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This article addresses the problem of synchronization of impulsive networks with switching topologies. A new synchronization framework is established with an emphasis on settling time estimation. The impulsive networks consist of physical nodes and cyber modules. For physical nodes, states are changed impulsively at discrete time instants due to some switching phenomena or unexpected sudden noises. For cyber modules, two cases of switching scenarios are considered for information exchange patterns during specific time intervals. In the first case, cyber modules lose all the communication links with others, resulting in disconnected topologies. Then, a distributed controller is proposed for nodes without intrinsic nonlinear dynamics. A distinguished feature of this controller is its capability to estimate a bound for settling time, beyond which the synchronization with respect to a virtual target is guaranteed. In the second case, cyber modules lose some communication links but build other new ones with the help of a smart communication center to form connected topologies. A distributed controller is further designed for nodes in the presence of intrinsic nonlinear dynamics. Accordingly, a sufficient condition is derived to achieve synchronization with an estimated settling time bound. For both cases, the estimated bounds are able to reveal the relationship between the impulsive strength and the synchronization performance. Finally, numerical examples including a case study on a modified IEEE 34 bus test feeder are provided to demonstrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

This article investigates the sliding-mode control design problem for uncertain time-varying delayed systems. A novel non-negative constraints approach is proposed, which can be used to determine the stability of the controlled systems during the sliding motion. A new stability condition is obtained, which is easy to satisfy and verify. The parameters of the sliding-mode surface can be calculated by solving the non-negative constraints-based optimization problem defined in this article. Simulation examples are presented to illustrate the effectiveness and advantages of the developed strategy. [ABSTRACT FROM AUTHOR]

A great deal of attention from various scientific communities has been recently drawn to complex network systems (CNSs), with many profound results established in this active research field. This article provides a state-of-the-art survey on coordination and control of CNSs with switching network topologies, with emphasis on relationships between the switchings among different topology candidates and the network controllability, and between the switchings among different topology candidates and the emergence of coordination behaviors (including synchronization, consensus, and containment) of such CNSs. First, some fundamental properties of CNSs and the essentials of analytical methodologies for the stability of the fixed point of switched dynamical systems are briefly reviewed. Then, network controllability and the emergence of coordination behaviors of CNSs with switching topologies and the corresponding analytical approaches are discussed in detail, where some of the existing results along these topics are presented in a tutorial-like fashion. This article ends by presenting some interesting future research topics on the coordination and control of CNSs with switching topologies. [ABSTRACT FROM AUTHOR]

This article presents a full mathematical proof of the characteristic modeling approach for high-order linear dynamical systems. It explores the nature of the characteristic model in rigorous mathematical forms, also showing why and how the high-order dynamics can be compressed into the lower-order characteristic model. The relationships between high-order linear continuous dynamical systems, discrete-time characteristic model coefficients, and sampling-time intervals are investigated. [ABSTRACT FROM AUTHOR]

In this paper, characteristic model-based modeling and control approaches for complex dynamical networks based on sampled data are studied. It shows that the characteristic model, in which underline network topological structures are simplified, can provide a straightforward and implicit description for network dynamics. The induced parameter estimation method can further make the model adaptive and purely data-driven. Moreover, a control law based on this model is also proposed to govern the network dynamics. Finally, the theoretical results are verified through numerical simulations of modeling and stabilizing a dynamical network. [ABSTRACT FROM AUTHOR]

The group consensus problems of heterogeneous multiagent networks with input time delays are investigated in this paper. In this complex networks, the agents’ dynamics are modeled by the first-order and the second-order multiagent systems, where a novel dynamic group consensus protocol is designed through the competitive relationship among the agents. By using matrix theory and the frequency-domain method, some algebraic criteria are theoretically established for reaching a group consensus in the following two cases: 1) with the identical and 2) different input time delays. Meanwhile, the conservative assumptions existed in the relevant literatures are absolutely relaxed, i.e., the in-degree balance and the geometric multiplicity of zero eigenvalue of Laplacian matrix are at least two. Finally, the effectiveness of our results is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

This paper proposes a sampled data-based modeling approach for complex network systems. A compression method, known as characteristic modeling, is used to construct microscopic models from macroscopic observations. Based on this model, a novel control method is also developed to achieve network synchronization. The proposed approach can reduce both the complexity of microscopic dynamics and overall networks. Its application to pinning control design validates the effectiveness of this approach. [ABSTRACT FROM AUTHOR]

