Energy-to-peak state estimation for Markov jump RNNs with time-varying delays via nonsynchronous filter with nonstationary mode transitions

Markovian RNN: An Adaptive Time Series Prediction Network With HMM-Based Switching for Nonstationary Environments

We investigate nonlinear regression for nonstationary sequential data. In most real-life applications such as business domains including finance, retail, energy, and economy, time series data exhibit nonstationarity due to the temporally varying dynamics of the underlying system. We introduce a novel recurrent neural network (RNN) architecture, which adaptively switches between internal regimes in a Markovian way to model the nonstationary nature of the given data. Our model, Markovian RNN employs a hidden Markov model (HMM) for regime transitions, where each regime controls hidden state transitions of the recurrent cell independently. We jointly optimize the whole network in an end-to-end fashion. We demonstrate the significant performance gains compared to conventional methods such as Markov Switching ARIMA, RNN variants and recent statistical and deep learning-based methods through an extensive set of experiments with synthetic and real-life datasets. We also interpret the inferred parameters and regime belief values to analyze the underlying dynamics of the given sequences.

Security-Based Passivity Analysis of Markov Jump Systems via Asynchronous Triggering Control

This article considers the security-based passivity problem for a class of discrete-time Markov jump systems in the presence of deception attacks, where the deception attacks aim to change the transmitted signal. Considering the impact of deception attacks on network disruption, it causes the existence of time-varying delays in signal transmission inevitably, which makes the controlled system and the controller work asynchronously. The asynchronous control method is employed to overcome the nonsynchronous phenomenon between the system mode and controller mode. On the other hand, to reduce the frequency of data transmission, a resilient asynchronous event-triggered control scheme taking deception attacks into account is designed to save communication resources, and the proposed controller can cover some existing ones as special examples. Moreover, different triggering conditions corresponding to different jumping modes are developed to decide whether state signals should be transferred. A new stability criterion is derived to ensure the passivity of the resultant system although there exist deception attacks. Finally, a simulation example is given to verify the theoretical analysis.

Parameterized Luenberger-Type H∞ State Estimator for Delayed Static Neural Networks

This article proposes a new Luenberger-type state estimator that has parameterized observer gains dependent on the activation function, to improve the H_∞ state estimation performance of the static neural networks with time-varying delay. The nonlinearity of the activation function has a significant impact on stability analysis and robustness/performance. In the proposed state estimator, a parameter-dependent estimator gain is reconstructed by using the properties of the sector nonlinearity of the activation functions that are represented as linear combinations of weighting parameters. In the reformulated form, the constraints of the parameters for the activation function are considered in terms of linear matrix inequalities. Based on the Lyapunov-Krasovskii function and the improved reciprocally convex inequality, enhanced conditions for designing a new state estimator that guarantees H_∞ performance are derived through a parameterization technique. The compared results with recent studies demonstrate the superiority and effectiveness of the presented method.

Event-Based Dissipative Filtering of Markovian Jump Neural Networks Subject to Incomplete Measurements and Stochastic Cyber-Attacks

In this article, the dissipativity-based filtering of the Markovian jump neural networks subject to incomplete measurements and deception attacks is investigated by adopting an event-triggered communication strategy, where the attackers are supposed to occur in a random fashion but obey the Bernoulli distribution. Consider that the information of the system mode is transmitted to the filter over the communication network that is vulnerable to external attacks, which may lead to the undesired performance of the resulting system by injecting malicious information from the attackers. As a result, the filter has difficulty completing information from the original system. Besides, an event-triggered communication mechanism is introduced to reduce the communication frequency between data transmission due to the limited network resources, and different triggering conditions corresponding to different jump modes are developed. Then, based on the above considerations, the sufficient condition is derived to ensure the stochastic stability and dissipativity of the resulting augmented system although the deception attacks and incomplete information exist. A numerical simulated example is provided to verify the theoretical analysis.

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.

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.

