This article investigates the practically predefined-time stabilization issue of fuzzy memristive neural networks (FMNNs) in the presence of stochastic disturbances and random deception attacks (RDAs). First, in this article, the concept of practically predefined-time stabilization in probability (PPDTSP) of FMNNs is introduced, and a novel Lyapunov-type criterion for PPDTSP is proposed. The novel criterion eases the restrictions on the differential operator of the Lyapunov function and can be reduced to the existing criterion of predefined-time stabilization in probability (PDTSP). Then, a simplified, practically predefined-time control scheme is constructed to ensure PPDTSP of FMNNs under the interference of stochastic disturbances and RDAs. Furthermore, by employing the simplified control scheme and in the absence of RDAs, some PDTSP results are presented as special instances of the PPDTSP conclusions given in this article. Finally, numerical simulations are conducted to validate the accuracy of the theoretical results.

This article studies a time-segmented design method to achieve prescribed-time formation control (PTFC) while ensuring collision avoidance (CA) by introducing the virtual reference signal for multiagent systems (MASs). Simultaneously achieving these control objectives is challenging, especially in situations where there is a conflict between PTFC and CA. Three different Lyapunov functions (LFs) in the steady-state and transient-state stages play an important role in analyzing the prescribed-time convergence and collision-free characteristics, where the prescribed time can also be set in advance and is not affected by the initial values and parameters of MASs. In addition, the mismatching terms in transient-state stages are dealt with by the designed event-triggered mechanism (ETM), which makes this control strategy more intelligent and determines whether MASs should perform the formation task or CA according to the relationship between the real-time distances of the agents. The conclusion is extended to a class ofn-order MASs, where they can compensate for the mismatching terms and adjust the transient behaviors by the backstepping method and high-order filter, rather than designing distinct controller forms for each of these tasks. Finally, the validity of the proposed control strategy is verified through simulation examples.

The capability of unisensory and multisensory information processing is crucial for bio-inspired intelligent systems. Based on biological nonassociative learning (NAL) and multisensory integration (MSI) mechanisms, a bio-inspired memristor-based neuromorphic circuit is proposed, which bridges multiple unisensory channels with a multisensory mutual associative memory (MMAM) unit. Inspired by the gill-withdrawal reflex in Aplysia, unisensory channels are capable of NAL processes, including habituation, sensitization, dishabituation, and spontaneous recovery, providing adaptation to innocuous stimuli and sensitivity to noxious stimuli. In light of the response enhancement and depression in the superior colliculus under multisensory cues, the MMAM unit enables the interaction between multiple sensory stimuli, thereby facilitating multisensory enhancement and depression, collectively known as MSI. By leveraging the proposed circuit, the artificial nociceptor and semantic satiation are mimicked. Furthermore, circuit performance analyses demonstrate the robustness and device tolerance. By further incorporating visual, auditory, tactile, olfactory, and gustatory sensors and scaling up the circuit, the neuromorphic system is promising for intelligent robot platforms with enhanced environmental perception and cognition capabilities.

In this article, leader-following consensus of time-scale-type heterogeneous nonlinear multiagent systems (HNMASs) is investigated with dynamic periodic event-triggered mechanism (DPETM). The event detection period in DPETM is determined by a function-dependent threshold, whose initial value and the value at each periodic event detection instant are used for the update of an auxiliary function in the DPETM. Furthermore, the auxiliary function with periodic jumps serves as a detection threshold. To guarantee the nonincreasing behavior of the designed non-negative analysis function, a weighted function is devised that shares the same derivative form as the function that determines the detection period during each detection period. Then, by integrating the theory of time scales and graph theory, leader-following consensus is achieved in a periodic communication fashion with fewer sampling updates. Two examples are presented to illustrate the validity of the results.

This article addresses the problem of fixed-time bipartite synchronization (FxTBS) of signed networks (SNs) affected by impulses. First, this article constructs a model of SNs that captures the multilayer properties of the network and takes into account the influence of nonlinear coupling strengths between nodes. To overcome the challenges brought by the introduction of nonlinear coupling strengths, this article adopts a Takagi–Sugeno fuzzy model to characterize the nonlinear variation of coupling strengths reasonably. Then, in the framework of average impulsive interval applicable to a wider range of impulsive signals, this article proposes a novel method for analyzing the fixed-time stability of impulsive systems, which not only loosens the restriction of the derivative of the Lyapunov function in the existing studies, but also gives a more accurate estimation of the settling time, and more importantly, provides a theoretical basis for designing appropriate impulsive signals to modulate the dynamic behavior of SNs toward achieving the desired goal. Based on the newly suggested method, this article derives a unified synchronization criterion suitable for evaluating the implementation of FxTBS of SNs under both desynchronizing and synchronizing impulses. Finally, this article visualizes the correctness of the aforementioned theoretical results utilizing a widely used numerical example.

