This paper investigates the dynamic event-triggered cooperative control problem for a class of nonlinear multi-agent systems (NMASs) with performance constraints and state time-delays. Firstly, a novel piecewise finite-time prescribed performance function is introduced, and an associated error transformation mechanism is constructed to guarantee that the tracking errors of the NMASs remain within the predefined performance bounds. Secondly, the Lyapunov-Krasovskii (LK) functional is incorporated into the conventional Lyapunov function to effectively address the influence of state time-delays on system stability. Meanwhile, an multi-dimensional Taylor network is employed to approximate the unknown nonlinear functions, which reduces the design complexity of the controller while improving the approximation accuracy. Thirdly, to reduce the number of information transmissions, a dynamic event-triggered mechanism (DETM) is designed to effectively decrease communication resource utilization. Theoretical stability analysis shows that under the proposed control strategy, all signals in the closed-loop system are bounded, the tracking error satisfies the prescribed performance requirements and Zeno behavior is excluded. Finally, a numerical simulation and a single-pendulum robotic manipulator example are provided to verify the effectiveness of the proposed control method.

In this paper, a novel dynamic event-triggered control scheme utilizing a multi-dimensional Taylor network (MTN) approximation technique is proposed for nonlinear multi-agent systems (MASs) subject to performance constraints and input delays. Firstly, a new switching function is constructed and integrated with a performance function. It not only imposes dynamic constraints on the tracking error but also eliminates the strict initial-error requirement inherent in conventional prescribed performance control. Secondly, an auxiliary system is introduced to compensate for the coupling effects caused by input delays. Furthermore, a dynamic event-triggered mechanism (DETM) is incorporated to reduce communication and computational burdens, while maintaining tracking accuracy and strictly preventing Zeno behavior. Lyapunov-based analysis demonstrates that the proposed scheme ensures system stability within a predefined time and achieves the prescribed performance, while all closed-loop signals remain bounded. Finally, simulation studies further validate the scheme’s effectiveness.

In this paper, an event-triggered adaptive tracking control strategy is proposed for strict-feedback stochastic nonlinear systems with predetermined finite-time performance. Firstly, a finite-time performance function (FTPF) is introduced to describe the predetermined tracking performance. With the help of the error transformation technique, the original constrained tracking error is transformed into an equivalent unconstrained variable. Then, the unknown nonlinear functions are approximated by using the multi-dimensional Taylor networks (MTNs) in the backstepping design process. Meanwhile, an event-triggered mechanism with a relative threshold is introduced to reduce the communication burden between actuators and controllers. Furthermore, the proposed control strategy can ensure that all signals of the closed-loop system are bounded in probability and the tracking error is within a predefined range in a finite time. In the end, the effectiveness of the proposed control strategy is verified by two simulation examples.

For the nonlinear systems with input delay, an adaptive fixed-time tracking control strategy based on multi-dimensional Taylor network (MTN) is proposed for the first time. First, to address the main challenge brought by input delay, an auxiliary system is constructed, which transforms the input delay systems into non-delay systems. Second, the MTNs are introduced into the backstepping design process, which reduce the design difficulty by approximating unknown nonlinear functions. Thus, a control scheme subject to low complexity is obtained. Third, aside from ensuring that the tracking error converges within a small neighbourhood of the origin within a fixed-time, the designed control scheme not only makes all signals in the closed-loop system remain bounded, but also avoids the problem of finite-time control relying on initial state. Finally, three simulations are given to prove the feasibility and superiority of the proposed control scheme.

This paper discusses the exponential stability of periodic solutions for stochastic neural networks with multiple time-varying delays. For these networks, sufficient conditions in the linear matrix inequality forms are rare in the literature. We constructed an appropriate Lyapunov-Krasovskii functional to eliminate the items with multiple delays and establish some sufficient conditions in linear matrix inequality forms, to ensure exponential stability of the periodic solutions. Several examples are provided to demonstrate that our results are effective and less conservative than previous ones.

