanism. The system parameters experience switches among finite modes according to a Markov chain. As an equal allocation scheme, the RR communication protocol is introduced for efficient usage of limited bandwidth and energy saving. The update matrix method is adopted to deal with the periodic time-delays resulting from the RR protocol. The objective of the addressed problem is to construct a state estimator for the MJNNs such that the dynamics of the estimation error is exponentially ultimately bounded in the mean square with a certain upper bound. Sufficient conditions are established for the existence of the desired state estimator by resorting to a combination of the Lyapunov stability theory and the stochastic analysis technique. Furthermore, the estimator gain matrices are characterized in terms of the solution to a convex optimization problem. Finally, a numerical simulation example is exploited to demonstrate the effectiveness of the proposed estimator design strategy.

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.

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.

Approximation-Based Adaptive Neural Tracking Control of Nonlinear MIMO Unknown Time-Varying Delay Systems With Full State Constraints

This paper deals with the tracking control problem for a class of nonlinear multiple input multiple output unknown time-varying delay systems with full state constraints. To overcome the challenges which cause by the appearances of the unknown time-varying delays and full-state constraints simultaneously in the systems, an adaptive control method is presented for such systems for the first time. The appropriate Lyapunov-Krasovskii functions and a separation technique are employed to eliminate the effect of unknown time-varying delays. The barrier Lyapunov functions are employed to prevent the violation of the full state constraints. The singular problems are dealt with by introducing the signal function. Finally, it is proven that the proposed method can both guarantee the good tracking performance of the systems output, all states are remained in the constrained interval and all the closed-loop signals are bounded in the design process based on choosing appropriate design parameters. The practicability of the proposed control technique is demonstrated by a simulation study in this paper.