Finite-time resilient H∞ state estimation for discrete-time delayed neural networks under dynamic event-triggered mechanism

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.

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.

Adaptive Set-Membership State Estimation for Nonlinear Systems Under Bit Rate Allocation Mechanism: A Neural-Network-Based Approach

In this article, the adaptive neural-network-based (NN-based) set-membership state estimation problem is studied for a class of nonlinear systems subject to bit rate constraints and unknown-but-bounded noises. The measurement output signals are transmitted from sensors to a remote estimator via a bit rate constrained communication channel. To relieve the communication burden and ameliorate the state estimation accuracy, a bit rate allocation mechanism is put forward for the sensor nodes by solving a constrained optimization problem. Subsequently, through the NN learning method, an NN-based set-membership estimator is designed to determine an ellipsoidal set that contains the system state, where the proposed estimator relies upon a prediction-correction structure. With the help of the mathematical induction technique and the set theory, sufficient conditions are obtained to ensure the existence of both the adaptive tuning parameters and the set-membership estimators, and then, the corresponding parameters and estimator gains are calculated by solving a set of optimization problems. In addition, the monotonicity of the upper bound on the squared estimation error with respect to the bit rate and the convergence of the NN weight are analyzed, respectively. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed state estimation algorithm.

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.

State Estimation for Discrete Time-Delayed Impulsive Neural Networks Under Communication Constraints: A Delay-Range-Dependent Approach

In this article, a delay-range-dependent approach is put forward to tackle the state estimation problem for delayed impulsive neural networks. A new type of nonlinear function, which is more general than the normal sigmoid function and functions constrained by the Lipschitz condition, is adopted as the neuron activation function. To effectively alleviate data collisions and save energy, the round-robin protocol is utilized to mitigate the occurrence of unnecessary network congestion in communication channels from sensors to the estimator. With the aid of the Lyapunov stability theory, a state observer is constructed such that the estimation error dynamics are asymptotically stable. The observer existence is ensured by resorting to a set of delay-range-dependent criteria which is dependent on both the impulsive time instant and a coefficient matrix. In addition, the synthesis of the observer is discussed by using linear matrix inequalities. Simulations are provided to illustrate the reasonability of our delay-range-dependent estimation approach.

Neural-Network-Based Set-Membership Fault Estimation for 2-D Systems Under Encoding-Decoding Mechanism

In this article, the simultaneous state and fault estimation problem is investigated for a class of nonlinear 2-D shift-varying systems, where the sensors and the estimator are connected via a communication network of limited bandwidth. With the purpose of relieving the communication burden and enhancing the transmission security, a new encoding-decoding mechanism is put forward so as to encode the transmitted data with a finite number of bits. The aim of the addressed problem is to develop a neural-network (NN)-based set-membership estimator for jointly estimating the system states and the faults, where the estimation errors are guaranteed to reside within an optimized ellipsoidal set. With the aid of the mathematical induction technique and certain convex optimization approaches, sufficient conditions are derived for the existence of the desired set-membership estimator, and the estimator gains and the NN tuning scalars are then presented in terms of the solutions to a set of optimization problems subject to ellipsoidal constraints. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed estimator design method.

Energy-to-Peak State Estimation With Intermittent Measurement Outliers: The Single-Output Case

This article is concerned with the energy-to-peak state estimation problem for a class of linear discrete-time systems with energy-bounded noises and intermittent measurement outliers (IMOs). In order to capture the intermittent nature, two sequences of step functions are introduced to model the occurrence of the IMOs. Furthermore, two special indices (i.e., minimum and maximum interval lengths) are adopted to describe the "occurrence frequency" of IMOs. Different from the considered energy-bounded noises, the outliers are assumed to have their magnitudes larger than certain thresholds. In order to achieve a satisfactory performance constraint on the energy-to-peak state estimation under the addressed kind of measurement outliers, a novel parameter-dependent (PD) state estimation strategy is developed to guarantee that the measurements contaminated by outliers would be removed in the estimation process. The proposed PD state estimation method is essentially a two-step process, where the first step is to examine the appearing and disappearing moments for each IMO by using a dedicatedly constructed outlier detection scheme, and the second step is to implement the state estimation task according to the outlier detection results. Sufficient conditions are obtained to ensure the existence of the desired estimator, and the gain matrix of the desired estimator is then derived by solving a constrained optimization problem. Finally, a simulation example is presented to illustrate the effectiveness of our developed PD state estimation strategy.

