Neuro-Adaptive Consensus Tracking of Multiagent Systems With a High-Dimensional Leader

Robust Predefined Output Containment for Heterogeneous Nonlinear Multiagent Systems Under Unknown Nonidentical Leaders' Dynamics

This article discusses the robust predefined output containment (RPOC) control problem for heterogeneous nonlinear multiagent systems having multiple uncertain nonidentical leaders. In order to solve this problem, a new kind of distributed observer-based RPOC control framework is presented. First, for obtaining the information of nonidentical leaders' dynamics, including uncertain parameters in leaders' system matrices, output matrices, states, and outputs, four kinds of adaptive observers are constructed in a fully distributed form without any knowledge of the dynamics of nonidentical leaders, exactly. Second, on the basis of adaptive learning technique, a new RPOC controller is then developed by using the presented observers, where the adaptive observers can make up for the uncertain parameter in followers' dynamics, and the solutions of output regulation equations can be obtained adaptively by the developed adaptive strategy. Furthermore, with the help of the output regulation method and Lyapunov stability theory, the RPOC criteria for the considered system under unknown nonidentical leaders' dynamics are derived from the constructed controller. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed RPOC controller.

Event-triggered protocol-based adaptive impulsive control for delayed chaotic neural networks

This article focuses on the synchronization problem of delayed chaotic neural networks via adaptive impulsive control. An adaptive impulsive gain law in a discrete-time framework is designed. The delay is handled skillfully by using the Lyapunov-Razumikhin method. To improve the flexibility of impulsive control, an event-triggered impulsive strategy to determine when the impulsive instant happens is designed. Additionally, it is proved that the event-triggered impulsive sequence cannot result in the occurrence of Zeno behavior. Some criteria are derived to guarantee synchronization for delayed chaotic neural networks. Eventually, an illustrative example is presented to empirically validate the effectiveness of the suggested strategy.

Asymptotical Neuro-Adaptive Consensus of Multi-Agent Systems With a High Dimensional Leader and Directed Switching Topology

We study the asymptotical consensus problem for multi-agent systems (MASs) consisting of a high-dimensional leader and multiple followers with unknown nonlinear dynamics under directed switching topology by using a neural network (NN) adaptive control approach. First, we design an observer for each follower to reconstruct the states of the leader. Second, by using the idea of discontinuous control, we design a discontinuous consensus controller together with an NN adaptive law. Finally, by using the average dwell time (ADT) method and the Barbǎlat's lemma, we show that asymptotical neuroadaptive consensus can be achieved in the considered MAS if the ADT is larger than a positive threshold. Moreover, we study the asymptotical neuroadaptive consensus problem for MASs with intermittent topology. Finally, we perform two simulation examples to validate the obtained theoretical results. In contrast to the existing works, the asymptotical neuroadaptive consensus problem for MASs is firstly solved under directed switching topology.

Distributed Fuzzy Optimal Consensus Control of State-Constrained Nonlinear Strict-Feedback Systems

This article investigates the distributed fuzzy optimal consensus control problem for state-constrained nonlinear strict-feedback systems under an identifier-actor-critic architecture. First, a fuzzy identifier is designed to approximate each agent's unknown nonlinear dynamics. Then, by defining multiple barrier-type local optimal performance indexes for each agent, the optimal virtual and actual control laws are obtained, where two fuzzy-logic systems working as the actor network and critic network are used to execute control behavior and evaluate control performance, respectively. It is proved that the proposed control protocol can drive all agents to reach consensus without violating state constraints, and make the local performance indexes reach the Nash equilibrium simultaneously. Simulation studies are given to verify the effectiveness of the developed fuzzy optimal consensus control approach.

