Stochastic Finite-Time H∞ State Estimation for Discrete-Time Semi-Markovian Jump Neural Networks With Time-Varying Delays

State Estimation for Markovian Jump Neural Networks Under Probabilistic Bit Flips: Allocating Constrained Bit Rates

In this article, the state estimation problem is studied for Markovian jump neural networks (MJNNs) within a digital network framework. The wireless communication channel with limited bandwidth is characterized by a constrained bit rate, and the occurrence of bit flips during wireless transmission is mathematically modeled. A transmission mechanism, which includes coding-decoding under bit-rate constraints and considers probabilistic bit flips, is introduced, providing a thorough characterization of the digital transmission process. A mode-dependent remote estimator is designed, which is capable of effectively capturing the internal state of the neural network. Furthermore, a sufficient condition is proposed to ensure the estimation error to remain bounded under challenging network conditions. Within this theoretical framework, the relationship between the neural network's estimation performance and the bit rate is explored. Finally, a simulation example is provided to validate the theoretical findings.

Design, Analysis, and Application of a Discrete Error Redefinition Neural Network for Time-Varying Quadratic Programming

Time-varying quadratic programming (TV-QP) is widely used in artificial intelligence, robotics, and many other fields. To solve this important problem, a novel discrete error redefinition neural network (D-ERNN) is proposed. By redefining the error monitoring function and discretization, the proposed neural network is superior to some traditional neural networks in terms of convergence speed, robustness, and overshoot. Compared with the continuous ERNN, the proposed discrete neural network is more suitable for computer implementation. Unlike continuous neural networks, this article also analyzes and proves how to select the parameters and step size of the proposed neural networks to ensure the reliability of the network. Moreover, how to achieve the discretization of the ERNN is presented and discussed. The convergence of the proposed neural network without disturbance is proven, and bounded time-varying disturbances can be resisted in theory. Furthermore, the comparison results with other related neural networks show that the proposed D-ERNN has a faster convergence speed, better antidisturbance ability, and lower overshoot.

Delay-dependent Lurie-Postnikov type Lyapunov-Krasovskii functionals for stability analysis of discrete-time delayed neural networks

This paper addresses the influence of time-varying delay and nonlinear activation functions with sector restrictions on the stability of discrete-time neural networks. Compared to previous works that mainly focuses on the influence of delay information, this paper devotes to activation nonlinear functions information to help compensate the analysis technique based on Lyapunov-Krasovskii functional (LKF). A class of delay-dependent Lurie-Postnikov type integral terms involving sector constraints of nonlinear activation function is proposed to complement the LKF construction. The less conservative criteria for the stability analysis of discrete-time delayed networks is given by using improved LKF. Numerical examples show that conservatism can be reduced by the delay-dependent integral terms involving nonlinear activation functions.

Finite-time synchronization for coupled neural networks with time-delay jumping coupling

The finite-time synchronization problem is studied for coupled neural networks (CNNs) with time-delay jumping coupling. Markovian switching topologies, imprecise delay models, uncertain parameters and the unavailable of topology modes are considered in this work. A mode-dependent delay with pre-known conditional probability is built to handle the imprecise delay model problem. A hidden Markov model with uncertain parameters is introduced to describe the mode mismatch problem, and an asynchronous controller is designed. Besides, a set of Bernoulli processes models the random packet dropouts during data communication. Based on Markovian switching topologies, mode-dependent delays, uncertain probabilities and packet dropout, a sufficient condition that guarantees the CNNs reach finite-time synchronization (FTS) is derived. Finally, a numerical example is derived to demonstrate the efficiency of the proposed synchronous technique.

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.

Type-Dependent Average Dwell Time Method and Its Application to Delayed Neural Networks With Large Delays

This article investigates the stability of delayed neural networks with large delays. Unlike previous studies, the original large delay is separated into several parts. Then, the delayed neural network is viewed as the switched system with one stable and multiple unstable subsystems. To effectively guarantee the stability of the considered system, the type-dependent average dwell time (ADT) is proposed to handle switches between any two sequences. Besides, multiple Lyapunov functions (MLFs) are employed to establish stability conditions. Adding more delayed state vectors increases the allowable maximum delay bound (AMDB), reducing the conservatism of stability criteria. A general form of the global exponential stability condition is put forward. Finally, a numerical example illustrates the effectiveness, and superiority of our method over the existing one.

Chance-Constrained H∞ State Estimation for Recursive Neural Networks Under Deception Attacks and Energy Constraints: The Finite-Horizon Case

In this article, the chance-constrained H∞ state estimation problem is investigated for a class of time-varying neural networks subject to measurements degradation and randomly occurring deception attacks. A novel energy-constrained deception attack model is proposed, in which both the occurrence of the attack and the selection of released faked packet are random and the energy of the deception attack is introduced, calculated, and analyzed quantitatively. The main purpose of the addressed problem is to design an H∞ estimator such that the prefixed probabilistic constraints of the system error dynamics are satisfied and the H∞ performance is also ensured. Subsequently, the explicit expression of the estimator gains is derived by solving a minimization problem subjected to certain recursive inequality constraints. Finally, a numerical example and a practical three-tank system are utilized to demonstrate the correctness and effectiveness of the proposed estimation scheme.

