In this article, fully distributed adaptive fuzzy consensus tracking control (CTC) is explored for heterogeneous networked hyperbolic partial differential equations (PDEs) with boundary actuator dynamics expressed as ordinary differential equations (ODEs). Control input only appears in ODEs instead of in PDE subsystems, which is an interesting and challenging problem. Unknown nonlinear actuator dynamics and complex communication interactions make the existing boundary control schemes no longer effective. Based on several state transformations and infinite-dimensional backstepping technique, the distributed CTC problem of the original systems is reduced to the design of virtual and actual controls for all followers. Using the finite-dimensional backstepping technique, novel adaptive virtual controllers are designed for stabilization control, with unknown nonlinear dynamics approximated by T-S fuzzy systems. Then, by using a first-order filter and the virtual control inputs, the actual controllers are reconfigured. By virtue of the proposed actual control algorithms, CTC is successfully achieved based on state feedback and output feedback. Lastly, the effectiveness and feasibility of the proposed CTC algorithms are validated via two numerical examples.

This article aims to address the problems of fixed-time synchronization (FTS) and fixed-time stabilization (FS) of memristive inertial neural networks (MINNs) with mixed-delays based on a novel lemma of FS. Through using aperiodically semi-intermittent control strategy and designing suitable Lyapunov function, the outcomes of FS and FTS about investigated MINNs are derived. Unlike the order reduction approach, this paper employs a non-order reduction research way to study the considered neural system. At the end of this article, to demonstrate the veracity of this outcomes, we display some simulation examples.

This work addresses the problem of predefined-time cluster lag synchronization for inertial neural networks. A dynamic event-triggered control scheme that incorporates a time-dependent exponential scaling function is proposed. Sufficient conditions are established to ensure the achievement of cluster lag synchronization within a prespecified time. In contrast to traditional Lyapunov-Krasovskii functional approaches that usually result in high-dimensional linear matrix inequalities, the criteria obtained in this paper are formulated as low-dimensional linear matrix inequalities that align with the dimension of the systems, which facilitates easy verification. Furthermore, an additional constraint is derived to preclude the occurrence of Zeno behavior in the closed-loop system. Finally, numerical simulation results are presented to validate the effectiveness of the proposed control strategy and the correctness of the theoretical derivations.

In this paper, the predefined-time synchronization of inertial neural networks with stochastic disturbances is investigated. First, an adaptive control strategy incorporating exponential scaling functions is designed to guarantee synchronization within a predefined time, independent of initial conditions and system parameters. Second, by combining Lyapunov stability theory with stochastic analysis techniques, sufficient criteria are derived to achieve predefined-time synchronization in the presence of stochastic perturbations. Unlike prior works, this paper explores the predefined-time synchronization while addressing the impact of stochastic disturbances. Moreover, the proposed results generalize previous findings on drive-response inertial neural networks to coupled inertial neural networks, offering a unified analytical framework. Finally, numerical simulations are performed to validate the theoretical results.

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 paper studies the stability of switched homogeneous positive systems involving time delays. In contrast to previous approaches that rely on the marginally stable assumption, our framework permits the consideration of subsystems that may exhibit partial divergence. Sufficient conditions are derived to ensure exponential stability for continuous-time switched positive systems, covering both delay-free cases and those with bounded delays. Furthermore, polynomial stability is examined for systems subject to proportional delays. In the discrete-time setting, asymptotic stability criteria are established for systems with constant delays, along with two specific instances of these conditions. The results presented here extend and refine several well-known findings in the literature. To validate the proposed theoretical criteria, three illustrative numerical examples are provided.

This paper investigates fixed-time projective synchronization (FXPS) and preassigned-time projective synchronization (PTPS) of a class of fuzzy neural networks (FNNs) with discontinuous activations and distributed delays. Firstly, based on non-smooth analysis and Lyapunov stability theory, this paper studies the issues of fixed-time stabilization (FTS) for the FNNs. Subsequently, by designing appropriate state feedback controllers, we obtain new criteria for FXPS and PTPS in such FNNs. Unlike recent works, our neural network system is more comprehensive since it incorporates fuzzy terms, mixed-time delays, and discontinuous activation functions. Furthermore, the results achieved in this paper are more generalized since we research the projective synchronization of FNNs, which includes a series of special synchronizations such as complete synchronization and anti-synchronization. Finally, example simulations are carried out to validate the effectiveness of the results achieved in the paper.

This paper addresses the stability issue of discrete-time switched positive nonlinear systems (SPNSs) characterized by partial unstable subsystems and constant delays. Firstly, we use a parameter to constrain the ratio of active durations of the stable and unstable modes, and derive the exponential stability conditions for SPNSs based on a key function. Then we analyze the relationship between convergence speed and the constant delay. Additionally, we obtain a stability criterion of SPNSs under a particular sequence of switching signals. Finally, we validate the results through a numerical example.

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 studies the distributed prescribed-time formation tracking control for nonlinear second-order multiagent systems with collision risk in a null-space-based behavioral control architecture. First, a simplified distributed observer is designed to accurately estimate the position information of a virtual leader within a prescribed time. In addition, we introduce a switching mechanism and potential-like terms to design the desired states that can simultaneously achieve obstacle avoidance and formation. Subsequently, a sliding-mode formation control scheme is proposed to track the desired trajectory generated by the null-space projection between behaviors. Utilizing Lyapunov stability theory, theoretical results for task design and trajectory tracking are obtained. Finally, numerical simulation verifies the effectiveness and superiority of the proposed method.

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, 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.

This paper discusses the exponential stability of continuous-time switched positive nonlinear systems (SPNSs) with time-varying delays. Firstly, we utilize each pair of vector fields to construct an equation to achieve the goal of dealing with each subsystem separately and quantifying the effect of the upper bounds of time delays on the convergence speed of SPNSs. Secondly, we construct a continuous function and derive the stability criterion of the SPNSs by using a proof by contradiction. Then, we obtain the stability for the SPNSs in a special case without delays. Finally, the accuracy of the results is verified through a 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.

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.

Stability theory of linear differential-difference system has been well-established, while fewer results can be found for nonlinear differential-difference systems. In this article, stability and boundedness of homogeneous differential-difference system with bounded delay is studied based on the system positivity. At first, an exponential stability criterion is obtained, which is an extension of an existing result. Next, another boundary is computed under the previous condition, which proves to be tighter than the first result at least in some cases. Then, a finite-time stability condition is achieved for the delay-free system, and an upper bound of the settling time and an explicit boundary of the state are derived. Finally, a numerical example is given to verify the results presented in this article.

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.