Proportional-Integral Observer-Based State Estimation for Markov Memristive Neural Networks With Sensor Saturations

Probabilistic-sampling-based asynchronous control for semi-Markov jumping neural networks with reaction-diffusion terms

This paper investigates the probabilistic-sampling-based asynchronous control problem for semi-Markov reaction-diffusion neural networks (SMRDNNs). Aiming at mitigating the drawback of the well-known fixed-sampling control law, a more general probabilistic-sampling-based control strategy is developed to characterize the randomly sampling period. The system mode is considered to be related to the sojourn-time and undetectable. The jumping of the controller depends on the observation mode, and is asynchronous with the jumping of the system mode. By utilizing the established hidden semi-Markov model and a stochastic analysis approach, some sufficient conditions are obtained to ensure the asymptotically stable of the SMRDNNs. Finally, an example is given to prove the validity and superiority of the conclusion.

DFA-mode-dependent stability of impulsive switched memristive neural networks under channel-covert aperiodic asynchronous attacks

This article is concerned with the deterministic finite automaton-mode-dependent (DFAMD) exponential stability problem of impulsive switched memristive neural networks (SMNNs) with aperiodic asynchronous attacks and the network covert channel. First, unlike the existing literature on SMNNs, this article focuses on DFA to drive mode switching, which facilitates precise system behavior modeling based on deterministic rules and input characters. To eliminate the periodicity and consistency constraints of traditional attacks, this article presents the multichannel aperiodic asynchronous denial-of-service (DoS) attacks, allowing for the diversity of attack sequences. Meanwhile, the network covert channel with a security layer is exploited and its dynamic adjustment is realized jointly through the dynamic weighted try-once-discard (DWTOD) protocol and selector, which can reduce network congestion, improve data security, and enhance system defense capability. In addition, this article proposes a novel mode-dependent hybrid controller composed of output feedback control and mode-dependent impulsive control, with the goal of increasing system flexibility and efficiency. Inspired by the semi-tensor product (STP) technique, Lyapunov-Krasovskii functions, and inequality technology, the novel exponential stability conditions are derived. Finally, a numerical simulation is provided to illustrate the effectiveness of the developed approach.

Sampled-Data State Estimation for LSTM

This article first introduces a sampled-data state estimator design method for continuous-time long short-term memory (LSTM) neural networks with irregularly sampled output. To this end, the structure of the LSTM is addressed to obtain its dynamic equation. As a result, the LSTM neural network is modeled as a continuous-time linear parameter-varying system that is dependent on the gate units. For this system, the sampled-data Luenberger- and Arcak-type state estimator design methods are presented in terms of linear matrix inequalities (LMIs) by using the properties of the gate units. Lastly, the proposed method not only provides a numerical example for analyzing absolute stability but also demonstrates it in practice by applying a pre-trained behavior generation model of a robot manipulator.

Analysis and Application of Matrix-Form Neural Networks for Fast Matrix-Variable Convex Optimization

Matrix-variable optimization is a generalization of vector-variable optimization and has been found to have many important applications. To reduce computation time and storage requirement, this article presents two matrix-form recurrent neural networks (RNNs), one continuous-time model and another discrete-time model, for solving matrix-variable optimization problems with linear constraints. The two proposed matrix-form RNNs have low complexity and are suitable for parallel implementation in terms of matrix state space. The proposed continuous-time matrix-form RNN can significantly generalize existing continuous-time vector-form RNN. The proposed discrete-time matrix-form RNN can be effectively used in blind image restoration, where the storage requirement and computational cost are largely reduced. Theoretically, the two proposed matrix-form RNNs are guaranteed to be globally convergent to the optimal solution under mild conditions. Computed results show that the proposed matrix-form RNN-based algorithm is superior to related vector-form RNN and matrix-form RNN-based algorithms, in terms of computation time.

Protocol-based control for semi-Markov reaction-diffusion neural networks

This paper addresses the asynchronous control problem for semi-Markov reaction-diffusion neural networks (SMRDNNs) under probabilistic event-triggered protocol (PETP) scheduling. A semi-Markov process with a deterministic switching rule is introduced to characterize the stochastic behavior of these networks, effectively mitigating the impacts of arbitrary switching. Leveraging statistical data on communication-induced delays, a novel PETP is proposed that adjusts transmission frequencies through a probabilistic delay division method. The dynamic adjustment of event trigger conditions based on real-time neural network is realized, and the responsiveness of the system is enhanced, which is of great significance for improving the performance and reliability of the communication system. Additionally, a dynamic asynchronous model is introduced that more accurately captures the variations between system modes and controller modes in the network environment. Ultimately, the efficacy and superiority of the developed strategies are validated through a simulation example.