Fuzzy Adaptive Cooperative Consensus Tracking of High-Order Nonlinear Multiagent Networks With Guaranteed Performances

This work addresses the distributed consensus tracking problem for an extended class of high-order nonlinear multiagent networks with guaranteed performances over a directed graph. The adding one power integrator methodology is skillfully incorporated into the distributed protocol so as to tackle high powers in a distributed fashion. The distinguishing feature of the proposed design, besides guaranteeing closed-loop stability, is that some transient-state and steady-state metrics (e.g., maximum overshoot and convergence rate) can be preselected a priori by devising a novel performance function. More precisely, as opposed to conventional prescribed performance functions, a new asymmetry local tracking error-transformed variable is designed to circumvent the singularity problem and alleviate the computational burden caused by the conventional transformation function and its inverse function, and to solve the nondifferentiability issue that exists in most existing designs. Furthermore, the consensus tracking error is shown to converge to a residual set, whose size can be adjusted as small as desired through selecting proper parameters, while ensuring closed-loop stability and preassigned performances. One numerical and one practical example have been conducted to highlight the superiority of the proposed strategy.

Cooperative Adaptive Model-Free Control With Model-Free Estimation and Online Gain Tuning

In this article, a distributed adaptive model-free control algorithm is proposed for consensus and formation-tracking problems in a network of agents with completely unknown nonlinear dynamic systems. The specification of the communication graph in the network is incorporated in the adaptive laws for estimation of the unknown linear and nonlinear terms, and in the online updating of the elements in the main controller gain matrix. The decentralized control signal at each agent in the network requires information about the states of the leader agent, as well as the desired formation variables of the agents in a local coordinate frame. These two sets of variables are provided at each agent by utilizing two recently proposed distributed observers. It is shown that only a spanning-tree rooted at the leader agent is enough for the convergence and stability of the proposed cooperative control and observer algorithms. Two simulation studies are provided to evaluate the performance of the proposed algorithm in comparison with two state-of-the-art distributed model-free control algorithms. With lower control effort as well as fewer offline gain tuning, the same level of consensus errors is achieved. Finally, the application of the proposed solution is studied in the formation-tracking control of a team of autonomous aerial mobile robots via simulation results.

Topology Identification of Multilink Complex Dynamical Networks via Adaptive Observers Incorporating Chaotic Exosignals

Topology identification of complex networks is an important and meaningful research direction. In recent years, the topology identification method based on adaptive synchronization has been developed rapidly. However, a critical shortcoming of this method is that inner synchronization of a network breaks the precondition of linear independence and leads to the failure of topology identification. Hence, how to identify the network topology when possible inner synchronization occurs within the network has been a challenging research issue. To solve this problem, this article proposes improved topology identification methods by regulating the original network to synchronize with an auxiliary network composed of isolated chaotic exosystems. The proposed methods do not require the sophisticated assumption of linear independence. The topology identification observers incorporating a series of isolated chaotic exosignals can accurately identify the network structure. Finally, numerical simulations show that the proposed methods are effective to identify the structure of a network even with large weights of edges and abundant connections between nodes.

Distributed Cooperative Compound Tracking Control for a Platoon of Vehicles With Adaptive NN

This article focuses on the distributed cooperative compound tracking issue of the vehicular platoon. First, a definition, called compound tracking control, is proposed, which means that the practical finite-time stability and asymptotical convergence can be simultaneously satisfied. Then, a modified performance function, named finite-time performance function, is designed, which possesses the faster convergence rate compared to the existing ones. Moreover, the adaptive neural network (NN), prescribed performance technique, and backstepping method are utilized to design a distributed cooperative regulation protocol. It is worth noting that the convergence time of the proposed algorithm does not depend on the initial values and design parameters. Finally, simulation experiments are given to further verify the effectiveness of the presented theoretical findings.

Resilient Delayed Impulsive Control for Consensus of Multiagent Networks Subject to Malicious Agents

Impulsive control is widely applied to achieve the consensus of multiagent networks (MANs). It is noticed that malicious agents may have adverse effects on the global behaviors, which, however, are not taken into account in the literature. In this study, a novel delayed impulsive control strategy based on sampled data is proposed to achieve the resilient consensus of MANs subject to malicious agents. It is worth pointing out that the proposed control strategy does not require any information on the number of malicious agents, which is usually required in the existing works on resilient consensus. Under appropriate control gains and sampling period, a necessary and sufficient graphic condition is derived to achieve the resilient consensus of the considered MAN. Finally, the effectiveness of the resilient delayed impulsive control is well demonstrated via simulation studies.