Reliable Filter Design of Takagi-Sugeno Fuzzy Switched Systems With Imprecise Modes

This paper is concerned with the problem of asynchronous and reliable filter design with performance constraint for nonlinear Markovian jump systems which are modeled as a kind of Takagi-Sugeno fuzzy switched systems. The nonstationary Markov chain is adopted to represent the asynchronous situation between the designed filter and the considered system. By using the mode-dependent Lyapunov function approach and the relaxation matrix technique, a sufficient condition is proposed to ensure the filtering error system, which is a dual randomly switched system, is stochastically stable and satisfies a given l₂-l_∞ performance index simultaneously. Two different approaches are developed to construct the asynchronous and reliable filter. Owing to the Finsler's lemma, the second approach has fewer decision variables and less conservatism than the first one. Finally, two examples are provided to show the correctness and effectiveness of the proposed methods.

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.

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.

Dissipativity-based asynchronous control for discrete-time singular Markov jump systems with multiplicative noises

The singular systems, which could widely describe more general systems and present traits of physical features, are discussed in this study. Taking the fact that noises always exist in the state and output measurement of one singular system into consideration, which may cause some errors and decrease system performance, this article devotes itself to the dissipative control for discrete-time singular Markov jump systems (SMJSs) with multiplicative noises. To deal with the asynchronous phenomena between the system modes and the controller modes, a set of Markov chains are constructed. To make sure the closed-loop singular system is dissipative, a set of sufficient conditions are derived based on the linear matrix inequalities, and then the asynchronous controller is designed to ensure that SMJSs are stochastically admissible and strictly dissipative. Finally, a simulation example is carried out to verify the correctness of the derived theorem. The designed asynchronous controller improves the robustness of the controller and overcomes the asynchronous phenomenon. This control method can be applied in the fields of robot control system.

Sliding mode control and sampling rate strategy for Networked control systems with packet disordering via Markov chain prediction

This paper investigates sliding mode control combined with sampling rate control for networked control systems subject to packet disordering via Markov chain prediction. The main objectives of the proposed method are to predict the probability of the occurrence of packet disordering when packet disordering is unknown in the networks, to control sampling rate to restrain heavy packet disordering, and to stabilize the Markovian jump system with variable parameters by sliding mode techniques. Firstly, an argument system with sampling rate and a plant state is established. Then, the Networked control system based on Markov chain probability prediction and statistical analysis of this probability is modeled as a Markovian jump system with two Markov chains. Next, sliding mode controller is designed to stabilize the dynamic Markovian jump system. Finally, experiments are conducted to illustrate the effectiveness and benefits of proposed method.

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.

Remote Estimator Design for Time-Delay Neural Networks Using Communication State Information

This paper investigates the estimator design for the neural networks, where distributed delays and imperfect measurements are included. A randomly occurred neuron-dependent nonlinearity is used to describe the uncertain measurements disturbed by neurons. The measurements are transmitted over multiple transmission channels, and Markov chains are introduced to model packet dropouts of these channels. A one-to-one map is constructed to transform $m$ independent Markov chains to an augmented one to facilitate system analysis. A new variable called channel state is defined based on the cases of packet dropouts, and the channel-state-dependent estimator is designed to trade off between the number and the performance of the estimator. Sufficient conditions are established to guarantee that the augmented system is stochastically stable and satisfies the strict $(Q, S, R)-\gamma -$ dissipativity. The estimator gains are derived using linear matrix methods. Finally, an example is applied to illustrate the effectiveness of the developed methods.

Event-Triggered Asynchronous Guaranteed Cost Control for Markov Jump Discrete-Time Neural Networks With Distributed Delay and Channel Fading

This paper is concerned with the guaranteed cost control problem for a class of Markov jump discrete-time neural networks (NNs) with event-triggered mechanism, asynchronous jumping, and fading channels. The Markov jump NNs are introduced to be close to reality, where the modes of the NNs and guaranteed cost controller are determined by two mutually independent Markov chains. The asynchronous phenomenon is considered, which increases the difficulty of designing required mode-dependent controller. The event-triggered mechanism is designed by comparing the relative measurement error with the last triggered state at the process of data transmission, which is used to eliminate dispensable transmission and reduce the networked energy consumption. In addition, the signal fading is considered for the effect of signal reflection and shadow in wireless networks, which is modeled by the novel Rice fading models. Some novel sufficient conditions are obtained to guarantee that the closed-loop system reaches a specified cost value under the designed jumping state feedback control law in terms of linear matrix inequalities. Finally, some simulation results are provided to illustrate the effectiveness of the proposed method.

