Distributed formation tracking control with obstacle avoidance of multiagent systems (MASs) under random switching topologies and external disturbances is considered in this article. To achieve the complex objective, an effective control strategy is developed in three steps. First, under the transition probability (TP)-based mode-dependent average dwell-time (MDADT) switching topologies, a distributed objective trajectory achieves almost sure global exponential tracking of the desired formation trajectory. Second, a safe objective trajectory approach is designed by geometrically projecting the unsafe parts of the existing formation trajectory onto the boundary of the obstacle region. Finally, an integral-multiplicative barrier Lyapunov function (IMBLF) is proposed to allow agents to track the safe objective trajectory, where the IMBLF can further guarantee the safety of the MASs. One of the interesting merits of our results is that the impulsive increasing of Lyapunov function at switching instants which is necessary for classical analysis methods has been removed. The feasibility of the proposed formation control method with obstacle avoidance is verified by simulations.

This article investigates the coordination control problem for heterogeneous uncrewed-aerial-vehicle–uncrewed-ground-vehicle systems subject to switching topology. To address the complexity and limited applicability arising from separate modeling, a unified linearized model is established to describe the joint dynamics of both aerial and ground agents. Furthermore, a novel barrier-enhanced dynamic event-triggered mechanism is proposed, wherein a barrier function is embedded to dynamically modulate the triggering threshold. This design effectively balances the tradeoff between strict collision avoidance and communication efficiency. Building on this mechanism, a distributed controller and a reference modifier are codesigned to ensure simultaneous coordination tracking and safety. To handle switching topology, the stability analysis employs dwell-time segmentation and convex combination techniques. This approach guarantees the monotonic decrease of the Lyapunov–Krasovskii functional at switching instants, thereby reducing conservatism. Finally, a numerical simulation and a real-world experiment are conducted to demonstrate the effectiveness and practicality of the proposed approach.

This article investigates secure formation control of a heterogeneous multi-unmanned aerial vehicle (UAV)-unmanned ground vehicle (UGV) system (HMUUS) under nonidentical malicious injection attacks and switching topologies. A unified motion description framework is established to address the system's heterogeneity. By decomposing attacked output signals into nonattacked and attack-related components, two observers are designed to estimate the leader and follower states based solely on nonattacked components, while simultaneously estimating the attack signal for each agent. Based on the estimated states, a distributed controller is designed to ensure that HMUUS can achieve formation. Sufficient conditions are derived to ensure the monotonic decrease of the Lyapunov–Krasovskii functional (LKF) over the entire time domain of HMUUS with communication delays by constructing a piecewise linear time-varying LKF, which significantly reduces conservatism. Simulations and experiments for the HMUUS are conducted to validate the formation under switching topologies and injection attacks.

This paper introduces a novel hierarchical control approach for feature matching, real-time tracking and inter-UAV collision avoidance in multiple unmanned aerial vehicle-unmanned ground vehicle (multi-UAV-UGV) collaborative tracking. Our approach divides into three layers: optimal feature matching, tracking control by reinforcement learning (RL), and collision avoidance using control barrier functions (CBFs). First, a distance cost matrix is cleverly constructed based on the feature matching capabilities of UAVs and UGVs to determine the optimal matching configuration. It allows UAVs to perform the tracking task while minimizing travel distance. Second, a RL-based tracker is developed to achieve precise real-time tracking without depending on UAV dynamic models. The tracker is trained in a single UAV-UGV environment, which reduces policy convergence difficulty by simplifying state space and interactions compared with training in complex multi-UAV-UGV scenarios. Third, a collision avoidance mechanism based on CBFs is introduced to transform RL commands into collision-free actions by solving a quadratic programming (QP) problem. Extensive simulations and real-world experiments demonstrate the effectiveness of the proposed approach.

Ensuring the safety of various real-world applications based on reinforcement learning (RL), such as quadcopter control, robotic manipulators, and autonomous robots, remains a critical challenge, despite RL’s remarkable success in solving complex decision-making tasks. Existing on-policy Lagrangian optimization methods in safe RL typically use a single policy to balance the trade-off between safety and return without taking the potential benefits of adopting multiple policies into account. In this paper, a new on-policy method is proposed, named Safe-Adjusted Policy Optimization(SAPO), which is a dual-policy framework designed to address safety constraint violations in RL. By incorporating a cost-oriented policy to dynamically adjust a reward-oriented policy, the SAPO effectively resolves the trade-off between safety and return. Moreover, to enhance performance in carrying out high-dimensional tasks, the Kullback-Leibler (KL) divergence and a Gaussian kernel are employed in the distance functions to facilitate the training. In addition, a quadcopter-safe-navigation task is designed to overcome the drawback of previous research on quadcopter-safe-navigation with RL that only pays attention to reward function design without considering policy-level optimization. Finally, experimental results verify the feasibility of the designed task. Meanwhile, indicated by the test on real device, the proposed algorithm is easy to be implemented, offers performance guarantees, and outperforms existing safe RL baselines.