Observer-based resilient dissipativity control for discrete-time memristor-based neural networks with unbounded or bounded time-varying delays

This work focuses on the issue of observer-based resilient dissipativity control of discrete-time memristor-based neural networks (DTMBNNs) with unbounded or bounded time-varying delays. Firstly, the Luenberger observer is designed, and additionally based on the observed states, the observer-based resilient controller is proposed. An augmented system is presented by considering both the error system and the DTMBNNs with the controller. Secondly, a novel sufficient extended exponential dissipativity condition is obtained for the augmented system with unbounded time-varying delays by proposing a system solutions-based estimation approach. This method is based on system solutions and without constructing any Lyapunov-Krasovskii functionals (LKF), thereby reducing the complexity of theoretical derivation and computational workload. In addition, an algorithm is proposed to solve the nonlinear inequalities in the sufficient condition. Thirdly, the sufficient extended exponential dissipativity condition for the augmented system with bounded time-varying delays is also obtained. Finally, the effectiveness of the theoretical results is illustrated through two simulation examples.

Preassigned-time synchronization for complex-valued memristive neural networks with reaction-diffusion terms and Markov parameters

This study addresses the preassigned-time synchronization for complex-valued memristive neural networks with reaction-diffusion terms and Markov parameters. Employing a preassigned-time stable control strategy, two distinct controllers with varying power exponent parameters are designed to ensure that synchronization can be achieved within a predefined time frame. Unlike existing finite/fixed-time results, a priori specification of the settling time is addressed. Furthermore, Green's formula and boundary conditions are efficiently applied to overcome potential symmetry loss. Additionally, the activation function's constraint range is more lenient compared to existing constraints. Finally, the effectiveness of the presented methods are demonstrated through two examples.

Input-to-state stability of positive delayed neural networks via impulsive control

This paper is concerned with the positivity and impulsive stabilization of equilibrium points of delayed neural networks (DNNs) subject to bounded disturbances. With the aid of the continuous dependence theorem for impulsive delay differential equations, a relaxed positivity condition is derived, which allows the neuron interconnection matrix to be Metzler if the activation functions satisfy a certain condition. The notion of input-to-state stability (ISS) is introduced to characterize internal global stability and disturbance attenuation performance for impulsively controlled DNNs. The ISS property is analyzed by employing a time-dependent max-separable Lyapunov function which is able to capture the positivity characterization and hybrid structure of the considered DNNs. A ranged dwell-time-dependent ISS condition is obtained, which allows to design an impulsive control law via partial state variables. As a byproduct, an improved global exponential stability criterion for impulse-free positive DNNs is obtained. The applicability of the achieved results is illustrated through three numerical examples.

Improved disturbance observer-based fixed-time adaptive neural network consensus tracking for nonlinear multi-agent systems

This paper is concerned with the problem of fixed-time consensus tracking for a class of nonlinear multi-agent systems subject to unknown disturbances. Firstly, a modified fixed-time disturbance observer is devised to estimate the unknown mismatched disturbance. Secondly, a distributed fixed-time neural network control protocol is designed, in which neural network is employed to approximate the uncertain nonlinear function. Simultaneously, the technique of command filter is applied to fixed-time control, which circumvents the "explosion of complexity" problem. Under the proposed control strategy, all agents are enable to track the desired trajectory in fixed-time, and the consensus tracking error and disturbance estimation error converge to an arbitrarily small neighborhood of the origin, meanwhile, all signals in the closed-loop system remain bounded. Finally, a simulation example is provided to validate the effectiveness of the presented design method.

Synchronization control of time-delay neural networks via event-triggered non-fragile cost-guaranteed control

This paper is devoted to event-triggered non-fragile cost-guaranteed synchronization control for time-delay neural networks. The switched event-triggered mechanism, which combines periodic sampling and continuous event triggering, is used in the feedback channel. A piecewise functional is first applied to fully utilize the information of the state and activation function. By employing the functional, various integral inequalities, and the free-weight matrix technique, a sufficient condition is established for exponential synchronization and cost-related performance. Then, a joint design of the needed non-fragile feedback gain and trigger matrix is derived by decoupling several nonlinear coupling terms. On the foundation of the joint design, an optimization scheme is given to acquire the minimum cost value while ensuring exponential stability of the synchronization-error system. Finally, a numerical example is used to illustrate the applicability of the present design scheme.

New Criteria for Synchronization of Multilayer Neural Networks via Aperiodically Intermittent Control

In this paper, the globally asymptotic synchronization of multi-layer neural networks is studied via aperiodically intermittent control. Due to the property of intermittent control, it is very hard to deal with the effect of time-varying delays and ascertain the control and rest widths for intermittent control. A new lemma with generalized Halanay-type inequalities are proposed first. Then, by constructing a new Lyapunov–Krasovskii functional and utilizing linear programming methods, several useful criteria are derived to ensure the multilayer neural networks achieve asymptotic synchronization. Moreover, an aperiodically intermittent control is designed, which has no direct relationship with control widths and rest widths and extends existing aperiodically intermittent control techniques, the control gains are designed by solving the linear programming. Finally, a numerical example is provided to confirm the effectiveness of the proposed theoretical results.