The practically fixed-time leaderless cluster synchronization is addressed for uncertain spatiotemporal networks (USTNs) with coopetition interactions, actuator faults and external disturbances. Firstly, by introducing sign-based coupling, a class of USTN is formulated to capture the dynamics of coopetition interactions among different clusters, which provides a more accurate representation compared to dynamical networks with unsigned coupling. Secondly, a practical fixed-time (PFT) convergence theorem is developed for a general partial differential system, which relaxes the constraints on the derivative of the Lyapunov function and provides a less conservative method for estimating the settling time. Subsequently, a distributed fault-tolerant control algorithm is designed to drive the cluster synchronization error to an adjustable attraction region in a fixed time. By exploring specific properties of the intra-cluster Laplacian matrix and proposing a new inter-degree balanced condition, several flexible synchronization criteria are derived and a quantitative relationship among control parameters, the settling time and the size of the attraction region is presented. Finally, the effectiveness of the developed controllers and criteria is validated through a coupled reaction-diffusion neural network.

This article focuses on the fixed-time (FXT) and preassigned-time (PAT) bipartite output regulation of heterogeneous linear multiagent systems (MASs), where both cooperative and adversarial interactions among neighboring agents are considered under a signed graph framework. Since the exosystem information may be unavailable to the agents, an FXT distributed observer and an FXT adaptive distributed observer are designed to accurately identify the exosystem's coefficient matrix and state, respectively. Subsequently, in the absence of the stabilizability and detectability of coefficient matrices, distributed state- and output-feedback control protocols are designed to ensure FXT bipartite output regulation. Besides, for a preset convergence time, the bipartite output regulation is explored by developing control protocols incorporating distributed PAT observers and controllers. Finally, the theoretical results are applied to warehouse automation robot systems.

This article focuses on the bipartite output synchronization for a type of fuzzy fractional output-coupled networks based on fractional-order fuzzy adaptive strategies. Firstly, in view of the unavailability of state information caused by irresistible factors and the coexistence of cooperative and competitive relations in reality, a class of T-S fuzzy fractional networks with output couplings is established under the signed graph framework. Next, a type of membership function-dependent fractional adaptive schemes is presented to automatically regulate the control gains, some criteria of bipartite output synchronization are derived based on the characteristic of the signed topology instead of traditional gauge transformation method. Particularly, a pinning adaptive control scheme is employed to investigate bipartite output synchronization for fuzzy fractional output-coupled networks with the positive-definite output matrix, which determines the pinning nodes just dependent of the cooperative links among nodes in signed graph. The developed criteria are finally confirmed by some examples.

Recently, gauge transformation-based bipartite synchronization has received much interest, but the method of gauge transformation alters the original signed topological structure and the competition or cooperation among individuals is obscured. In addition, the heterogeneity of nodes brings great difficulty and challenge for heterogeneous networks to achieve complete synchronization like homogeneous networks. In this article, without converting signed graph into corresponding unsigned structure via the gauge transformation, the bipartite complete synchronization of heterogeneous fractional networks is explored. Above all, a mathematic model of fractional networks with signed topology and heterogeneous nodes’ dynamics is introduced, in which the topological graph possesses both negative and positive edges to illustrate the competition and cooperation between individuals, and the desired synchronized state is an arbitrarily specified smooth orbit and not necessarily the decoupled state. Additionally, two innovative control schemes with logarithmic quantizer are developed, and several conditions are obtained to reach bipartite complete synchronization of fractional heterogeneous networks just by virtue of the Laplacian matrix of the original signed graph rather than the traditional technique of gauge transformation. The theoretical analysis is eventually confirmed by several numerical results.

This article is concerned about fixed-time (FT) synchronization of spatiotemporal networks (STNs) with the Robin boundary condition. Above all, a switching-type FT stability theorem and an integral inequality are established, which provide a novel theoretical tool for the rigorous analysis of FT control in STNs. Subsequently, three kinds of nontrivial power-law controllers are developed which are separately acted on the interior, the boundary, and the whole of the spatial domain. Based on these control schemes and Lyapunov-like method, several flexible criteria are obtained to achieve FT synchronization of STNs, and the upper bound of the synchronization time is explicitly estimated. Note that, the derived results here are also perfectly applicable to STNs with Neumann or Dirichlet boundary condition. Several illustrate examples are presented at final to confirm the developed controllers and criteria.

The problem of fixed-time (FXT) and preassigned-time (PAT) optimization is concerned in this article based on multiagent systems (MASs) and power-law algorithms. Under the framework of strong convexity of the cost functions, two types of piecewise algorithms are proposed, which ensure that the FXT optimization can be solved either by first achieving the FXT consensus or by first achieving local optimization. Correspondingly, the PAT optimization problem is also considered by designing several piecewise protocols, where the finished time of optimization can be arbitrary prescribed according to actual demands. Furthermore, these piecewise power-law algorithms on the weighted undirected graphs are generalized to the weighted digraphs. Finally, by providing two numerical examples, the presented algorithms are further verified.

In this article, the fixed-time (FXT) synchronization of discontinuous competitive neural networks (CNNs) involving time-varying delays is investigated. Firstly, two kinds of discontinuous FXT control schemes are proposed and two forms of Lyapunov function are constructed based on p-norm and 1-norm to discuss the FXT synchronization of CNNs. By means of nonsmooth analysis and some inequality techniques, some simple criteria are obtained to achieve FXT synchronization and the upper bound of the settling time with less conservativeness is provided. Furthermore, the effect of time scale on FXT synchronization of CNNs is considered. Lastly, some numerical results for an example are provided to demonstrate the derived theoretical results.