In finite-time consensus tracking (FCT) missions of unmanned aerial vehicles (UAVs), faults in aircraft actuators are crucial factors causing tracking precision degradation. In order to solve this problem, this paper develops a fuzzy fault-tolerant cooperative control scheme for UAVs to achieve FCT missions with predefined precision. Compared to existing results, the settling time formulation approach of consensus errors is significantly simplified, which facilitates operators to preset the settling time. Then a switching event-triggered mechanism is designed to flexibly change the transmission frequency of control signals, enabling the limited communication resources of UAVs to be reasonably consumed before and after the settling time. Based on the Lyapunov stability theory, it is proved that all signals of systems are bounded, and consensus errors can achieve prescribed precision in a finite time. Moreover, Zeno behavior is excluded. Finally, a simulation study demonstrates the efficiency and feasibility of the designed control scheme under various uncertainties. Note to Practitioners—In the existing FCT control schemes for UAVs, the formulation approaches of settling time depend on the structure of the communication network and the initial states of the aircraft, which hampers these schemes implemented in large-scale UAVs control tasks. How to effectively simplify the formulation approach of settling time has crucial practical significance and research value. In addition, since the communication bandwidth of UAVs is limited, the existing control strategies introduce event-triggered mechanisms to decrease the communication burden. However, adopting a single event-triggered mechanism cannot flexibly change the transmission frequency of control signals, which may make the limited communication resources fail to be reasonably consumed before and after the settling time. In order to solve the above problems, this paper develops a switching event-triggered FCT control scheme for UAVs, where the designed trigger mechanism can flexibly change the transmission frequency of control signals. Meanwhile, the settling time can be directly formulated following the wishes of operators.

This paper presents a novel control framework that combines reinforcement learning (RL) with filtered position barrier certificate (FPBC) for distributed collision-free multi-agent systems (MASs) control. By introducing a filtered position model on the basis of a velocity-controlled double-integral system, the collision avoidance analysis is greatly simplified. The proposed FPBC is designed based on this filtered position model and enables collision-free interaction among agents using a less conservative first-order control barrier function (CBF), thereby eliminating the need for complex high-order CBFs (HOCBFs). The proposed FPBC is used in a Quadratic Program (QP)-based safety filter that enforces collision avoidance on the actions generated by a RL controller. This RL controller only needs to be trained in a single-agent setting and can learn an effective policy through a stability-optimality reward function to reduce computing resource consumption. Furthermore, a deadlock resolution mechanism is proposed to prevent agent stagnation and task failure in large-scale MASs. Extensive simulations and real-world experiments in UGV and UAV environments validate the proposed framework, which demonstrates superior safety and performance compared to conventional HOCBFs. The experiment video and other supplementaries are available at https://github.com/mahafeeling/FPBC.

This paper proposes three gradient-based neurodynamic optimization approaches for Nash equilibrium seeking in non-cooperative games. The decoupled-gradient and coupled-gradient neurodynamic optimization approaches achieve Nash equilibrium with different fixed-time convergence upper bounds, which are invariant to initial conditions, while the proposed mixed-gradient neurodynamic approach exponentially converges to the Nash equilibrium. The robustness of the proposed fixed-time neurodynamic approaches under vanishing disturbances is also investigated. In addition, three novel analog circuit frameworks are introduced, where the actions of neurons are simulated through a feedback loop composed of multipliers, operational amplifiers, resistors, capacitors, and other basic operation models. The circuits demonstrate that the stable output voltages correspond to the Nash equilibrium. Finally, an example is simulated on Multisim 14.3 to validate the superiority and practicality of the proposed analog circuits.

Autonomous object-searching is crucial for various applications of unmanned aerial vehicles (UAVs). Considering the fact that existing autonomous exploration methods either focus only on maximizing the exploration of unknown areas or suffer from insufficient searches due to repeated and unnecessary exploration, this article introduces an effective object-searching strategy for UAVs in large-scale and complex environments. A novel method is proposed to empower UAVs with the capability to conduct fast, secure, and efficient searches for interested objects in large-scale and complex environments. A Kalman filter-based YOLO algorithm is first proposed to achieve robust object position estimation in cluttered and occlusion-prone scenarios, and a mode-based method is then introduced to conduct a computationally efficient viewpoint generation. A hierarchical searching method is proposed, which not only can increase computational and search efficiency but also can leverage frontier data for search-planning, including coarse global searching paths and optimizing local refined searching trajectories. Experimental results in six different environments indicate that our proposed method outperforms existing techniques in terms of both reduced searching times and computing time. Moreover, the effectiveness of the proposed method is substantiated in various real-world scenarios.

This article develops a novel event-triggered finite-time control strategy to investigate the finite-time synchronization (F-tS) of fractional-order memristive neural networks with state-based switching fuzzy terms. A key distinction of this approach, compared with existing event-based finite-time control schemes, is the linearity of the measurement error function in the event-triggering mechanism (ETM). The advantage of linear measurement error not only simplifies computational tasks but also aids in demonstrating the exclusion of Zeno behavior for fractional-order systems (FSs). Furthermore, to derive F-tS criteria in the form of linear matrix inequalities (LMIs), a novel finite-time analytical framework for FSs is proposed. This framework includes two original inequalities and a weighted-norm-based Lyapunov function. The effectiveness and superiority of the theoretical results are demonstrated through two examples. Both theoretical and experimental results suggest that the criteria obtained using the new analytical framework are less conservative than existing results.