Couple-Group Consensus of Cooperative-Competitive Heterogeneous Multiagent Systems: A Fully Distributed Event-Triggered and Pinning Control Method

This article discusses the couple-group consensus for heterogeneous multiagent systems via event-triggered and pinning control methods. Considering cooperative-competitive interaction among the agents, a novel group consensus protocol is designed. As inducing the time-correlation threshold function, a class of fully distributed event-triggered conditions without depending on any global information is proposed. Utilizing the Lyapunov stability theory, some sufficient conditions are obtained. Under hybrid event triggered and pinning control, pinning control strategies are first introduced. It is shown that under the proposed strategies, all agents can asymptotically achieve pinning couple-group consensus with discontinuous communication in a fully distributed way. Furthermore, the Zeno behavior for each agent is overcome. Finally, the reduction of the systems' controller update frequency and the correctness of our conclusions are illustrated by some simulations.

Distributed Adaptive Consensus of Nonlinear Heterogeneous Agents With Delayed and Sampled Neighbor Measurements

In this article, the adaptive output consensus problem of high-order nonlinear heterogeneous agents is addressed using only delayed, sampled neighbor output measurements. A class of auxiliary variables is introduced which are n -times differentiable functions and include the agent's output along with delayed, sampled output neighbor measurements. It is proven that if these variables are bounded and regulated to zero then asymptotic consensus among all agent outputs is ensured. In view of this property, an adaptive distributed backstepping design procedure is presented that guarantees boundedness and regulation of the proposed variables. This design procedure ensures not only the desired asymptotic output consensus but also the uniform boundedness of all closed-loop variables. The main feature of our approach is that, in the proposed control law for each agent, the entire state vector of the neighbors is not needed and only delayed sampled measurements of the neighbors' outputs are utilized. The simulation results are also presented that verify our theoretical analysis.

On Containment for Linear Systems With Switching Topologies: A Novel State Transition Matrix Perspective

This article studies the containment control problem for a group of linear systems, consisting of more than one leader, over switching topologies. The input matrices of these linear systems are not required to have full-row rank and the switching can be arbitrary, making the problem quite general and challenging. We propose a novel analysis framework from the viewpoint of a state transition matrix. Specifically, according to the inherent linearity, we successfully establish a connection between state transition matrices of the above multileader system and a virtual leader-following system obtained by combining those leaders. This enlightening result relates the containment problem to a consensus one. Then, by analyzing the property of the state transition matrix, we uncover that each component of any follower's state converges to the convex hull spanned by the corresponding components of the leaders', provided some mild conditions are satisfied. These conditions are derived in terms of the concept of a positive linear system. A special case of the second-order linear system is further discussed to illustrate these conditions. Moreover, two different design methods of the feedback gain matrix are provided, which additionally require that the network topology contains a united spanning tree all the time.

Model-Independent Formation Tracking of Multiple Euler-Lagrange Systems via Bounded Inputs

This article addresses two kinds of formation tracking problems, namely: 1) the practical formation tracking (PFT) problem and 2) the zero-error formation tracking (ZEFT) problem for multiple Euler-Lagrange systems with input disturbances and unknown models. In these problems, the bounded input constraint, which can be possibly caused by actuator saturation and power limitations, is taken into consideration. Then, the two classes of model-independent distributed control approaches, in which the prior information (i.e., the structures and features) of the system model is not used, are proposed correspondingly. Based on the nonsmooth analysis and Lyapunov stability theory, several novel criteria for achieving PFT and ZEFT of multiple Euler-Lagrange systems are derived. Finally, numerical simulations and comparisons are presented to verify the validity and effectiveness of the proposed control approaches.