Observer-based state estimation for discrete-time semi-Markovian jump neural networks with round-robin protocol against cyber attacks

This paper investigates an observer-based state estimation issue for discrete-time semi-Markovian jump neural networks with Round-Robin protocol and cyber attacks. In order to avoid the network congestion and save the communication resources, the Round-Robin protocol is used to schedule the data transmissions over the networks. Specifically, the cyber attacks are modeled as a set of random variables satisfying the Bernoulli distribution. On the basis of the Lyapunov functional and the discrete Wirtinger-based inequality technique, some sufficient conditions are established to guarantee the dissipativity performance and mean square exponential stability of the argument system. In order to compute the estimator gain parameters, a linear matrix inequality approach is utilized. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed state estimation algorithm.

Finite-Time Estimation for Markovian BAM Neural Networks With Asymmetrical Mode-Dependent Delays and Inconstant Measurements

The issue of finite-time state estimation is studied for discrete-time Markovian bidirectional associative memory neural networks. The asymmetrical system mode-dependent (SMD) time-varying delays (TVDs) are considered, which means that the interval of TVDs is SMD. Because the sensors are inevitably influenced by the measurement environments and indirectly influenced by the system mode, a Markov chain, whose transition probability matrix is SMD, is used to describe the inconstant measurement. A nonfragile estimator is designed to improve the robustness of the estimator. The stochastically finite-time bounded stability is guaranteed under certain conditions. Finally, an example is used to clarify the effectiveness of the state estimation.

Finite-Time Stability of Nonlinear Impulsive Systems With Applications to Neural Networks

This article studies the problem of finite-time stability (FTS) and finite-time contractive stability (FTCS) for nonlinear impulsive systems, where the possibility of time delay in impulses is fully considered. Some sufficient conditions for FTS/FTCS are constructed in the framework of Lyapunov function methods. A relationship between impulsive frequency and the time delay existing in impulses is established to reveal FTS/FTCS performance. As an application, we apply the theoretical results to finite-time state estimation of neural networks, including time-varying neural networks and switched neural networks. Finally, two illustrated examples are given to show the effectiveness and distinctiveness of the proposed delay-dependent impulsive schemes.

Dissipativity-based synthesis for semi-Markovian systems with simultaneous probabilistic sensors and actuators faults: A modified event-triggered strategy

Aided by a modified event-triggered communication policy (ETCP), this article addresses the dissipativity-based control synthesis problem for semi-Markovian switching systems (SMSSs) with simultaneous multiplicative probabilistic faults on sensors and actuators modules. The resulting model under consideration is more extensive, which covers semi-Markovian switching coefficients, transmission delays, and randomly occurring sensors and actuators faults in a unified systematic analytical framework instead of investigating separately in some existing works. More specifically, the probabilistic faults are assumed to happen on both the sensors and actuators modules simultaneously, and the distortion probability for each sensor and actuator is irrelevant, which can be characterized by multiplicate mutually independent stochastic variables that obeys certain statistical features and probabilistic distribution delineate on the interval [0,✠](✠≥1). To reduce the bandwidth usage, a novel event-triggered strategy is designed. Additionally, in the light of this newly developed ETCP, and considering the effects of the signal transmission delays and multitudinous probabilistic failures, a generalized and more realistic faulty pattern for SMSSs is presented, which is more fit for real applications. Hereby, the principal superiority of the established new type faulty pattern lies in its practicality and generality, which contains some previous faulty models as special scenarios. By constructing an appropriate semi-Markovian Lyapunov functional (SMLF) together with mathematical analysis technique and matrix inequality decoupling operation, sojourn-time-dependent sufficient conditions for determining both the control gain matrices and triggered configuration coefficients are developed and formulated in terms of a group of feasible linear matrix inequalities (LMIs). Eventually, several practical examples are exploited to substantiate the validity and practicability of the developed control design methodology.

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.

Reachable Set Estimation of Delayed Markovian Jump Neural Networks Based on an Improved Reciprocally Convex Inequality

This brief investigates the reachable set estimation problem of the delayed Markovian jump neural networks (NNs) with bounded disturbances. First, an improved reciprocally convex inequality is proposed, which contains some existing ones as its special cases. Second, an augmented Lyapunov-Krasovskii functional (LKF) tailored for delayed Markovian jump NNs is proposed. Thirdly, based on the proposed reciprocally convex inequality and the augmented LKF, an accurate ellipsoidal description of the reachable set for delayed Markovian jump NNs is obtained. Finally, simulation results are given to illustrate the effectiveness of the proposed method.

Extended Dissipativity Analysis for Markovian Jump Neural Networks via Double-Integral-Based Delay-Product-Type Lyapunov Functional

This brief studies the problem of extended dissipativity analysis for the Markovian jump neural networks (MJNNs) with time-varying delay. A double-integral-based delay-product-type (DIDPT) Lyapunov functional is first constructed in this brief, which makes full use of the information of time delay. Moreover, some unnecessary constraints on the system structure are removed, which leads to more general results. A numerical example is employed to illustrate the advantages of the proposed method.