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.

In recent years, adaptive drive-response synchronization (DRS) of two continuous-time delayed neural networks (NNs) has been investigated extensively. For two timescale-type NNs (TNNs), how to develop adaptive synchronization control schemes and demonstrate rigorously is still an open problem. This article concentrates on adaptive control design for synchronization of TNNs with unbounded time-varying delays. First, timescale-type Barbalat lemma and novel timescale-type inequality techniques are first proposed, which provides us practical methods to investigate timescale-type nonlinear systems. Second, using timescale-type calculus, novel timescale-type inequality, and timescale-type Barbalat lemma, we demonstrate that global asymptotic synchronization can be achieved via adaptive control under algebraic and matrix inequality criteria even if the time-varying delays are unbounded and nondifferentiable. Adaptive DRS is discussed for TNNs, which implies our control schemes are suitable for continuous-time NNs, their discrete-time counterparts, and any combination of them. Finally, numerical examples on TNNs and timescale-type chaotic Ikeda-like oscillator with unbounded time-varying delays are carried out to verify the adaptive control schemes.

The vast majority of published event-triggered mechanisms (ETMs) are constructed based on measurement errors, which introduces a problem naturally that they are updated when the measurement errors exceed the thresholds although the current obtained sampling states can make systems converge well. With this problem in mind, we redesign ETMs for quasi-synchronization of T-S fuzzy neural networks (FNNs) with time delays on time scales. First, a novel ETM is designed for continuous-time FNNs with time-varying delays to achieve quasi-synchronization, with which synchronization errors is suppressed to globally exponentially converge to a ball. Second, we introduce the ETM for continuous-time FNNs to discrete-time FNNs, owing to the existence of discrete-time states, the Lypunov function of synchronization errors run over the exponentially decay curve, but it can be suppressed to evolve under another exponentially decay curve. Third, for FNNs on time scales with constant and time-varying delays, we estimate the forward jump operator of the Lyapunov functions and design ETMs to guarantee that the Lypunov functions evolve under the exponentially decay curves, so quasi-synchronization can be achieved. Last but not least, we prove that Zeno behavior will not happen and four numerical examples are introduced to verify the validity and the superiority of the proposed ETMs in reducing information transmission.

This article attempts to study observer-based output-feedback tracking control problems of multiple-input multiple-output strict-feedback nonlinear systems (MIMOSFNSs) on time scales. If all nonlinear dynamics are known, the corresponding virtual and actual controllers are designed based on system output and observer states such that system output closely tracks the desired signal. If all nonlinear dynamics are unknown, they are approximated by introducing several Takagi–Sugeno fuzzy systems, then a fuzzy observer, the corresponding virtual and actual controllers, and novel parameter adaptive laws are proposed to achieve output-feedback tracking control for MIMOSFNSs on time scales. It is worth emphasizing that our control schemes are applicable to high-order high-dimensional MIMOSFNSs without using complex nonlinear transformations, and the contradiction of causality in the recursive control design can be avoided. Last but not least, since MIMOSFNSs have been investigated on time scales, our theoretical results can be appropriate for continuous-time MIMOSFNSs, their discrete-time counterparts and arbitrary combination of them. Finally, simulation studies are conducted to verify the validity of the proposed output-feedback tracking control schemes.

This article unifies the stability criteria of asymptotic, exponential, and finite-time control within a single framework for fuzzy neural networks (FNNs) with infinite time delays. First, the boundedness and differentiability for time delays are removed. Then, Lipschitz condition for activation function is relaxed, which is allowed to have jumping discontinuous points. To stabilize FNNs, the analytical method is established by comparison principle, contradiction method and inequality techniques. Moreover, different from the traditional Lyapunov method and finite-time stability theorem, several sufficient conditions are deduced and the suppression functions are designed to guarantee asymptotic, exponential, and finite-time stabilization for FNNs by adjusting the parameters of the same controller. There is not necessary to construct the complex integral-type Lyapunov functional to deal with infinite time delays and to design power function in controller for finite-time stabilization. In addition, the designed event-triggered mechanism has the inherent advantages of saving communication resources and indirectly eliminates the chattering caused by signum function. Finally, simulations are presented to illustrate the feasibility and effectiveness of the theoretical results.

Master-slave synchronization of two delayed neural networks with adaptive controller has been studied in recent years; however, the existing delays in network models are bounded or unbounded with some derivative constraints. For more general delay without these restrictions, how to design proper adaptive controller and prove rigorously the convergence of error system is still a challenging problem. This article gives a positive answer for this problem. By means of the stability result of unbounded delayed system and some analytical techniques, we prove that the traditional centralized adaptive algorithms can achieve global asymptotical synchronization even if the network delays are unbounded without any derivative constraints. To describe the convergence speed of the synchronization error, adaptive designs depending on a flexible ω -type function are also provided to control the synchronization error, which can lead exponential synchronization, polynomial synchronization, and logarithmically synchronization. Numerical examples on delayed neural networks and chaotic Ikeda-like oscillator are presented to verify the adaptive designs, and we find that in the case of unbounded delay, the intervention of ω -type function can promote the realization of synchronization but may destroy the convergence of control gain, and this however will not happen in the case of bounded delay.

The quasisynchronization of nonidentically coupled dynamical networks (NCDNs) with proportional delay is achieved by the event-triggered mechanism (ETM). Heterogeneity and proportional delay greatly increase the difficulty on synchronization of NCDNs. As an unbounded delay in the coupling term, proportional delay is dealt with by the comparison principle, constructing parameter equations, and contradiction method. Moreover, different impulsive effects based on ETM are taken into account to reduce the burden of communication, and the quasisynchronization criteria for NCDNs are derived by the impulsive comparison principle and extended variable parameter formula. The synchronization errors and the exponential convergence rates under different impulsive effects are obtained. It is proven that the proposed ETM can avoid Zeno behavior. Finally, examples show the effectiveness of the proposed control scheme.

This article considers the quasisynchronization of memristive neural networks (MNNs) with communication delays via event-triggered impulsive control (ETIC). In view of the limited communication and bandwidth, we adopt a novel switching event-triggered mechanism (ETM) that not only decreases the times of controller update and the amount of data sent out but also eliminates the Zeno behavior. By using an appropriate Lyapunov function, several algebraic conditions are given for quasisynchronization of MNNs with communication delays. More important, there is no restriction on the derivation of the Lyapunov function, even if it is an increasing function over a period of time. Then, we further propose a switching ETM depending on communication delays and aperiodic sampling, which is more economical and practical and can directly avoid Zeno behavior. Finally, two simulations are presented to validate the effectiveness of the proposed results.

This paper investigates the quasi-synchronization of delayed memristive neural networks (MNNs) via a novel hybrid impulsive control algorithm which combines time-triggered and event-triggered impulsive control. The relationship between a predesigned non-negative auxiliary function and a given exponentially decreasing threshold function is used to describe the switching. Under this novel controller, sufficient conditions for the quasi-synchronization are derived by the impulsive differential inequality. In addition, by choosing appropriate parameters or initial conditions such that the initial value of the non-negative auxiliary function is less than that of the event-triggered function, the quasi-synchronization can be realized theoretically as long as the event-triggered impulsive intensity is less than 1. This greatly reduces the conservatism of the existing quasi-synchronization results. Furthermore, the event-triggered rules can avoid the Zeno behavior as long as the event-triggered impulsive intensity is less than 1. This hybrid mechanism can reduce the amount of impulsive control and lessen the network communication. Finally, one example is given to illustrate the validness of the obtained results.