H∞ Proportional-Integral State Estimation for T-S Fuzzy Systems Over Randomly Delayed Redundant Channels With Partly Known Probabilities

In this article, we consider the H_∞ proportional-integral (PI) state estimation (SE) problem for discrete-time T-S fuzzy systems subject to transmission delays, external disturbances, and redundant channels. Multiple redundant communication channels are utilized between the sensors and the remote estimator to enhance the reliability of data transmissions. In order to characterize the transmission delays in network-based communication, a family of random variables with partly known probabilities, which are independent and identically distributed, is adopted to describe the random behavior of the transmission delays with the redundant channels. The objective of this work is to put forward a PI state estimator such that the dynamics of the estimation error is exponentially mean-square stable and satisfies the prescribed H_∞ performance index of the disturbance attenuation/rejection. By employing the stochastic analysis approach, the error dynamics of the SE under the proposed state estimator is analyzed and sufficient conditions are obtained to ensure the existence of the required PI state estimator. Furthermore, the desired estimator parameters are derived by solving a nonlinear optimization problem. Finally, two simulation examples are exploited to demonstrate the validity of the proposed SE scheme.

A Dynamic Event-Triggered Approach to Recursive Nonfragile Filtering for Complex Networks With Sensor Saturations and Switching Topologies

In this article, the nonfragile filtering issue is addressed for complex networks (CNs) with switching topologies, sensor saturations, and dynamic event-triggered communication protocol (DECP). Random variables obeying the Bernoulli distribution are utilized in characterizing the phenomena of switching topologies and stochastic gain variations. By introducing an auxiliary offset variable in the event-triggered condition, the DECP is adopted to reduce transmission frequency. The goal of this article is to develop a nonfragile filter framework for the considered CNs such that the upper bounds on the filtering error covariances are ensured. By the virtue of mathematical induction, gain parameters are explicitly derived via minimizing such upper bounds. Moreover, a new method of analyzing the boundedness of a given positive-definite matrix is presented to overcome the challenges resulting from the coupled interconnected nodes, and sufficient conditions are established to guarantee the mean-square boundedness of filtering errors. Finally, simulations are given to prove the usefulness of our developed filtering algorithm.

Encoding-decoding strategy based resilient state estimation for bias-corrupted stochastic nonlinear systems

This paper is concerned with the resilient state estimation problem for a type of stochastic nonlinear systems, in which the possible dynamical bias is considered that is depicted by a dynamical equation. In pursuit of enhancing the robustness of the propagated data, a binary encoding strategy (BES) is exploited in the binary symmetric channel (BSC). While the random bit errors caused by the channel noise may take place during the propagation of the binary bit string via the memoryless BSC. To characterize the occurrence of the bit errors, a series of Bernoulli distributed random variables is adopted. More specifically, in order to deal with the possible gain fluctuation of the estimator in the execution process, a resilient state estimator is employed. This paper intends to put forward a novel resilient estimation scheme under the BES, which can assure that the estimation error dynamics is exponentially ultimately bounded in mean square. A sufficient criterion is first acquired for the existence of the expected resilient estimator and the estimator parameter is achieved by solving a convex optimization problem. Finally, an illustrative simulation example is provided to verify the validity of the theoretical results.

Multiloop Decentralized H∞ Fuzzy PID-Like Control for Discrete Time-Delayed Fuzzy Systems Under Dynamical Event-Triggered Schemes

This article is concerned with the multiloop decentralized H_∞ fuzzy proportional-integral-derivative-like (PID-like) control problem for discrete-time Takagi-Sugeno fuzzy systems with time-varying delays under dynamical event-triggered mechanisms (ETMs). The sensors of the plant are grouped into several nodes according to their physical distribution. For resource-saving purposes, the signal transmission between each sensor node and the controller is implemented based on the dynamical ETM. Taking the node-based idea into account, a general multiloop decentralized fuzzy PID-like controller is designed with fixed integral windows to reduce the potential accumulation error. The overall decentralized fuzzy PID-like control scheme involves multiple single-loop controllers, each of which is designed to generate the local control law based on the measurements of the corresponding sensor node. These kinds of local controllers are convenient to apply in practice. Sufficient conditions are obtained under which the controlled system is exponentially stable with the prescribed H_∞ performance index. The desired controller gains are then characterized by solving an iterative optimization problem. Finally, a simulation example is presented to demonstrate the correctness and effectiveness of the proposed design procedure.

Periodic Event-Triggered Synchronization for Discrete-Time Complex Dynamical Networks

In this article, we investigate the periodic event-triggered synchronization of discrete-time complex dynamical networks (CDNs). First, a discrete-time version of periodic event-triggered mechanism (ETM) is proposed, under which the sensors sample the signals in a periodic manner. But whether the sampling signals are transmitted to controllers or not is determined by a predefined periodic ETM. Compared with the common ETMs in the field of discrete-time systems, the proposed method avoids monitoring the measurements point-to-point and enlarges the lower bound of the inter-event intervals. As a result, it is beneficial to save both the energy and communication resources. Second, the "discontinuous" Lyapunov functionals are constructed to deal with the sawtooth constraint of sampling signals. The functionals can be viewed as the discrete-time extension for those discontinuous ones in continuous-time fields. Third, sufficient conditions for the ultimately bounded synchronization are derived for the discrete-time CDNs with or without considering communication delays, respectively. A calculation method for simultaneously designing the triggering parameter and control gains is developed such that the estimation of error level is accurate as much as possible. Finally, the simulation examples are presented to show the effectiveness and improvements of the proposed method.