This article develops a methodology employing partial differential equations (PDEs) to facilitate the exponential deployment of large-scale heterogeneous nonlinear multiagent systems (MASs). The considered MASs comprise a multitude of nonlinear first-order agents (FOAs) and second-order agents (SOAs). Two heterogeneous nonlinear PDEs are established to model the considered MASs by designing appropriate network communication protocols. Unlike previous PDE-based approaches for multiagent deployment, the topological weights between neighboring agents are defined as series-dependent. An informed agent, which is able to measure the location information of other agents and transmit its location information to neighboring agents through the communication network, is placed between the final FOA and the initial SOA. This novel network-based control scheme is referred to as single-point control, which could ensure the well-posedness and exponential stability of the error system. Accordingly, pointwise and distributed measurements are employed for delay-free and time-delayed cases, respectively. Numerical examples are provided in 3-D space to substantiate the obtained theoretical results.

In this article, the bipartite consensus problem of multiagent systems on time scales under switching topologies is investigated. A dynamic event-triggered control strategy is designed to reduce the number of triggers. Sufficient condition to guarantee the consensus is obtained by constructing a non-negative function and combining with the theory of time scale calculus. In addition, it is proved through a categorical discussion that the entire triggering sequence determined by the switching topology and the triggering function does not display Zeno behavior. Lastly, to confirm that the theoretical results are feasible, a numerical simulation and an application to spacecraft formation flight are provided.

For a class of 2-D spatial distributed parameter systems (DPSs) with space-dependent diffusivity, this article aims to achieve exponential realization of their desired profiles. To reduce the number of required sensors and actuators, a planar output feedback boundary control strategy is proposed with combining two nonfull-domain measurement methods, boundary collocated measurement and planar linear measurement, in which only two boundaries of the considered 2-D spatial DPSs are controlled and a little output information is measured. Moreover, by employing the Poincaré-Wirtinger inequality and variable substitution dexterously, the final exponential convergence criteria of the error system can be obtained with method of "Diverse treatment for same term." Finally, we provide a general numerical example and an application example in 2-D heat conduction systems to illustrate the effectiveness and practicability of the proposed measurement and control schemes.

In this article, global exponential stabilization of Takagi–Sugeno (T–S) fuzzy systems with discrete time-varying delays on time scales under denial-of-service (DoS) attacks is investigated. When a DoS attack occurs, the control channel is blocked and the controller is disabled. Combining analytical method, inequality techniques, and time scale theory, stabilization criterion for the underlying systems is obtained via a fuzzy controller. Furthermore, the corresponding outcomes on continuous and discrete time domains are provided, respectively. Finally, two numerical simulations and an application of the Chua's circuit are exhibited to validate the effectiveness of the theories.

Multi-agent-based cooperation of autonomous vehicles(AVs) holds the potential to improve road safety, reduce emissions, and increase transport efficiency. However, the presence of uncertainties stemming from various sources poses a risk to the communication network and can alter the network topology, potentially causing instability in the multi-vehicle system. These uncertainties originate from two main sources: internal multi-vehicle system and external traffic environment. Time delays and packet losses contribute to uncertainties within the internal multi-vehicle system due to the uncontrollability of communication quality. Additionally, the dynamic nature of traffic environments introduces uncertainties related to the number of vehicles, interaction relationships, tasks, and destinations, thereby affecting communication resources and network topologies. Consequently, it is imperative to study the uncertainties faced by the multi-agent system and explore consensus methods for addressing these uncertainties. Notably, this study represents the first comprehensive review of consensus methods for both platooning and broader multi-agent cooperation in the presence of uncertain networks. Furthermore, a systematic summary of multi-agent consensus methods is presented, explicitly addressing two aspects of network uncertainty: imperfect communication transmission and the intricacies of traffic dynamics. The conclusion provides insights into open research issues, paving the way for future studies aimed at enhancing overall multi-vehicle system performance, including aspects such as convergence rate, robustness, and resilience.