Fully Adaptive Practical Time-Varying Output Formation Tracking for High-Order Nonlinear Stochastic Multiagent System With Multiple Leaders

Fully adaptive practical time-varying output formation tracking issues of high-order nonlinear stochastic multiagent systems with multiple leaders are researched, where the adaptive fuzzy-logic system (FLS) is introduced for estimating the mismatched integrated uncertain items. Distinctive with former results, stochastic noise is considered in the dynamics, and the followers are required for achieving the time-varying output formation tracking in probability of the convex combination of the leaders' outputs. First, a fully adaptive practical time-varying output formation tracking protocol is put forward, which only utilizes the neighboring relative information, and the global interaction topology information is not used. Besides, the designed protocol employs the adaptive FLSs to estimate the mismatched uncertainties of the followers and the leaders, and the uncertain boundary functions of the stochastic noise. Then, the design process of control protocol and parameter adaptive update law is summarized within four steps in an algorithm. Third, the stability and the properties of the proposed protocol and algorithm are analyzed by employing the Lyapunov theories and stochastic stability theories. Finally, numerical simulation results illustrate the effectiveness of achieved protocol and algorithm.

Formation Control of Multiagent Systems With Communication Noise: A Convex Analysis Approach

Under practical environments, some certain noises may arise from the communication of agents due to electromagnetic interference, sensor error, and other disturbances, which are usually modeled by additive noise in the relative position state between an agent and its neighbors. In this article, a formation control strategy is considered for this kind of relative position state with the additive noise, where the unmeasured velocity information is estimated by an observer-based strategy. On the other hand, the considered problem is transformed into a convergence problem of infinite products of a sequence of general stochastic matrices. The general stochastic matrix means that a matrix has row sum one but its entries do not necessarily require non-negative. This article develops the convex analysis to cope with such infinite products. Then, a sufficient condition is obtained to ensure that the specified formation shape in a noisy environment can be achieved. Subsequently, an example is presented to show the effectiveness of the result.

Distributed Optimization of Multiagent Systems Subject to Inequality Constraints

In this paper, we study a distributed convex optimization problem with inequality constraints. Each agent is associated with its cost function, and can only exchange information with its neighbors. It is assumed that each cost function is convex and the optimization variable is subject to an inequality constraint. The objective is to make all the agents reach consensus, and meanwhile converge to the minimum point of the sum of local cost functions. A distributed protocol is proposed to guarantee that all agents can reach consensus in finite time and converge to the optimal point within the inequality constraints. Based on the ideas of parameter projection, the protocol includes two decent directions. One makes the cost function decrease, and the other makes agents step forward to the constraint set. It is shown that the proposed protocol solves the problem under connected undirected graphs without using a Lagrange multiplier technique. Especially, all of the agents could reach the constraint sets in finite time and stay in there after. The method could also be used in the centralized optimization problems.

Distributed Finite-Horizon Extended Kalman Filtering for Uncertain Nonlinear Systems

In this paper, the state estimation problem is investigated for a class of discrete nonlinear systems via sensor networks. A novel robust distributed extended Kalman filter, which can handle norm-bounded uncertainties in both the system model and its Taylor series expansion, is developed with ensured estimation performance. The filter is distributed in the sense that for each sensor, only its own measurements and its neighbors' information are utilized to optimize the upper bound of the estimation error covariance. Besides, a sufficient condition for the proposed algorithm is derived, which is simple and user-friendly since it depends on the property of the original nonlinear system instead of the estimation error covariance calculated at every step. Finally, the simulation results are presented to demonstrate the effectiveness of the filtering algorithm.

Adaptive Cooperative Control With Guaranteed Convergence in Time-Varying Networks of Nonlinear Dynamical Systems

In this paper, we investigate the adaptive cooperative control problem with guaranteed convergence for a class of nonlinear multiagent systems with unknown control directions and time-varying topologies. A key lemma is first derived which involves dynamically changing interaction topologies, and then a new kind of distributed control algorithms with Nussbaum-type functions are proposed based on this lemma. It is proven that if the topologies are time varying with integral weight uniform upper bound and reciprocity, then convergence is guaranteed with the proposed algorithms for nonlinear multiagent systems with nonidentical unknown control directions. An important feature of this paper is that, under time-varying topologies, the designed algorithms can deal with nonidentical unknown control directions by using classical Nussbaum-type functions. Moreover, with the proposed algorithms, we extend the adaptive cooperative control results to the case of δ -connected graphs. In particular, the adaptive leaderless consensus of high-order nonlinear agents with nonidentical unknown control directions and a directed graph having a spanning tree is also tackled as a special case. Finally, theoretical results are illustrated by a group of Genesio-Tesi systems with distributed control algorithms under time-varying topologies and some special network topologies.