This article proposes two novel projection neural networks (PNNs) with fixed-time ( ) convergence to deal with variational inequality problems (VIPs). The remarkable features of the proposed PNNs are convergence and more accurate upper bounds for arbitrary initial conditions. The robustness of the proposed PNNs under bounded noises is further studied. In addition, the proposed PNNs are applied to deal with absolute value equations (AVEs), noncooperative games, and sparse signal reconstruction problems (SSRPs). The upper bounds of the settling time for the proposed PNNs are tighter than the bounds in the existing neural networks. The effectiveness and advantages of the proposed PNNs are confirmed by numerical examples.

In this article, several novel time-varying momentum-like neurodynamic optimization approaches are proposed for Nash equilibrium (NE) seeking of noncooperative games. It is shown that the dynamics trajectories converge to NE within fixed-time from arbitrary initial conditions, achieving a quicker convergence rate through the selection of distinct time-varying coefficients. Moreover, the upper bounds of the settling time for the proposed NE seeking neurodynamic approaches are explicitly provided. In addition, the study investigates the robustness of the designed neurodynamic approaches in the presence of bounded noises. The superior convergence properties and practicability of our approaches are demonstrated through a simulation example involving energy consumption games.

Considering the memory property of the fractional calculus and the potential diverging state of the open-loop mode, existing analysis methods are difficult to solve the finite-time issue of intermittently controlled fractional-order systems (FOSs). This article studies the finite-time synchronization of coupled FOSs with nonlinearity via fuzzy intermittent quantized control and two novel fractional-order differential inequalities. An interval-type 2 Takagi–Sugeno fuzzy technique is introduced, which not only facilitates the handling of the nonlinear term in the error dynamic system, but also greatly simplifies the control design. Synchronization conditions in form of linear matrix inequalities are provided by designing a novel Lyapunov function on the basis of ellipsoidal norm. Moreover, two corollaries show the generality of the new analysis framework. Compared with existing results, it is amazing that the decreasing magnitude of Lyapunov function on the control intervals can be smaller than its increasing magnitude on the subsequent noncontrol interval. Finally, Chua’s system is used to clarify the effectiveness of theoretical outcomes.

Abstract In this paper, a two-neuron reaction–diffusion neural network with discrete and distributed delays is proposed, and the state feedback control strategy is adopted to achieve control of its spatiotemporal dynamical behaviours. Adding two virtual neurons, the original system is transformed into a neural network only containing the discrete delay. The conditions under which Hopf bifurcation and Turing instability arise are determined through analysis of the characteristic equation. Additionally, the amplitude equations are derived with the aid of weakly nonlinear analysis, and the selection of the Turing patterns is determined. The simulation results demonstrate that the state feedback controller can delay the onset of Hopf bifurcation and suppress the generation of Turing patterns.

In this article, several fixed-time (FT) neurodynamic algorithms with time-varying coefficients are introduced for composite optimization problems. The remarkable features of neurodynamic algorithms are FT convergence from arbitrary initial conditions with faster convergence rate by choosing different time-varying coefficients. The FT convergence of neurodynamic algorithms can be proved by the Polyak-${\L}$ojasiewicz condition, which is beyond strong convexity condition. The upper bounds of the settling time for time-varying neurodynamic algorithms are explicitly given. The robustness of neurodynamic algorithms under bounded noises are further studied. In addition, the proposed neurodynamic algorithms are also utilized for dealing with absolute value equations and sparse signal reconstruction problems. The circuit framework for FT neurodynamic algorithms is subsequently introduced, and an example simulated in Multisim 14.3 is provided to verify the practicability of the proposed analog circuits. Numerical experiments on image recovery and sparse logistic regression are conducted to validate the superiority of the proposed algorithms.

This paper proposes a new dual-design framework to investigate the consensus tracking problem of general switched heterogeneous nonlinear multi-agent systems (MASs) with an uncertain target. A distributed observer that only uses the neighbors’ information is constructed to estimate the target signal by designing a time-varying positive-define matrix function and mode-dependent observer gain matrices. After that, a distributed tracking algorithm is developed to solve the three consensus issues among the observer states, tracker states, and target states at the same time by utilizing the neighbors’ observer states and designing additional mode-dependent feedback gain matrices. The distinct merit of the research is that the designed Lyapunov function is strict monotone decreasing at switching instants, discovering the positive effect of the switching on the consensus. As an application, heterogeneous switched Chua’s circuits are provided to demonstrate the distributed observers and tracking algorithms.