In this paper, an adaptive prescribed performance tracking control(PPTC) problem of uncertain nonlinear systems with unknown hysteresis input is investigated. For the purpose of implementing the PPTC, a performance function and an error conversion function are introduced. Moreover, a backlash-like hysteresis model is adopted to describe the hysteresis nonlinearity, which makes the controller design feasible. Additionally, by converting the backlash-like hysteresis model into a linear model with bounded error, the difficulties caused by hysteresis behavior on controller design are settled. Thus, integrating multi-dimensional Taylor network(MTN) approximation technique into adaptive backstepping method, an adaptive control scheme for uncertain nonlinear systems is proposed. Apart from ensuring that all signals of the closed-loop system keep bounded, the proposed control scheme not only makes the tracking error converge to an arbitrarily small neighborhood around the origin, but also guarantees the tracking error trajectory within the limits set by PPTC. Ultimately, two simulations are applied to verify the validity of the proposed control scheme.

This paper investigates the adaptive tracking control problem of a class of nonlinear systems with intermittent actuator faults and prescribed performance. In the backstepping design process, a performance function is incorporated to ensure that the tracking error adheres to the prescribed performance criteria. Simultaneously, multi-dimensional Taylor networks are used to approximate the unknown nonlinear functions in the system. Subsequently, to avoid jumps in the improved Lyapunov function when faults occur, a boundary estimation method is presented, which effectively compensates for the impact of intermittent actuator faults. Ultimately, based on Lyapunov stability theory, it is proven that all signals of the closed-loop system are bounded, and the tracking error can satisfy the prescribed transient and steady-state performance. Simulation results demonstrate the effectiveness of the proposed scheme.

Maybe because Cohen-Grossberg neural networks with multiple time-varying delays and distributed delays cannot be converted into the vector-matrix forms, the stability results of such networks are relatively few and the stability conditions in the linear matrix inequality forms have not been established. So this paper investigates the exponential stability of the networks and gives the sufficient condition in the linear matrix inequality forms. Two examples are provided to demonstrate the effectiveness of the theoretical results.

Global exponential periodicity of nonlinear neural networks with multiple time-varying delays is investigated. Such neural networks cannot be written in the vector-matrix form because of the existence of the multiple delays. It is noted that although the neural network with multiple time-varying delays has been investigated by Lyapunov-Krasovskii functional method in the literature, the sufficient conditions in the linear matrix inequality form have not been obtained. Two sets of sufficient conditions in the linear matrix inequality form are established by Lyapunov-Krasovskii functional and linear matrix inequality to ensure that two arbitrary solutions of the neural network with multiple delays attract each other exponentially. This is a key prerequisite to prove the existence, uniqueness, and global exponential stability of periodic solutions. Some examples are provided to demonstrate the effectiveness of the established results. We compare the established theoretical results with the previous results and show that the previous results are not applicable to the systems in these examples.

In this paper, a mathematical model for solid avascular tumor growth with a time delay in regulatory apoptosis is studied. In the model, two types of cell apoptoses are considered, one is natural apoptosis and the other is regulatory apoptosis. The process of regulatory apoptosis is delayed compared to the processes of proliferation and natural apoptosis. The existence and uniqueness of a solution to the model are proved. The long-time asymptotic behavior of the solutions is studied. The results show that the dynamical behavior of solutions to this mathematical model is similar to that of the corresponding quasi-stationary problem for some special parameter values. Numerical simulations of some special parameter values are also given to verify our results.

This paper deals with the attractor problem of Hopfield neural networks with multiple time-varying delays. The mathematical expression of the networks cannot be expressed in the vector-matrix form due to the existence of the multiple delays, which leads to the existence condition of the attractor cannot be easily established by linear matrix inequality approach. We try to derive the existence conditions of the linear matrix inequality form of pullback attractor by employing Lyapunov-Krasovskii functional and inequality techniques. Two examples are given to demonstrate the effectiveness of our theoretical results and illustrate the conditions of the linear matrix inequality form are better than those of the algebraic form.