Fixed-Time Leader-Following Consensus for Multiple Wheeled Mobile Robots

This article deals with the problem of leader-following consensus for multiple wheeled mobile robots. Under a directed graph, a distributed observer is proposed for each follower to estimate the leader state in a fixed time. Based on the observer and a constructed nonlinear manifold, a novel protocol is designed such that the estimated leader state is tracked in a fixed time. Moreover, a switching protocol together with a linear manifold is proposed to ensure that fixed-time leader-following consensus is realized for any initial conditions without causing singularity issues. In contrast to alternative fixed-time consensus protocols in some existing results, the protocol proposed in this article is designed by constructing the nonlinear or linear manifold, which builds a new framework for fixed-time leader-following consensus. Furthermore, the obtained upper bound of settling time is explicitly linked with a single parameter in the protocol, which facilitates the adjustment of the bound under different performance requirements. Finally, the proposed protocol is applied to formation control of wheeled mobile robots.

Dynamic Intermittent Feedback Design for H∞ Containment Control on a Directed Graph

This article develops a novel distributed intermittent control framework with the ultimate goal of reducing the communication burden in containment control of multiagent systems communicating via a directed graph. Agents are assumed to be under disturbance and communicate on a directed graph. Both static and dynamic intermittent protocols are proposed. Intermittent H_∞ containment control design is considered to attenuate the effect of the disturbance and the game algebraic Riccati equation (GARE) is employed to design the coupling and feedback gains for both static and dynamic intermittent feedback. A novel scheme is then used to unify continuous, static, and dynamic intermittent containment protocols. Finally, simulation results verify the efficacy of the proposed approach.

Delayed Impulsive Control for Consensus of Multiagent Systems With Switching Communication Graphs

Delayed impulsive controllers are proposed in this paper to enable the agents in a class of second-order multiagent systems (MASs) to achieve state consensus, based, respectively, on the relative full-state and partial-state sampled-data measurements among neighboring agents. It is a challenging task to analyze the consensus behaviors of the considered MASs as the dynamics of such MASs will be subjected to joint effects from delay-dependent impulses, aperiodic sampling, and switchings among different communication graphs. A novel analytical approach, based upon the discretization method, state augmentation, and linear state transformation, is developed to establish the sufficient consensus criteria on the range of the impulsive intervals and the control parameters. Remarkably, it is found that consensus in the closed-loop MASs can be always ensured by skillfully selecting the control parameters as long as the nonuniform delays and the impulsive intervals are bounded. A numerical example is finally performed to validate the effectiveness of the proposed delayed impulsive controllers.

On Complete Stability of Recurrent Neural Networks With Time-Varying Delays and General Piecewise Linear Activation Functions

This paper addresses the problem of complete stability of delayed recurrent neural networks with a general class of piecewise linear activation functions. By applying an appropriate partition of the state space and iterating the defined bounding functions, some sufficient conditions are obtained to ensure that an n -neuron neural network is completely stable with exactly ∏_i=1ⁿ(2K_i-1) equilibrium points, among which ∏_i=1ⁿK_i equilibrium points are locally exponentially stable and the others are unstable, where K_i (i=1,…,n) are non-negative integers which depend jointly on activation functions and parameters of neural networks. The results of this paper include the existing works on the stability analysis of recurrent neural networks with piecewise linear functions as special cases and hence can be considered as the improvement and extension of the existing stability results in the literature. A numerical example is provided to illustrate the derived theoretical results.