Energy-to-Peak State Estimation for Static Neural Networks With Interval Time-Varying Delays

This paper is concerned with energy-to-peak state estimation on static neural networks (SNNs) with interval time-varying delays. The objective is to design suitable delay-dependent state estimators such that the peak value of the estimation error state can be minimized for all disturbances with bounded energy. Note that the Lyapunov-Krasovskii functional (LKF) method plus proper integral inequalities provides a powerful tool in stability analysis and state estimation of delayed NNs. The main contribution of this paper lies in three points: 1) the relationship between two integral inequalities based on orthogonal and nonorthogonal polynomial sequences is disclosed. It is proven that the second-order Bessel-Legendre inequality (BLI), which is based on an orthogonal polynomial sequence, outperforms the second-order integral inequality recently established based on a nonorthogonal polynomial sequence; 2) the LKF method together with the second-order BLI is employed to derive some novel sufficient conditions such that the resulting estimation error system is globally asymptotically stable with desirable energy-to-peak performance, in which two types of time-varying delays are considered, allowing its derivative information is partly known or totally unknown; and 3) a linear-matrix-inequality-based approach is presented to design energy-to-peak state estimators for SNNs with two types of time-varying delays, whose efficiency is demonstrated via two widely studied numerical examples.

Dissipativity-Based Resilient Filtering of Periodic Markovian Jump Neural Networks With Quantized Measurements

The problem of dissipativity-based resilient filtering for discrete-time periodic Markov jump neural networks in the presence of quantized measurements is investigated in this paper. Due to the limited capacities of network medium, a logarithmic quantizer is applied to the underlying systems. Considering the fact that the filter is realized through a network, randomly occurring parameter uncertainties of the filter are modeled by two mode-dependent Bernoulli processes. By establishing the mode-dependent periodic Lyapunov function, sufficient conditions are given to ensure the stability and dissipativity of the filtering error system. The filter parameters are derived via solving a set of linear matrix inequalities. The merits and validity of the proposed design techniques are verified 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.

Reachable Set Estimation for Markovian Jump Neural Networks With Time-Varying Delays

In this paper, the reachable set estimation problem is investigated for Markovian jump neural networks (NNs) with time-varying delays and bounded peak disturbances. Our goal is to find a set as small as possible which bounds all the state trajectories of the NNs under zero initial conditions. In the framework of Lyapunov-Krasovskii theorem, a newly-found summation inequality combined with the reciprocally convex approach is used to bound the difference of the proposed Lyapunov functional. A new less conservative condition dependent on the upper bound, the lower bound and the delay range of the time delay is established to guarantee that the state trajectories are bounded within an ellipsoid-like set. Then the result is extended to the case with incomplete transition probabilities and a more general condition is derived. Finally, examples including a genetic regulatory network are given to demonstrate the usefulness and the effectiveness of the results obtained in this paper.

Dissipativity-Based Reliable Control for Fuzzy Markov Jump Systems With Actuator Faults

This paper is concerned with the problem of reliable dissipative control for Takagi-Sugeno fuzzy systems with Markov jumping parameters. Considering the influence of actuator faults, a sufficient condition is developed to ensure that the resultant closed-loop system is stochastically stable and strictly ( Q, S,R )-dissipative based on a relaxed approach in which mode-dependent and fuzzy-basis-dependent Lyapunov functions are employed. Then a reliable dissipative control for fuzzy Markov jump systems is designed, with sufficient condition proposed for the existence of guaranteed stability and dissipativity controller. The effectiveness and potential of the obtained design method is verified by two simulation examples.