This article considers both the semi-Markov jumping phenomenon and spatial distribution characteristics when investigating the exponential stabilization of memristive neural networks (MNNs). The introduction of the semi-Markov jumping parameters relaxes the restriction on the sojourn time of Markovian MNNs. To increase the operability while ensuring control effect, a novel event-based spatially pointwise-piecewise switching control scheme is presented under a unified spatial division criterion, in which the pointwise and piecewise control can switch according to the preset event condition for the applicability to different control requirements. Moreover, by constructing a semi-Markov Lyapunov functional and utilizing the properties of the considered cumulative distribution function, the final exponential stabilization criterion and two related corollaries are obtained. Finally, simulation results illustrate the effectiveness and superiority of the proposed control strategy.

In this article, exponential synchronization of complex dynamical networks (CDNs) on time scales is researched. An IDET control strategy is designed to decrease the number of the event-triggered updating instants. Leveraging intermittent event detections and event-triggered sampling, and combining the analytical method with the time-scale theory, synchronization criteria are obtained for the underlying CDNs. Moreover, a parameter selection algorithm is given to acquire control parameters. In addition, two lemmas on exponential functions of time scales are proposed to prove the exclusion of Zeno behavior. Two numerical simulations and an application of formation control of spacecrafts are given to verify the validity of theoretical results.

This article considers the consensus problem of uncertain multiagent systems, which is addressed by neuroadaptive impulsive control schemes. The proposed control schemes indicate that the communication among agents only occurs impulsively, while the dynamics uncertainty is addressed by adaptive schemes using neural networks. Based on such approaches, two specific control schemes are designed. One is that with impulsive feedback, the control scheme uses continuous-time information, which implies that the adaptive process is continuous over time. Another is that by adopting sampled information, the update of all systems, including the feedbacks on agents, the update of neural networks, and the estimation for uncertainty, can be executed only at impulsive instants. The latter case can reduce the energy cost for communication and control, but extra assistant systems are required. The estimation and consensus prove to be achieved with errors if some conditions are fulfilled. Numerical simulations, including a practical system example, are presented.

This article tackles the global exponential stability for a class of delayed complex-valued inertial neural networks in a discrete-time form. It is assumed that the activation function can be separated explicitly into the real part and imaginary part. Two methods are employed to deal with the stability issue. One is based on the reduced-order method. Two exponential stability criteria are obtained for the equivalent reduced-order network with the generalized matrix-measure concept. The other is directly based on the original second-order system. The main theoretical results complement each other. Some comparisons with the existing works show that the results in this article are less conservative. Two numerical examples are given to illustrate the validity of the main results.

Synchronization of a class of drive-response timescale-type nonautonomous proportional-delayed neural networks (TNPNNs) is addressed in this article. The key technique to cope with the proportional term is using comparison principle. By timescale theory, inequality technique, and comparison principle, criteria of synchronization are obtained. The method used in this article is effective to cope with TNPNNs and it is a direct approach as well by eliminating the conventional exponential transformation. The obtained results are verified with three examples.

Contrary to many existing works based on the continuous-time inertial neural network, this article considers the quasisynchronization issue for the discrete-time inertial neural network. To obtain the main results, we adopt the generalized matrix-measure concept. A condition ensuring the quasisynchronization is attained at first. To make the result less conservative, further analysis based on the generalized matrix measure is proceeded. An example is given to demonstrate the validity and effectiveness of the main results.

This note introduces a unified matrix-measure concept to study the stability of a class of inertial neural networks with bounded time delays on time scales. The novel matrix-measure concept unifies the classic matrix-measure and the generalized matrix-measure concept. One sufficient global exponential stability criterion is obtained based on this key matrix-measure and no Lyapunov function is required. To make the stability performance better, another stability criterion in which more detailed information is involved has been acquired. The theoretical results in this note contain and extend some existing continuous-time and discrete-time works. A numerical example is given to show the validity of the results.