Consensus in networked multi-robot systems via local state feedback robust control

In the article, the consensus problem is considered for networked multi-robot systems, in which the dynamical equation of all robots is non-holonomic and nonlinear systems. In the multi-robot systems, each robot updates its current states and receives the states from the neighboring robots. Under the assumption that if the network graph is bidirectional, a local information-based state feedback robust controller is designed to make sure the convergence of the individual robots’ states to a common value. Finally, the effectiveness of the presented method is illustrated by the simulation results of a group of four mobile robots.

Spectral Learning Algorithm Reveals Propagation Capability of Complex Networks

In network science and the data mining field, a long-lasting and significant task is to predict the propagation capability of nodes in a complex network. Recently, an increasing number of unsupervised learning algorithms, such as the prominent PageRank (PR) and LeaderRank (LR), have been developed to address this issue. However, in degree uncorrelated networks, this paper finds that PR and LR are actually proportional to in-degree of nodes. As a result, the two algorithms fail to accurately predict the nodes' propagation capability. To overcome the arising drawback, this paper proposes a new iterative algorithm called SpectralRank (SR), in which the nodes' propagation capability is assumed to be proportional to the amount of its neighbors after adding a ground node to the network. Moreover, a weighted SR algorithm is also proposed to further involve a priori information of a node itself. A probabilistic framework is established, which is provided as the theoretical foundation of the proposed algorithms. Simulations of the susceptible-infected-removed model on 32 networks, including directed, undirected, and binary ones, reveal the advantages of the SR-family methods (i.e., weighted and unweighted SR) over PR and LR. When compared with other 11 well-known algorithms, the indices in the SR-family always outperform the others. Therefore, the proposed measures provide new insights on the prediction of the nodes' propagation capability and have great implications in the control of spreading behaviors in complex networks.

Adaptive Compensation for Nonlinear Time-Varying Multiagent Systems With Actuator Failures and Unknown Control Directions

This paper investigates a problem of designing an adaptive asymptotic cooperative control scheme for nonlinear time-varying multiagent systems, which can simultaneously tolerate unknown actuator failures and unknown control directions. To address such the problem, we propose a conditional inequality, which allows multiple piecewise Nussbaum functions to acquire the control robustness. Benefiting from this robustness, a part of failure uncertainties and system errors are compensated for, while the remaining parts are handled by adaptive control technique. Moreover, structural properties of the proposed adaptive laws are utilized so that Barbalat's lemma is applicable to make all the followers asymptotically converge to the leader based on the neighborhood information.

Exponential Synchronizationlike Criterion for State-Dependent Impulsive Dynamical Networks

This paper focuses on the problem of the exponential synchronizationlike criteria for state-dependent impulsive dynamical networks (SIDNs). Two types of sufficient conditions, which are applied to ensure every solution intersecting each impulsive surface exactly once, are derived. For each type of collision conditions, combining with comparison principle and inequality techniques, some sufficient conditions are obtained to ensure local exponential synchronizationlike for SIDN. Moreover, a quiet different impulsive strategy concerning the trigger rules of impulsive instants is proposed. Finally, an example is given to demonstrate the effectiveness of our results.

Consensus of Discrete-Time Multiagent Systems With Input Delays by Truncated Pseudo-Predictor Feedback

The consensus problem for multiagent systems (MASs) described by discrete-time linear systems with multiple input delays is investigated. Under two reasonable assumptions, a truncated pseudo-predictor feedback (TPPF) approach is established to solve the consensus problem. The proposed TPPF protocols allow arbitrarily large yet bounded delays and are easy to implement in practice since they are finite dimensional and only use the relative current state information of neighboring agents. Moreover, the proposed protocols can also achieve semi-global consensus of MASs if the actuators are subject to saturations. A numerical example is given to illustrate the effectiveness of the proposed approaches.