Distributed Quasiconsensus Control for Stochastic Multiagent Systems Under Round-Robin Protocol and Uniform Quantization

In this article, the problem of consensus control is investigated for a class of multiagent systems (MASs) with both stochastic noises and nonidentical exogenous disturbances. The signal transmission among agents is implemented through a digital communication network subject to both uniform quantization and round-robin protocol as a reflection of network constraints. The consensus strategy is designed by adopting the estimates of the relative states of the agent to its neighbors, which renders the distributed nature of the controller. A new consensus concept, namely, quasiconsensus in probability, is employed to evaluate the state response of the agents to the stochastic noises, the exogenous disturbances, and the quantization error. An augmented system is first formed that relies on the deviations of the individual state from the average state, the observer error of the relative state, as well as the relative measurement output. Based on the augmented model, an analysis approach on dynamical behaviors is developed to facilitate the consensus analysis of MASs by means of the switching Lyapunov function technique and the stochastic analysis methods. Then, the existence condition and the explicit expression of the time-varying gain matrices are proposed for the expected controller by resorting to the feasibility of several matrix inequalities. Numerical simulation results are presented to demonstrate the applicability of the theoretical results.

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.

Electric vehicle charging station planning with dynamic prediction of elastic charging demand: a hybrid particle swarm optimization algorithm

This paper is concerned with the electric vehicle (EV) charging station planning problem based on the dynamic charging demand. Considering the dynamic charging behavior of EV users, a dynamic prediction method of EV charging demand is proposed by analyzing EV users’ travel law via the trip chain approach. In addition, a multi-objective charging station planing problem is formulated to achieve three objectives: (1) maximize the captured charging demands; (2) minimize the total cost of electricity and the time consumed for charging; and (3) minimize the load variance of the power grid. To solve such a problem, a novel method is proposed by combining the hybrid particle swarm optimization (HPSO) algorithm with the entropy-based technique for order preference by similarity to ideal solution (ETOPSIS) method. Specifically, the HPSO algorithm is used to obtain the Pareto solutions, and the ETOPSIS method is employed to determine the optimal scheme. Based on the proposed method, the siting and sizing of the EV charging station can be planned in an optimal way. Finally, the effectiveness of the proposed method is verified via the case study based on a test system composed of an IEEE 33-node distribution system and a 33-node traffic network system.

Empower parameterized generative adversarial networks using a novel particle swarm optimizer: algorithms and applications

In this paper, a novel parameterized generative adversarial network (GAN) is proposed where the parameters are introduced to enhance the performance of image segmentation. The developed algorithm is applied to the image-based crack detection problem on the thermal data obtained through the non-destructive testing process. A new regularization term, which contains three tunable hyperparameters, embedded into the objective function of the GAN in order to improve the contrast ratio of certain areas of the image so as to benefit the crack detection process. To automate the selection of the optimal hyperparameters of the GAN, a new particle swarm optimization (PSO) algorithm is put forward where a neighborhood-based velocity updating strategy is developed for the purpose of thoroughly exploring the problem space. The proposed PSO-based GAN algorithm is shown to 1) work well in detecting cracks on the thermal data generated by the eddy current pulsed thermography technique; and 2) outperforms other conventional GAN algorithms.

A New GAN-Based Approach to Data Augmentation and Image Segmentation for Crack Detection in Thermal Imaging Tests

As a popular nondestructive testing (NDT) technique, thermal imaging test demonstrates competitive performance in crack detection, especially for detecting subsurface cracks. In thermal imaging test, the temperature of the crack area is higher than that of the non-crack area during the NDT process. By extracting the features of the thermal image sequences, the temperature curve of each spatial point is employed for crack detection. Nevertheless, the quality of thermal images is influenced by the noises due to the complex thermal environment in NDT. In this paper, a modified generative adversarial network (GAN) is employed to improve the image segmentation performance. To improve the feature extraction ability and alleviate the influence of noises, a penalty term is put forward in the loss function of the conventional GAN. A data preprocessing method is developed where the principle component analysis algorithm is adopted for feature extraction. The data argumentation technique is utilized to guarantee the quantity of the training samples. To validate its effectiveness in thermal imaging NDT, the modified GAN is applied to detect the cracks on the eddy current pulsed thermography NDT dataset.

Memory-Event-Triggered H∞ Output Control of Neural Networks With Mixed Delays

This article investigates the problem of memory-event-triggered H∞ output feedback control for neural networks with mixed delays (discrete and distributed delays). The probability density of the communication delay among neurons is modeled as the kernel of the distributed delay. To reduce network communication burden, a novel memory-event-triggered scheme (METS) using the historical system output is introduced to choose which data should be sent to the controller. Based on a constructed Lyapunov-Krasovskii functional (LKF) with the distributed delay kernel and a generalized integral inequality, new sufficient conditions are formed by linear matrix inequalities (LMIs) for designing an event-triggered H∞ controller. Finally, experiments based on a computer and a real wireless network are executed to confirm the validity of the developed method.

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.

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.