This article presents a new event-triggered adaptive finite-time control strategy using a fuzzy state observer for a class of nonlinear cyber-physical systems (CPSs) under malicious deception attacks with a more general form. Compared with the traditional assumptions on the deception attacks in the existing results, a more general assumption on deception attacks is given in this article. During the design process, real system states are initially estimated by developing an improved state observer, which effectively addresses the problem of state unavailability. Then, a coordinate transformation technology, in which the estimated states of observer are considered, is presented to stabilize the studied system. By constructing the singularity-free finite time virtual controls, the singularity problem in the traditional finite time design algorithms is cleverly avoided. Furthermore, to minimize communication overhead, a final finite-time controller is established by using a relative threshold event-triggered scheme. The developed event-triggered adaptive finite-time control strategy guarantees that all signals in the closed-loop system are semi-globally bounded in finite time without Zeno behavior. Finally, the correctness of the proposed control strategy is validated through two simulation results.

This article focuses on the stability issue of switched network control systems (SNCSs) under deception attacks described by a Bernoulli process with unknown probability distribution. The false information in deception attacks is unknown but bounded and may be state dependent or state independent. By means of the input-to-state stability (ISS) tool and the convex combination method, an improved lemma is first developed for SNCSs, which facilitates the derivations of our results. After that, some attack-independent sufficient conditions for the ISS of SNCSs are obtained for mode-dependent average dwell time switching and stochastic switching, respectively. Different from existing results, the concerned switching contributes to the stability of SNCSs, which benefits the ISS performance of SNCSs even though the unknown deception attacks cause all subsystems to be non-ISS. The proposed results provide an effective solution with strong robustness to deal with unknown deception attacks or denial-of-service attacks.

This article investigates multiasynchronous control for asymptotic stabilization (AS) in mean-square and nonweighted$\mathcal {L}_{2}$-gain for a class of switched Takagi–Sugeno fuzzy systems with both time-varying delay and infinite-time distributed delay (mixed delays) as well as cyber-attacks. The proposed event-triggered controller not only is mode-dependent but also excludes Zeno behavior automatically with two tunable parameters to adjust the event-triggering (ET) number. A novel Lyapunov–Krasovskii functional (LKF) with a negative term is established to greatly reduce the conservatism and simplify the analysis of nonweighted$\mathcal {L}_{2}$-gain by ensuring its increment at switching instants be smaller than one. Three main results are provided to guarantee the AS in mean-square and design the control gains and weights of the ET mechanism, as well as the optimal nonweighted$\mathcal {L}_{2}$-gain. Compared with existing results, the new asynchronous control techniques eliminate the limitation of divergence in mismatched intervals for LKF. Numerical simulations demonstrate the merits of the theoretical analysis.

This article focuses on finite-time$\mathcal {L}_{2}$stabilization of T–S fuzzy systems with time delays and parameter uncertainties via intermittent control. To cope with the effects of parameters uncertainties, time delays, and intermittent divergence simultaneously, a new finite-time stability lemma for intermittently controlled systems is presented. Then, a weighted 2-norm Lyapunov–Krasovskii functional (LKF) is established, which has the advantage that it is convenient to derive less conservative linear matrix inequality sufficient conditions and to overcome the difficulty in analyzing$\mathcal {L}_{2}$performance under intermittent control frameworks. Another advantage of our result over existing results is that the growth increment of the LKF on the noncontrolled interval can be larger than the decreasing magnitude on the controlled interval. The merits of the theoretical results are examined by a numerical example and a coupled Chua's circuit.

State estimation issue is investigated for a switched complex network (CN) with time delay and external disturbances. The considered model is general with a one-sided Lipschitz (OSL) nonlinear term, which is less conservative than Lipschitz one and has wide applications. Adaptive mode-dependent nonidentical event-triggered control (ETC) mechanisms for only partial nodes are proposed for state estimators, which are not only more practical and flexible but also reduce the conservatism of the results. By using dwell-time (DT) segmentation and convex combination methods, a novel discretized Lyapunov–Krasovskii functional (LKF) is developed such that the value of LKF at switching instants is strict monotone decreasing, which makes it easy for nonweighted$\mathcal{L}_2$-gain analysis without additional conservative transformation. The main results are given in the form of linear matrix inequalities (LMIs), by which the control gains of the state estimator are designed. A numerical example is given to illustrate the advantages of the novel analytical method.

This article considers a sort of continuous-time switched T–S fuzzy systems, in which each subsystem switches based on the mode-dependent average dwell time and transition probability and the mixed delay includes time-varying and infinite-time distributed delay. An event-triggered controller (ETC) with mode-dependent random deception attacks is put forward such that the considered system realizes exponential stabilization almost surely (ES a.s.). The ETC is not only mode-dependent but also excludes Zeno behavior automatically with tunable parameters to adjust the event-triggering (ET) numbers according to practical needs. By using the ergodic theory and designing Lyapunov–Krasovskii functional, two criteria are set up to ensure the ES a.s. It is interesting to discover that the ETC is not necessary to control each mode to be stable and the dwell time of an unstable mode can be very large, which greatly reduces the conservatism and saves the control cost. Moreover, the weights of ET mechanism and control gains are obtained for all the switching modes by solving linear matrix inequalities. A simulation example is given to illustrate the merits of theoretical analysis.