Distributed Optimization for Multiagent Systems: An Edge-Based Fixed-Time Consensus Approach

This paper deals with the problem of distributed optimization for multiagent systems by using an edge-based fixed-time consensus approach. In the case of time-invariant cost functions, a new distributed protocol is proposed to achieve the state agreement in a fixed time while the sum of local convex functions known to individual agents is minimized. In the case of time-varying cost functions, based on the new distributed protocol in the case of time-invariant cost functions, a distributed protocol is provided by taking the Hessian matrix into account. In both cases, stability conditions are derived to ensure that the distributed optimization problem is solved under both fixed and switching communication topologies. A distinctive feature of the results in this paper is that an upper bound of settling time for consensus can be estimated without dependence on initial states of agents, and thus can be made arbitrarily small through adjusting system parameters. Therefore, the results in this paper can be applicable in an unknown environment such as drone rendezvous within a required time for military purpose while optimizing local objectives. Case studies of a power output agreement for battery packages are provided to demonstrate the effectiveness of the theoretical results.

Swarming Behavior of Multiple Euler-Lagrange Systems With Cooperation-Competition Interactions: An Auxiliary System Approach

In this paper, the swarming behavior of multiple Euler-Lagrange systems with cooperation-competition interactions is investigated, where the agents can cooperate or compete with each other and the parameters of the systems are uncertain. The distributed stabilization problem is first studied, by introducing an auxiliary system to each agent, where the common assumption that the cooperation-competition network satisfies the digon sign-symmetry condition is removed. Based on the input-output property of the auxiliary system, it is found that distributed stabilization can be achieved provided that the cooperation subnetwork is strongly connected and the parameters of the auxiliary system are chosen appropriately. Furthermore, as an extension, a distributed consensus tracking problem of the considered multiagent systems is discussed, where the concept of equi-competition is introduced and a new pinning control strategy is proposed based on the designed auxiliary system. Finally, illustrative examples are provided to show the effectiveness of the theoretical analysis.

Reaching Non-Negative Edge Consensus of Networked Dynamical Systems

In this paper, the problem of non-negative edge consensus of undirected networked linear time-invariant systems is addressed by associating each edge of the network with a state variable, for which a distributed algorithm is constructed. Sufficient conditions referring only to the number of edges are derived for non-negative edge consensus of the networked systems. Subsequently, the linear programming method and a low-gain feedback technique are introduced to simplify the design of the feedback gain matrix for achieving the non-negative edge consensus. It is found that the low-gain feedback technique has a good effect on the non-negative edge consensus of the networked systems subject to input saturation. Numerical simulations are presented to verify the effectiveness of the theoretical results.

Cooperative Tracking of Networked Agents With a High-Dimensional Leader: Qualitative Analysis and Performance Evaluation

Cooperative consensus tracking and its -gain performance is investigated in this paper for a class of multiple agent systems (MASs) in the presence of a single high-dimensional leader. Compared with the traditional models for MASs, the inherent dynamics of the leader are allowed to be different with those of the followers in the present framework, which is thus much more favorable in various practical applications. A new kind of distributed controllers associated with a reduced-order state observer are designed for each follower to track the high-dimensional leader under directed switching topology. With the help of -matrix theory and stability analysis methods of switched systems, some efficient criteria are derived for cooperative consensus tracking of MASs without any external disturbance under directed switching topology. Theoretical analysis is further extended to the case of consensus tracking for MASs subject to unknown external disturbances by showing that, a finite -gain performance for tracking errors against external disturbances can be ensured if some suitable conditions are satisfied. At last, the synthesis issue of designing an observer-based controller to achieve a prescribed -gain performance for consensus tracking is studied by using tools from control theory, where the underlying topology is assumed to be undirected and fixed. The effectiveness of theoretical results is verified by performing numerical simulations.

Finite-Time Synchronization of Coupled Hierarchical Hybrid Neural Networks With Time-Varying Delays

This paper is concerned with the finite-time synchronization problem of coupled hierarchical hybrid delayed neural networks. This coupled hierarchical hybrid neural networks consist of a higher level switching and a lower level Markovian jumping. The time-varying delays are dependent on not only switching signal but also jumping mode. By using a less conservative weighted integral inequality and stochastic multiple Lyapunov-Krasovskii functional, new finite-time synchronization criteria are obtained, which makes the state trajectories be kept within the prescribed bound in a time interval. Finally, an example is proposed to demonstrate the effectiveness of the obtained results.