This paper proposes a control framework, called pulse-modulated intermittent control, which unifies impulsive control and sampled control. Specifically, the concept of pulse function is introduced to characterize the control/rest intervals and the amplitude of the control. By choosing some specified functions as the pulse function, the proposed control scheme can be reduced to sampled control or impulsive control. The proposed control framework is applied to consensus problems of multiagent systems. Using discretization approaches and stability theory, several necessary and sufficient conditions are established to ensure the consensus of the controlled system. The results show that consensus depends not only on the network topology, the sampling period and the control gains, but also the pulse function. Moreover, a lower bound of the asymptotic convergence factor is derived as well. For a given pulse function and an undirected graph, an optimal control gain is designed to achieve the fastest convergence. In addition, impulsive control and sampled control are revisited in the proposed control framework. Finally, some numerical examples are given to verify the effectiveness of theoretical results. [ABSTRACT FROM PUBLISHER]

This article investigates the distributed average tracking (DAT) problem for disturbed second-order multiagent systems, where a crowd of agents is required to track the average of the multiple time-varying signals. First, a new kind of distributed average estimator is developed for each agent to estimate the average of the multiple time-varying signals in finite time. The protocol possesses the distinguished feature of robustness to initialization errors, which can recover from network alterations. Then, an observer-based finite-time tracking protocol is proposed to make each agent exactly track the average of the multiple time-varying signals in finite time in the absence of velocity measurement. By carefully analyzing the dynamic properties of the tracking error system, a suitable Lyapunov function is constructed to estimate the settling time for convergence of the tracking error system theoretically. Furthermore, an adaptive DAT protocol is proposed, which is a fully distributed protocol because it can solve the DAT problem without using any global information. Finally, two simulation examples are provided to verify the effectiveness of the methods. [ABSTRACT FROM AUTHOR]

Distributed stabilization problem is studied in this article for multiple heterogeneous agents in the uncertain strong–weak competition network with exogenous disturbances, where the agents are modeled by the second-order systems with different nonlinear intrinsic dynamics, and the network uncertainty is characterized by unknown nonzero parameters, which contains three different relationships among agents: 1) cooperation; 2) strong competition; and 3) weak competition. To achieve distributed stabilization, the whole network is first divided into two parts: 1) identifiable part and 2) unidentifiable part, and a new distributed robust integral sign of the error (RISE) controller is designed for each agent, where the selection rules of the corresponding parameters are given. It is shown that the heterogeneous multiagent system (MAS) can achieve distributed stabilization no matter whether the identifiable part is structurally balanced or not. Furthermore, it is proved that the global distributed stabilization is achieved for the heterogeneous agents provided that the partial derivatives of the nonlinear intrinsic dynamics are bounded. Finally, two numerical examples are given to demonstrate the effectiveness of the designed controller. [ABSTRACT FROM AUTHOR]

Distributed consensus tracking problem of networked agent systems with directed topologies under denial-of-service (DoS) attacks is investigated. The considered networked agent network consists of a physical layer with fixed physical links and a cyber layer with cyber control units. Both the communication network connecting these two layers and the cyber communication network within the cyber layer may subject to malicious DoS attacks. These two types of attacks have different impacts on the networked system; the former one affects the timely update of control inputs, and the latter influences the connection weights of the cyber communication graph. First, for DoS signals occurring in the communication network which transmits the state and control input information between the two layers, the distributed control protocol based on the event-triggered scheme and locally deployed estimators are designed. Efficient algorithms for selecting event-triggered control parameters and Zeno-free triggered parameters are given to ensure the mean-square consensus. The relationships between the system’s parameters and the features of DoS attacks are successfully revealed. Second, corresponding theoretical analysis is derived for consensus tracking of the networked systems when DoS attacks are launched within the cyber layer. Conditions concerning the length of repairing time and indexes of DoS attacks are given by utilizing hybrid control theory. At last, the effectiveness of the obtained results is demonstrated by performing simulations on multirobot systems. [ABSTRACT FROM AUTHOR]