This article proposes an asymptotic consensus control algorithm for a vehicle platoon with time-varying communication delays and external disturbances. To avoid continuously monitoring the state of the vehicles and utilize network communication resources efficiently, an event-triggered control (ETC) with three free parameters based on periodic sampling is designed. Consider a switched topology, a novel method is constructed to make the discretized Lyapunov–Krasovskii functional (LKF) monotonically decreasing at switching instants, which allows for better analysis of nonweighted$\mathcal {L}_{2}$-gain. The main results give the sufficient conditions for global asymptotic consensus by linear matrix inequalities (LMIs). Finally, a numerical simulation is presented to show the validity of the new analysis technique.

The current paper is devoted to studying global asymptotic$H_{\infty }$drive-response synchronization for a kind of switched nonlinear time-delay systems with output random injection attacks (IAs). An attack-decomposition method is proposed to derive an attack-free signal, by which an observer is designed to estimate the state of the driving system. Then, two mode-dependent event-triggering mechanisms (MDETMs) are respectively designed for observer-controller (O-C) and controller-actuator (C-A) channels to save the communication resources as much as possible. In order to analyze the effects of the switching on the$H_{\infty }$performance, a mode-dependent discretized Lyapunov-Krasovskii functional (LKF) is developed, which has the merit of monotone decreasing on any time-interval and switching instants. Sufficient criteria are given to ensure the$H_{\infty }$synchronization with non-weighted$\mathcal {L}_{2}$-gain, whether the attack is related to the output or not. Numerical simulations are provided to verify the non-weighted$\mathcal {L}_{2}$-gain performance with low conservatism.

This article investigates$H_{\infty }$global asymptotic synchronization (GAS) of switched nonlinear systems with delay. By introducing mode-dependent double event-triggering mechanisms (DETMs), the communication resources in both system–controller (S-C) channel and controller–actuator (C-A) channel are saved as much as possible. By designing a new multiple Lyapunov–Krasovskii functional (LKF) with time-varying matrices and developing novel analysis techniques such that the increment of the LKF at switching instant is smaller than one, not only the conservatism of obtained results is greatly reduced but also the nonweighted$\mathcal {L}_{2}$-gain is convenient to be derived without using any conservative transformation. The exclusion of the Zeno behavior of the DETMs is proved. Synchronization criteria formulated by linear matrix inequalities (LMIs) are given, by which the control gains, event-triggering weights, as well as the minimum$\mathcal {L}_{2}$-gain are simultaneously designed. Numerical examples demonstrate the low conservatism of the theoretical analysis. Meanwhile, image processing on the basis of the$H_{\infty }$GAS is provided to further illustrate the perfect performance.

It is challenging to synchronize switched time-delay systems when some modes are uncontrolled and the dwell time (DT) of controlled mode is very small. Therefore, in this article, global exponential synchronization almost surely (GES a.s.) in a cluster of switched neural networks (NNs) with hybrid delays (time-varying delay and infinite-time distributed delay) is investigated, where transition probability (TP)-based random mode-dependent average DT (MDADT) switching is considered. A novel mode-dependent pinning event-triggered controller with nonidentical deception attacks is proposed to save the communication resource and derive less conservative results. The two necessary and restrictive conditions in existing papers that the value of the Lyapunov-Krasovskii functional (LKF) before switching instants should be smaller than that after corresponding instant and the DT of each switching mode is restricted by the sampling intervals of the event trigger are moved. Sufficient conditions in terms of linear matrix inequalities (LMIs) are given to guarantee the GES a.s., even though both synchronizing and nonsynchronizing modes coexist and maybe the minimum DT of synchronizing modes is very small. Numerical examples, including image encryption, are provided to demonstrate the merits of the new technique.

It is challenging to deal with the relationship between the triggering interval and the dwell time when mode-pendent event-triggered control is considered for switched systems, especially complete actuator faults occur in some subsystems (or modes). Therefore, this article considers the exponential stabilization almost surely (ES a.s.) for a class of Takagi–Sugeno fuzzy systems with delay and stochastic switching by designing a novel mode-dependent event-triggered output control. It is assumed that only the measured output can be utilized in designing the controller and complete actuator faults occur in some modes. Periodic sampling is utilized to avoid the Zeno phenomenon. Combining the sampling interval with delay-partitioning method, a fuzzy Lyapunov–Krasovskii functional (LKF) is designed on the basis of the derivative of the membership functions to obtain less conservative results. Especially, the increment coefficient of the multiple LKF at switching instant is smaller than one. The maximum feasible value of the sampling interval is derived and the control gains are designed by solving linear matrix inequalities. Our results show that the ES a.s. is ensured though some modes are not controlled. Numerical simulations demonstrate the merits of the theoretical analysis. It is significant to find by numerical simulations that the time delay cannot be divided into too small values though the delay-partitioning method is effective in reducing the conservativeness.