A class of nonautonomous recurrent neural networks (NRNNs) with time-varying delays is considered on time scales. Bounded delays and unbounded delays have been taken into consideration, respectively. First, a new generalized Halanay inequality on time scales is constructed by time-scale theory and some analytical techniques. Based on this inequality, the stabilization of NRNNs with bounded delays is discussed on time scales. The results are also applied to the synchronization of a class of drive-response NRNNs. Furthermore, the stabilization of NRNNs with unbounded delays is investigated. Especially, the stabilization of NRNNs with proportional delays is obtained without any variable transformation. The obtained generalized Halanay inequality on time scales develops and extends some existing ones in the literature. The stabilization criteria for the NRNNs with bounded or unbounded delays cover the results of continuous-time and discrete-time NRNNs and hold the results for the systems that involved on time interval as well. Some examples are given to demonstrate the validity of the results. An application to image encryption and decryption is addressed.

This paper considers generalized discrete-time inertial neural network (GDINN). By timescale theory, the original network is rewritten as a timescale-type inertial NN. Two different scenarios are considered. In a first scenario, several criteria guaranteeing the global exponential stability for the addressed GDINN are obtained based on the generalized matrix measure concept. In this case, Lyapunov function or functional is not necessary. In a second scenario, some inequality analytical and scaling techniques are used to achieve the global exponential stability for the considered GDINN. The obtained criteria are also applied to the global exponential synchronization of drive-response GDINNs. Several illustrative examples, including applications to the pseudorandom number generator and encrypted image transmission, are given to show the effectiveness of the theoretical results.

The existing results of passivity for neural networks mainly concentrated on first-order derivative of the states, whereas it is also significant to study the passivity with high-order derivative. In this paper, a class of memristor-based inertial neural networks (MINNs) with external inputs and outputs are concerned. First, by choosing appropriate variable transformation, the original networks are rewritten as first-order differential equations. Then a criterion of passivity for the MINNs is presented by nonsmooth analysis and linear matrix inequality (LMI) techniques, which could also result in NP-hard problem since it needs at least exponential-time to solve the passivity condition. Meanwhile, based on the obtained passivity criterion, asymptotic stability criterion is accordingly derived for MINNs. In order to avoid the NP-hard problem, we employ matrix-analysis-techniques with the property that the difference-matrix between the given matrix and the proposed matrix is seminegative definite. Then the time complexity for solving the proposed passivity criterion is reduced to constant-time with respect to the number of LMIs. Robust passivity for MINNs is also studied for bounded uncertain parameters. The MINN widens the application ranges for designing neural networks. Finally, relevant simulation examples are given to show the effectiveness of the obtained results.

A class of Takagi-Sugeno (T-S) fuzzy memristor-based inertial neural networks (FMINNs) is studied on time scales. The second-order derivative of the state variable in the network denotes the inertial term. At first, one timescale-type FMINNs is formulated on the basis of T-S fuzzy rules. By a variable transformation, the original network is transformed into first-order differential equations. Then, passivity criteria for the FMINNs are presented based on the characteristic function approach, linear matrix inequality techniques, and the calculus of time scales. Furthermore, two classes of control protocols, i.e., memristor- and fuzzy-related control protocols are designed to solve the passification problem for the considered FMINNs. The optimization problem of the passivity performance is also involved. Finally, simulation examples are given to show the effectiveness and validity of the obtained results, and an application is also given in pseudorandom number generation.

The existed results of Lagrange stability for neural networks (NNs) are scale-free, and hence, conservativeness appears naturally. A class of Takagi-Sugeno (T-S) fuzzy memristive NNs (FMNNs) with time-varying delays is considered on time scales. First, a class of FMNNs is formulated using characteristics of memristors and T-S fuzzy rules. Then some new scale-limited criteria of global exponential stability in Lagrange sense are obtained for FMNNs with bounded feedback functions on the basis of inequalities on time scales and inequality scaling techniques. Also, novel criteria for Lurie-type feedback functions are given, which mainly employ the constructed scale-limited generalized Halanay inequality. Moreover, by matrix-norm strategies, some matrix-norm-based scale-limited criteria are derived for bounded and Lurie-type feedback functions, respectively. It also can be seen that the matrix-norm-based criteria are in accordance with the matrix-measure-based conditions provided the time scale is specified as real set. All scale-limited criteria for Lagrange stability not only include continuous-time criteria and its discrete-time analogues, but also contain more complex cases such as the arbitrary combination of them. In the end, some numerical simulations exhibit the validity of the obtained results.