One fundamental yet challenging issue in security control for resilient complex networks is to construct distributed control laws for the networks to perform various cooperative tasks in the presence of failures and attacks, where resilient indicates that the complex networks are exposed to the environment with cyber uncertainties and malicious adversaries. This is particularly important in today’s critical infrastructure networks since most of them are vulnerable to attacks in the era of the Internet. Inspired by this observation, this paper focuses on synchronization control for resilient complex networks subject to cyber and physical attacks, where the states of nodes being attacked may change abruptly (i.e., the synchronization error may suffer impulsive disturbances), and some nodes as well as their corresponding connections may not work in some instances. Suppose that a smart control center is equipped in the considered network to detect the attacks in real time. Furthermore, the nodes and communication channels are assumed to be recovered through some repair work after detecting the attacks. On the theoretical side, by using the ${M}$ -matrix theory, we get a few sufficient criteria to guarantee the achievement of secure synchronization against attacks on both nodes and communication links. On the algorithmic side, security control algorithm and architecture are proposed to select the coupling strength and the feedback gain matrix to realize synchronization. Finally, we perform two simulation examples to validate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a robust neighbor-based distributed cooperative control strategy is proposed for dc cyber-physical microgrids, considering communication delays and slow switching topologies. The proposed robust control strategy can synchronize the voltages of a dc microgrid to the desired value while achieving the optimal load sharing for minimizing distributed energy resources’ (DERs) generation cost to achieve their economic operation at the same layer via a sparse communication network considering communication delays and slow switching topologies synchronously. The continuous interaction of physical–electrical and cyber networks generally exacerbates the occurrence of communication delays. Moreover, the arbitrary switching topologies could destroy the system’s transient characteristics at the switching time instants. To further quantify these impacts on the system stability, the communication delay and average switching dwell-time-dependent control conditions for the proposed control strategy are proved based on the Lyapunov–Krasovskii theory. Some sufficient conditions for the exponential stability of the cyber-physical delayed-switching system are developed, which guarantees the robustness of the proposed strategy against the communication delays and dynamically changing interaction topologies. The proposed control protocols are shown to be fully distributed and implemented through a sparse communication network. Finally, several cases on a modified IEEE 34-bus test network are investigated which demonstrate the effectiveness and performance of the results. [ABSTRACT FROM AUTHOR]

This article investigates the distributed optimal cooperation problems for multiple high-order systems, in which the dynamics of each agent is allowed to be subject to unknown nonlinearities. To eliminate the effect caused by unknown nonlinearities, a nonlinearity estimator is developed based on agents’ states, which successfully reconstructs the nonlinear dynamics if the unknown nonlinearities are bounded. And to minimize the sum of multiple local nonlinear cost functions with Lipschitz-type gradients, a couple of static and adaptive state-dependent algorithms are designed, respectively, where each agent may only have access to its own local cost function. It is challenging to solve such an optimal cooperation problem as the performance of the whole multiagent network is evaluated by the sum of all local performance functions. In order to fulfill the goal of cooperative optimization, a state-dependent distributed optimal cooperation algorithm is proposed first. By utilizing tools from the Lyapunov stability theory and convex optimization analysis, it is proven that the considered distributed optimal cooperation problem for high-order nonlinear systems can be solved by the proposed optimal cooperation algorithm if the state-dependent parameters are suitably selected. It is noted that the selections of the state-dependent parameters depend on some global information of the multiagent systems. Furthermore, by incorporating the proposed optimal cooperation algorithm with adaptive parameters strategy, the optimal cooperation problem is solved in a fully distributed manner. Finally, a numerical simulation is shown to verify the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article is concerned with the problem of global finite-time output stabilization for a class of second-order nonlinear systems with both uncertain nonlinear dynamics and unknown external disturbance. Specifically, at the first step, without considering the external disturbance, a global finite-time state feedback controller is proposed to dominate uncertain nonlinear dynamics of the second-order system. To address the more challenging case where only the system output is available, a novel design idea of the nonseparation principle is employed. By treating the unknown external disturbance as a generalized state, a finite-time convergent extended state observer is constructed to estimate the unmeasured state and the unknown external disturbance. Based on this observer, an output-based composite controller with finite-time convergence is developed. The global uniform finite-time stability of the overall closed-loop system is proven based on the Lyapunov method. Simulation results of the inverted pendulum system demonstrate the superiority of the proposed control method in terms of both convergence performance and disturbance rejection performance. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of designing a control strategy to guarantee stability in probability for high-order stochastic systems. The control hinges on the sliding-mode scheme. We first prove that the control design can stabilize a fast terminal sliding-mode function. We further show that the stable sliding mode is able to assure the stability in probability for the high-order stochastic system. The resulting system may account nonvanishing diffusion terms, which is regarded as a novelty. The derived control strategy has implications for applications—experiments are carried out to control the pitch angle of a one-degree-of-freedom aerial device. The corresponding experimental results demonstrate the benefits and effectiveness of our approach. [ABSTRACT FROM AUTHOR]