This article focuses on the membership-mismatched impulsive exponential stabilization for fuzzy unconstrained multilayer neural networks (MNNs) with node-dependent time-varying delays (NDTVDs). To begin with, this work proposes a novel MNNs model with unconstrained interlayer and intralayer parameters, which may allow nodes in all layers to have inconsistent attributes and structures. Meanwhile, the novel model considers the NDTVDs and removes the strict constraints including node alignment and one-to-one interlayer connection to meet diverse modeling requirements in complex applications. Then, the proposed fuzzy impulsive controller does not need to share the same fuzzy parameters as the fuzzy MNNs model, reducing the implementation complexity of the fuzzy impulsive controller. To derive the main results using the augmented vector form of unconstrained MNNs, the sparse matrix method is proposed to convert the node-dependent delayed MNNs model into an equivalent model with multiple delays. Moreover, the time-dependent Lyapunov function (TDLF) technique is adopted to improve the reliability of the stabilization conditions by fully utilizing the state information of both the current and neighboring impulsive intervals. Finally, the main results are verified using numerical simulation.

This article is concerned with exponential stabilization almost surely for a class of discrete-time switched T–S fuzzy systems (DTSTSFSs), in which each mode switches according to transition probability and evolves with mode-dependent average dwell time. Parallel distributed compensation (PDC) event-triggered dynamic output quantization (ETDOQ) control is considered for the DTSTSFSs, where event-triggered (ET) mechanism without Zeno behavior is designed, which is mode-dependent and does not restrict the dwell time of each mode. By using the mode-dependent Lyapunov function method, two sufficient conditions termed by linear matrix inequalities are provided. Different from most of existing results, no inequality is resorted in dealing with the uncertainties coming from the quantization. It is interesting that the controlled modes are not required to be stable. New algorithm is designed for the control gains of the ETDOQ controller and the parameters of the ET condition, which overcomes the mismatching difficulty of the parameters induced by the PDC. Numerical simulations demonstrate the merits of the theoretical analysis.

This article is devoted to investigating finite-time synchronization (FTS) for coupled neural networks (CNNs) with time-varying delays and Markovian jumping topologies by using an intermittent quantized controller. Due to the intermittent property, it is very hard to surmount the effects of time delays and ascertain the settling time. A new lemma with novel finite-time stability inequality is developed first. Then, by constructing a new Lyapunov functional and utilizing linear programming (LP) method, several sufficient conditions are obtained to assure that the Markovian CNNs achieve synchronization with an isolated node in a settling time that relies on the initial values of considered systems, the width of control and rest intervals, and the time delays. The control gains are designed by solving the LP. Moreover, an optimal algorithm is given to enhance the accuracy in estimating the settling time. Finally, a numerical example is provided to show the merits and correctness of the theoretical analysis.

This article considers the stabilization issue of switched discrete-time positive systems (SDPSs) with delay by using asynchronous control. Combining transition probability (TP) with mode-dependent average dwell time (MDADT), called TP-based MDADT switching, the SDPSs are more practical than classical models with average dwell-time (ADT) switching. With the aid of a co-positive Lyapunov–Krasovskii functional (CLKF), sufficient conditions ensuring the exponential stability almost surely (ES a.s.) of the SDPSs without control is studied, where the mode is not necessary to be stable. After that, a mode-dependent controller with switching delay is designed to stabilize the SDPSs in the case that there are unstable subsystems. An algorithm is provided to design the control gains. It is discovered that the mode in the closed-loop SDPSs is not required to be stable on synchronous and asynchronous switching intervals. Numerical simulations verify the merits of the new results.

This article is dedicated to solving the coordination problem using a reset algorithm that consists of linear impulsive dynamics, over which antagonistic reciprocity among interacting individuals is inevitable. It shows that reciprocal agents are convergent (including consensus and clusters) whenever the scaling parameters of an agent, corresponded to continuous/discrete dynamics, enjoy the same proportion value that matches to all agents. Otherwise, all participating agents share nothing eventually, that is, they achieve stability. This immediately gives rise to that the final aggregated values of agents are entirely determined by the underlying parameters, on condition that the connection property of communication topologies is preserved. Therefore, the proposed setup features a unified perspective on consensus, clusters (including bipartite consensus), and stability that are separately studied in most of the existing literature. The developed method is well supported via numerical examples.

This article considers global exponential synchronization almost surely (GES a.s.) for a class of switched discrete-time neural networks (DTNNs). The considered system switches from one mode to another according to transition probability (TP) and evolves with mode-dependent average dwell time (MDADT), i.e., TP-based MDADT switching, which is more practical than classical average dwell time (ADT) switching. The logarithmic quantization technique is utilized to design mode-dependent quantized output controllers (QOCs). Noticing that external perturbations are unavoidable, actuator fault (AF) is also considered. New Lyapunov-Krasovskii functionals and analytical techniques are developed to obtain sufficient conditions to guarantee the GES a.s. It is discovered that the TP matrix plays an important role in achieving the GES a.s., the upper bound of the dwell time (DT) of unsynchronized subsystems can be very large, and the lower bound of the DT of synchronized subsystems can be very small. An algorithm is given to design the control gains, and an optimal algorithm is provided for reducing conservatism of the given results. Numerical examples demonstrate the effectiveness and the merits of the theoretical analysis.