This article mainly focuses on the problem of synchronization in finite and fixed time for fully complex-variable delayed neural networks involving discontinuous activations and time-varying delays without dividing the original complex-variable neural networks into two subsystems in the real domain. To avoid the separation method, a complex-valued sign function is proposed and its properties are established. By means of the introduced sign function, two discontinuous control strategies are developed under the quadratic norm and a new norm based on absolute values of real and imaginary parts. By applying nonsmooth analysis and some novel inequality techniques in the complex field, several synchronization criteria and the estimates of the settling time are derived. In particular, under the new norm framework, a unified control strategy is designed and it is revealed that a parameter value in the controller completely decides the networks are synchronized whether in finite time or in fixed time. Finally, some numerical results for an example are provided to support the established theoretical results.

In this paper, without dividing complex-variable networks into two subsystems with real values, the finite-time synchronization is considered for complex-valued dynamical networks with fractional order by means of the theory of complex-variable functions. First of all, as a generalization of the real-valued sign function, the sign functions of complex-valued numbers and complex-valued vectors are introduced and some formulas about them are established. Under the sign function framework, two complex-valued control strategies are designed based on two different norms of complex numbers. Some synchronization criteria are derived and the settling times of synchronization are effectively estimated by developing fractional-order finite-time differential inequalities and utilizing the theory of complex-variable functions. The established theoretical results are demonstrated and the effect of the fractional order of the network model on the finite-time synchronization is revealed finally by providing some numerical simulations.

In this paper, the problem of the finite-time synchronization is addressed for a kind of fractional-order memristive neural networks (FMNNs). First, a new power law inequality with fractional-order and two finite-time fractional differential inequalities are established by means of L'Hospital rule, Laplace transform, and reduction to absurdity, which greatly extend some existing results. In addition, unlike the traditional maximum absolute value-based method to propose memristive synaptic weights, by introducing some transformations, FMNNs are translated to a type of fractional-order systems with uncertain parameters. Furthermore, the finite-time synchronization of FMNNs is investigated by designing a discontinuous control scheme and several criteria are derived based on the developed fractional inequalities and M-matrix theory. Note that in addition to the traditional Lyapunov function with absolute value form, a more general Lyapunov function is constructed to deal with the finite-time synchronization, which makes the derived criteria more flexible and less conservative. Lastly, the derived theoretical results are verified via numerical simulations.

In this paper, spatial diffusions are introduced to fractional-order coupled networks and the problem of synchronization is investigated for fractional-order coupled neural networks with reaction-diffusion terms. First, a new fractional-order inequality is established based on the Caputo partial fractional derivative. To realize asymptotical synchronization, two types of adaptive coupling weights are considered, namely: 1) coupling weights only related to time and 2) coupling weights dependent on both time and space. For each type of coupling weights, based on local information of the node's dynamics, an edge-based fractional-order adaptive law and an edge-based fractional-order pinning adaptive scheme are proposed. Furthermore, some new analytical tools, including the method of contradiction, L'Hopital rule, and Barbalat lemma are developed to establish adaptive synchronization criteria of the addressed networks. Finally, an example with numerical simulations is provided to illustrate the validity and effectiveness of the theoretical results.

This paper investigates exponential stability of fractional-order impulsive control systems (FICSs) and exponential synchronization of fractional-order Cohen-Grossberg neural networks (FCGNNs). First, under the framework of the generalized Caputo fractional-order derivative, some new results for fractional-order calculus are established by mainly using L'Hospital's rule and Laplace transform. Besides, FICSs are translated into impulsive differential equations with fractional-order via utilizing the definition of Dirac function, which reveals that the effect of impulsive control on fractional systems is dependent of the order of the addressed systems. Furthermore, exponential stability of FICSs is proposed and some novel criteria are obtained by applying average impulsive interval and the method of induction. As an application of the stability for FICSs, exponential synchronization of FCGNNs is considered and several synchronization conditions are established under impulsive control. Finally, several numerical examples are provided to illustrate the effectiveness of the derived results.

In this paper, the consensus of fractional-order multiagent systems (FOMASs) is considered via sampled-data control over directed communication topology with the order 0 <; α <; 1. Two cases are considered. One is FOMASs without leader, and the other is FOMASs with a leader. For each case, by applying matrix theory and algebraic graph theory, some algebraic-type necessary and sufficient conditions based on the sampling period, the fractional-order, the coupling gain, and the structure of the network are established for achieving consensus of the system. Moreover, for the network with a dynamic leader, the sampling period, the coupling gain, and the spectrum of the Laplacian matrix are carefully devised, respectively. Finally, several simulation examples are employed to validate the effectiveness of the theoretical results.

In this paper, the exponential synchronization for a class of complex networks with finite distributed delays coupling is studied via periodically intermittent control. Some novel and useful criteria are derived by utilizing a different technique compared with some correspondingly previous results. As a special case, some sufficient conditions ensuring the exponential synchronization for a class of coupled neural networks with distributed delays are obtained. Furthermore, a feasible region of the control parameters is derived for the realization of exponential synchronization. It is worth noting that the synchronized state in this paper is not an isolated node but a non-decoupled state, in which the inner coupling matrix and the degree of the nodes play a central role. Additionally, the traditional assumptions on control width, non-control width, and discrete delays are removed in our results. Finally, some numerical simulations are given to demonstrate the effectiveness of the proposed control method.