In this paper, the global pinning synchronization problem is studied for a complex dynamical network to follow a dynamic target system. A distinguished feature of the present network model is that the target system may have some predesigned control inputs. This implies that, when pinning synchronization is guaranteed, the states of the nodes within such a pinning-controlled dynamical network may approach a specified trajectory which does not satisfy the system equation of the uncoupling individual node system within the network. The practical constraint that the external control inputs acting on the target system are unknown to any node in the considered network poses a big challenge in solving such a pinning synchronization problem. The designed scheme for achieving pinning synchronization is executed in two steps. Specifically, the first step is to select some nodes to pin such that the augmented interaction topology has at least one directed spanning tree rooted at the node describing the target system, while the second step is to construct a coupling law to synchronize all the states of nodes within the network. Moreover, two kinds of discontinuous coupling laws with static and adaptive coupling gains are, respectively, proposed to achieve pinning synchronization. Meanwhile, by utilizing nonsingular ${M}$ -matrix theory and Lyapunov stability analysis for nonsmooth system, some efficient criteria are established for guaranteeing synchronization in the pinning-controlled networks. Numerical simulations on pinning synchronization of networking Chua’s circuit systems are finally given to verify the analytic results. [ABSTRACT FROM AUTHOR]

The finite-iteration tracking for singular coupled systems with packet-dropping learning controllers is discussed in this paper. The singular coupled systems are constructed to describe systems with some algebraic constraints, and iterative learning controllers are then designed to achieve the finite-iteration tracking of singular systems. The definition of the finite-iteration tracking is first proposed and the settling iteration is explicitly calculated. Moreover, the iterative learning controllers are designed to consider the case of packet losses. Simulation results are given to elaborate the correctness of the given theorems. [ABSTRACT FROM AUTHOR]

In this paper, the robust fixed-time consensus problem for multiagent systems with nonlinear dynamics and uncertain disturbances under a weighted undirected topology is investigated. Some nonlinear control protocols are proposed under which fixed-time consensus in the considered multiagent systems can be ensured. Compared with the initial-condition based finite-time consensus, it is theoretically shown that any prescribed convergence time for the achievement of consensus can be guaranteed within fixed time regardless of the initial conditions. Furthermore, the achievement of consensus is shown to be robust against bounded uncertain disturbances affecting the agents. Finally, some numerical examples are provided to illustrate the performance and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with a consensus tracking problem for multiagent systems (MASs) with Lipschitz-type nonlinear dynamics and directed switching topology. Unlike most existing works where the relative full state measurements of neighboring agents are utilized, it is assumed that only the relative output measurements of neighboring agents are available for coordination. To achieve consensus tracking in the considered MASs, a new class of observer-based protocols is proposed. By appropriately constructing some topology-dependent multiple Lyapunov functions, it is theoretically shown that distributed consensus tracking in the closed-loop MASs equipped with the designed protocols can be ensured if each possible topology contains a directed spanning tree rooted at the leader and the dwell time for the switchings among different topology is less than a derived positive quantity. Interestingly, it is found that the communication topology for observers’ states may be independent with that of the feedback signals. The derived results are further extended to the case of directed switching topology with only average dwell time constraints. Finally, the effectiveness of the analytical results is demonstrated via numerical simulations. [ABSTRACT FROM PUBLISHER]

This paper investigates the fuzzy control issue for uncertain active suspension systems via dynamic sliding-mode method. The Takagi–Sugeno fuzzy approach is adopted on the background of the varying masses to describe the prescribed nonlinear system in order to achieve the design targets via the method of sector nonlinearity. This paper employs the dynamic sliding-mode scheme to control nonlinear active suspension systems. In the proposed sliding-mode control scheme, the sliding surface function is formed linearly with the system states and control inputs. Then, a fuzzy dynamic term is utilized to construct the sliding-mode feedback controller. In existing results, the sliding mode is achieved and maintained with no consideration of the system perturbations. Thus, sufficient conditions are proposed to make the sliding surface reachable with the existence of the system perturbations to make the augmented system stable. Finally, simulation results are presented to verify the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

In the above paper [1], there are errors regarding the description of (4), and misquotes in Algorithm 1 and 2. In Algorithm 1, the first equation referenced should be (5) and not (40). In Algorithm 2, the first equation referenced should be (40) and not (5). The correction for (4) is as follows: \begin{equation*} \mathcal {L}^{(\sigma (t))}=\left [{\begin{array}{cc} \widetilde {\mathcal {L}}^{(\sigma (t))}& \mathrm {a}^{(\sigma (t))}\\ \mathrm {0}_{N}^{T}& 0 \end{array}}\right ] \tag{4}\end{equation*} where \widetilde \mathcal L^(\sigma (t))\in \mathbb R^N\times N , \mathrm a^(\sigma (t))=-[a1(N+1)^(\sigma (t)),a2(N+1)^(\sigma (t)),\cdots ,~aN(N+1)^(\sigma (t))]^{T}\in \mathbb {R}^{N} , and \mathcal A^(\sigma (t)) = [aij^(\sigma (t))](N+1) \times (N+1) is the adjacency matrix of \mathcal G^(\sigma (t)) . [ABSTRACT FROM AUTHOR]