This paper investigates the pullback attractor of Cohen–Grossberg neural networks with multiple time-varying delays. Compared with the existing references, the networks considered here are more general and cannot be expressed in the vector-matrix form due to multiple time-varying delays. After constructing a proper Lyapunov–Krasovskii functional and eliminating the terms involving multiple time-varying delays, two sets of new sufficient criteria on the existence of the pullback attractor are derived based on the theory of pullback attractors. In the end, two examples are given to demonstrate the effectiveness of our theoretical results.

This paper investigates the problem for exponential stability of stochastic Hopfield neural networks involving multiple discrete time-varying delays and multiple distributed time-varying delays. The exponential stability of such neural systems has not been given much attention in the past literature because this type of neural systems cannot be transformed into the vector forms and it is difficult to derive the easily verified stability conditions expressed in terms of the linear matrix inequality. Therefore, this paper tries to establish the easily verified sufficient conditions of the linear matrix inequality forms to ensure the mean-square exponential stability and the almost sure exponential stability for this type of neural systems by constructing a suitable Lyapunov-Krasovskii functional and inequality techniques. Four examples are provided to demonstrate the effectiveness of the proposed theoretical results and compare the established stability conditions to the previous results.

The asymptotic behaviors of a class of impulsive delayed Hopfield neural networks are investigated. By applying the property of nonnegative matrix and an integral inequality, some novel sufficient conditions are derived to ensure the existence of the global attracting set and the stability in a Lagrange sense for the considered networks.

该文探讨了一类具有变时滞的非线性及非自治的神经型Hopfield神经网络的渐近性质.利用非负矩阵的性质和矩阵不等式,得到了保证该系统全局吸引集存在和Lagrange稳定性的充分条件.最后,给出一个例子说明理论的有效性.

A nonlinear size-structured population model with distributed delay in birth process is stud-ied.The time lag in birth process and the internal competition are considered in the model.Sufficient conditions for the existence of steady states are obtained by using the method of semigroups.

This paper presents a new method amongst developing computer vision algorithms for the detection of multiple sclerosis (MS). Lesions caused by MS are detectable on MRI images. CV algorithms present subjective approaches in detection. In this study, we used the grey-level co-occurrence matrix to extract detailed texture features from the spatial distribution of greytone on MRI images. Multi-layered feedforward neural network was used as the classifier. Then, we selected biogeography-based optimisation algorithm to train this classifier. Through cross-validation, the method achieved sensitivity, specificity and accuracy of 92.75±1.31%, 92.76±1.65%, and 92.75±1.43% respectively. We validated the efficiency of the classifier, but overall, the method is inferior to state-of-art algorithms of MS lesion detection in all aspects.

The asymptotic behaviors of a class of delayed Hopfield neural networks are investigated. By applying the property of nonnegative matrix and an integral inequality, some novel sufficient conditions are derived to ensure the existence of the global attracting set and the stability in a Lagrange sense for the considered networks. Finally, a numerical example is given to demonstrate the effectiveness of our theoretical result. Our criteria are easily tested by Matlab LMI Toolbox.

This paper investigates the attractor of Hopfield neural networks with time-varying delays. By using Lyapunov–Krasovskii functional as well as linear matrix inequality, some novel delay-dependent sufficient conditions are derived to ensure the existence of pullback attractor of the considered networks. The constraint that the derivative function of the delay function is less than 1 is removed. Finally, two examples are given to demonstrate the effectiveness of our theoretical result.

Pullback attractor for Cohen–Grossberg neural networks with time-varying delays is investigated. By using the theory of pullback attractors and Lyapunov-Krasovskii functional, some novel criteria are established to ensure the existence of pullback attractor for Cohen–Grossberg neural networks. Finally, two examples are given to illustrate our theoretical results and indicate that two sets of criteria do not include each other.