This article investigates global exponential synchronization almost surely (GES a.s.) of complex networks (CNs) with node delay and switching topology. By introducing transition probability (TP) and mode-dependent average dwell time (MDADT) to the switching signal, the considered model is more practical than the systems with average dwell-time (ADT) switching. Controllers with both impulsive effects and actuator fault feedback are considered. New analytical techniques are developed to obtain sufficient conditions to guarantee the GES a.s. Different from the existing results on the synchronization of switched systems, our results show that the GES a.s. can still be achieved even in the case that the upper bound of the dwell time (DT) of uncontrolled nodes is very large and the lower bound of the DT of controlled nodes is very small. Numerical examples demonstrate the effectiveness and the merits of the theoretical analysis.

In the literature, the effects of switching with average dwell time (ADT), Markovian switching, and intermittent coupling on stability and synchronization of dynamic systems have been extensively investigated. However, all of them are considered separately because it seems that the three kinds of switching are different from each other. This article proposes a new concept to unify these switchings and considers global exponential synchronization almost surely (GES a.s.) in an array of neural networks (NNs) with mixed delays (including time-varying delay and unbounded distributed delay), switching topology, and stochastic perturbations. A general switching mechanism with transition probability (TP) and mode-dependent ADT (MDADT) (i.e., TP-based MDADT switching in this article) is introduced. By designing a multiple Lyapunov-Krasovskii functional and developing a set of new analytical techniques, sufficient conditions are obtained to ensure that the coupled NNs with the general switching topology achieve GES a.s., even in the case that there are both synchronizing and nonsynchronizing modes. Our results have removed the restrictive condition that the increment coefficients of the multiple Lyapunov-Krasovskii functional at switching instants are larger than one. As applications, the coupled NNs with Markovian switching topology and intermittent coupling are employed. Numerical examples are provided to demonstrate the effectiveness and the merits of the theoretical analysis.

This paper investigates the fixed-time synchronization (FDTS) of complex networks with stochastic perturbations. A new control scheme is designed to realize the synchronization goal. Moreover, the designed controller without sign function is continuous, which means the chattering phenomenon in some previous results can be avoided. By constructing Lyapunov functionals, using the properties of the Weiner process as well as applying a designed comparison system, several FDTS criteria are obtained. Synchronization criteria of this paper are very general and can be utilized in directed and undirected weighted networks. Numerical simulations are given to illustrate the theoretical results.

The asymptotic synchronization of coupled reaction-diffusion neural networks with proportional delay and Markovian switching topologies is considered in this brief where the diffusion space does not need to contain the origin. The main objectives of this brief are to save communication resources and to reduce the conservativeness of the obtained synchronization criteria, which are carried out from the following two aspects: 1) mode-dependent quantized control technique is designed to reduce control cost and save communication channels and 2) Wirtinger inequality is utilized to deal with the reaction-diffusion terms in a matrix form and reciprocally convex technique combined with new Lyapunov-Krasovskii functional is used to derive delay-dependent synchronization criteria. The obtained results are general and formulated by linear matrix inequalities. Moreover, combined with an optimal algorithm, control gains with the least magnitude are designed.

This technical correspondence considers finite-time synchronization of dynamical networks by designing aperiodically intermittent pinning controllers with logarithmic quantization. The control scheme can greatly reduce control cost and save both communication channels and bandwidth. By using multiple Lyapunov functions and convex combination techniques, sufficient conditions formulated by a set of linear matrix inequalities are derived to guarantee that all the node systems are synchronized with an isolated trajectory in a finite settling time. Compared with existing results, the main characteristics of this paper are twofold: 1) quantized controller is used for finite-time synchronization and 2) the designed multiple Lyapunov functions are strictly decreasing. An optimal algorithm is proposed for the estimation of settling time. Numerical simulations are provided to demonstrate the effectiveness of the theoretical analysis.

This paper investigates the problem of finite-time drive-response synchronization for a class of neural networks with discontinuous activations, time-varying discrete and infinite-time distributed delays, and mismatched parameters. In order to cope with the difficulties induced by discontinuous activations, time delays, as well as mismatched parameters simultaneously, new 1-norm-based analytical techniques are developed. Both state feedback and adaptive controllers with and without the sign function are designed. Based on differential inclusion theory and Lyapunov functional method, several sufficient conditions on the finite-time synchronization are obtained. Our results show that the controllers with a sign function can reduce the conservativeness of control gains and the controllers without a sign function can overcome the chattering phenomenon. Numerical examples are given to show the effectiveness of the theoretical analysis.

This paper considers the position-based consensus in a network of agents with double-integrator dynamics and directed topology. Two types of distributed observer algorithms are proposed to solve the consensus problem by utilizing continuous and intermittent position measurements, respectively, where each observer does not interact with any other observers. For the case of continuous communication between network agents, some convergence conditions are derived for reaching consensus in the network with a single constant delay or multiple time-varying delays on the basis of the eigenvalue analysis and the descriptor method. When the network agents can only obtain intermittent position data from local neighbors at discrete time instants, the consensus in the network without time delay or with nonuniform delays is investigated by using the Wirtinger's inequality and the delayed-input approach. Numerical examples are given to illustrate the theoretical analysis.

This paper considers the global exponential synchronization of drive-response memristive neural networks (MNNs) with heterogeneous time-varying delays. Because the parameters of MNNs are state-dependent, the MNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, traditional robust control scheme cannot guarantee the synchronization of MNNs. Under the framework of Filippov solution, the drive and response MNNs are first transformed into systems with interval parameters. Then suitable controllers are designed to overcome the problem of mismatched parameters and synchronize the coupled MNNs. Based on some novel Lyapunov functionals and interval matrix inequalities, several sufficient conditions are derived to guarantee the exponential synchronization. Moreover, adaptive control is also investigated for the exponential synchronization. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

Visually comparing human brain networks from multiple population groups serves as an important task in the field of brain connectomics. The commonly used brain network representation, consisting of nodes and edges, may not be able to reveal the most compelling network differences when the reconstructed networks are dense and homogeneous. In this paper, we leveraged the block information on the Region Of Interest (ROI) based brain networks and studied the problem of blockwise brain network visual comparison. An integrated visual analytics framework was proposed. In the first stage, a two-level ROI block hierarchy was detected by optimizing the anatomical structure and the predictive comparison performance simultaneously. In the second stage, the NodeTrix representation was adopted and customized to visualize the brain network with block information. We conducted controlled user experiments and case studies to evaluate our proposed solution. Results indicated that our visual analytics method outperformed the commonly used node-link graph and adjacency matrix design in the blockwise network comparison tasks. We have shown compelling findings from two real-world brain network data sets, which are consistent with the prior connectomics studies.

This paper considers the asymptotic and finite-time synchronization of drive-response memristive neural networks (MNNs) with time-varying delays. It is known that the parameters of MNNs are state-dependent, and hence the traditional robust control and analytical techniques cannot be directly applied. This difficulty is overcome by using the concept of Filippov solution. However, the special characteristics of MNNs may lead to unexpected parameter mismatch issue when different initial conditions are chosen. Based on a new robust control design, the mismatching issue is solved. Sufficient conditions are derived to guarantee the asymptotic synchronization of the considered MNNs with delays, which may be less conservative than synchronization criterion obtained by using existing methods. Moreover, without using the existing finite-time stability theorem, finite-time synchronization of the MNNs with delays is also investigated. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

This paper is concerned with the cluster synchronization in finite time for a class of complex networks with nonlinear coupling strengths and probabilistic coupling delays. The complex networks consist of several clusters of nonidentical discontinuous systems suffered from uncertain bounded external disturbance. Based on the Takagi-Sugeno (T-S) fuzzy interpolation approach, we first obtain a set of T-S fuzzy complex networks with constant coupling strengths. By developing some novel Lyapunov functionals and using the concept of Filippov solution, some new analytical techniques are established to derive sufficient conditions ensuring the cluster synchronization in a setting time. In particular, this paper extends the pinning control strategies for networks with continuous-time dynamics to discontinuous networks. Numerical simulations demonstrate that the theoretical results are effective and the T-S fuzzy approach is important for relaxed results.

In this paper, a general model of coupled neural networks with Markovian jumping and random coupling strengths is introduced. In the process of evolution, the proposed model switches from one mode to another according to a Markovian chain, and all the modes have different constant time-delays. The coupling strengths are characterized by mutually independent random variables. When compared with most of existing dynamical network models which share common time-delay for all modes and have constant coupling strengths, our model is more practical because different chaotic neural network models can have different time-delays and coupling strength of complex networks may randomly vary around a constant due to environmental and artificial factors. By designing a novel Lyapunov functional and using some inequalities and the properties of random variables, we derive several new sufficient synchronization criteria formulated by linear matrix inequalities. The obtained criteria depend on mode-delays and mathematical expectations and variances of the random coupling strengths as well. Numerical examples are given to demonstrate the effectiveness of the theoretical results, meanwhile right-continuous Markovian chain is also presented.

This paper investigates the problem of adaptive lag synchronization for a kind of competitive neural network with discrete and distributed delays (mixed delays), as well as uncertain nonlinear external and stochastic perturbations (hybrid perturbations). A simple but robust adaptive controller is designed such that the response system can lag-synchronize with a drive system. Based on the Lyapunov stability theory and some suitable Lyapunov-Krasovskii functionals, several sufficient conditions ensuring the lag synchronization are developed. Our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. Some existing results are improved and extended. Moreover, the designed adaptive controller has better anti-interference capacity and is more practical than the usual adaptive controller. Numerical simulations are exploited to show the effectiveness of the theoretical results.