Search

This contribution considers the containment control problem for linear multi‐agent systems (MAS) using continuum models in form of linear parabolic PDEs. For this, a networked controller is designed, that ensures the asymptotic convergence of finite‐dimensional agents into a containment area specified by dynamic leaders. This problem is traced back to an output regulation problem for a continuum model independent of the number of agents, which also takes disturbances into account. A prescribed formation is assigned for the MAS in the containment area by using Bézier curves. Using bilateral backstepping a tracking controller is designed, which allows to distribute the control effort between the two boundary agents. The states are estimated by an infinite‐dimensional disturbance observer. For this, both a folding observer with network communication and two boundary observers without network communication are introduced. A fully distributed solution of the containment control problem is obtained by employing a continuum signal model observer, which communicates the states of the leader and disturbance model to all agents. The desired communication topology is imposed after the design by a spatial discretization. A simulation example illustrates the effectiveness of the new method for the networked controller design. [ABSTRACT FROM AUTHOR]

This work addresses the discrete-time containment control problem for first-order and second-order systems, incorporating position constraints, nonuniform time delays, and switching topologies. Projection operators are introduced to maintain agent states within the position constraints. Then, model transformation methods, along with stochastic properties of matrices, are employed to handle coupled nonlinearities stemming from position constraints and time delays. By using local information, distributed projection-based control schemes are proposed for multi-agent systems. Theoretical analysis shows that all followers ultimately converge into the convex hull spanned by leaders if the union of the communication topologies contains a directed spanning tree within each specified time interval. Finally, the theoretical results are verified by numerical simulations. • Containment control is studied for systems with constraints, delays, and switching. • A projection-based algorithm improves convergence to the leader-forming convex hull. • Model transformation is used to eliminate effects of non-uniform communication delays. • Numerical simulations validate the theoretical results. [ABSTRACT FROM AUTHOR]

Copyright of Automatisierungstechnik is the property of De Gruyter and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper investigates the containment control of multiple unmanned surface vessels with nonlinear dynamics. To solve the leader-follower synchronization problem in a containment control system, a hierarchical control framework with a topology reconfiguration mechanism is proposed, and the process of containment control is converted into the tracking of a reference signal for each vessel on its respective target heading by means of the light-of-sight (LOS) guidance. In a control system, the neural networks (NNs) are adopted to consider the uncertainty. In the follower layer, a connectivity controller with a topology reconfiguration mechanism is embedded, to change the converging positions of followers so as to avoid collision within the system, and to maintain the system connectivity when the communication equality is poor. The effectiveness of the hierarchical control framework proposed in this paper is valid by simulation. [ABSTRACT FROM AUTHOR]

In the containment control problem of multi-agent systems (MASs), the convergence of followers is always a potential threat to the security of system operations. From the perspective of system topology, the inherently non-linear properties of the algebraic connectivity of the follower2follower (F2F) network, combined with the influence of the leader2follower (L2F) topology on the system, make it difficult to design the convergence positions of the followers through mere mathematical analysis. Therefore, in the background of temporary networking tasks for large-scale systems, to achieve the goal of forecasting the performance of the whole system when networking is only completed with local information, this paper investigates the application and effectiveness of recurrent neural networks (RNNs) in the containment control system performance identification, thus improving the efficiency of system networking while ensuring system security. Two types of identification models based on two types of neural networks (NNs), MLP and standard RNN are developed, according to the range of information required for performance identification. Evaluation of the models is carried out by means of the coefficient of determination ( R 2 ) as well as the root-mean-square error (RMSE). The results show that each model may produce a better forecasting accuracy than the other models in specific cases, with models based on the standard RNN possessing smaller errors. With the proposed method, model identification can be achieved, but in-depth development of the model in further studies is still necessary to the extent the accuracy of the model. [ABSTRACT FROM AUTHOR]

This paper investigates the output feedback containment control problem of multi-agent systems (MASs) with multiple leaders described by partial differential equations (PDEs). In contrast to MASs modeled by ODEs, the PDEs system studied in this paper considers additional spatial variables, which leads to traditional ODEs control design methods inapplicable, then the design of observer based adaptive distributed protocols is more challenging. Considering that leaders may be task-driven, the control inputs of the leaders are non-zero and time-varying. Through the introduction of nonlinear terms in the containment controller to eliminate the influence of leader control inputs, the paper ultimately achieves bounded tracking errors and containment errors for agents under undirected graph topologies. Finally, the designed control scheme is validated through examples. [ABSTRACT FROM AUTHOR]

This article investigates the model-free containment control of multiple underactuated unmanned surface vessels (USVs) subject to unknown kinetic models. A novel cooperative control architecture is presented for achieving a containment formation under switching topologies. Specifically, a path-guided distributed containment motion generator (CMG) is first proposed for generating reference points according to the underlying switching topologies. Next, guiding-vector-field-based guidance laws are designed such that each USV can track its reference point, enabling smooth transitions during topology switching. Finally, data-driven neural predictors by utilizing real-time and historical data are developed for estimating total uncertainties and unknown input gains, simultaneously. Based on the learned knowledge from neural predictors, adaptive kinetic control laws are designed and no prior information on kinetic model parameters is required. By using the proposed method, the fleet is able to converge to the convex hull spanned by multiple virtual leaders under switching topologies regardless of fully unknown kinetic models. Through stability analyses, it is proven that the closed-loop control system is input-to-state stable and the tracking errors are uniformly ultimately bounded. Simulation results verify the effectiveness of the proposed cooperative control architecture for multiple underactuated USVs with fully unknown kinetic models. [ABSTRACT FROM AUTHOR]

This paper is devoted to the nonconvex control input constrained containment control problem for multi-agent systems with non-particle leaders, switching topologies, and communication delays. A decentralized algorithm is adopted for followers with discrete-time high-order dynamics. Through model transformations and by analyzing the convergence of the maximum distance from the followers to the convex hull, it is demonstrated that each follower finally moves into the convex hull created by the leaders, even in the presence of nonconvex input constraints, non-particle leaders, switching topologies, and communication delays. Finally, numerical examples demonstrate the effectiveness of the theoretical conclusions. [ABSTRACT FROM AUTHOR]

In this article, an event-triggered practical fixed-time containment control issue for stochastic nonlinear multiagent systems is addressed. The event-triggering mechanism is designed for the controller update which is reduced update frequency. In combination with the backstepping technique and fuzzy logic systems, an adaptive fuzzy containment control strategy is developed for stochastic uncertain multiagent systems. By adopting the protocol, an adaptive containment controller is devised, which can ensure that the containment errors gather to a small range in fixed time. Finally, simulation results for the practical example demonstrate the correctness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this article, we consider the problem of distributed adaptive leader-follower coordination of partial differential systems (i.e., reaction-diffusion neural networks, RDNNs) with directed communication topology in the case of multiple leaders. Different from the dynamical networks with ordinary differential dynamics, the design of adaptive protocols is more difficult due to the existence of spatial variables and nonlinear terms in the model. Under directed networks, a novel adaptive control protocol is proposed to solve the containment control problem of RDNNs. By constructing proper Lyapunov functional and adopting some important prior knowledge, the stability of containment for coupled RDNNs is theoretically proved. Furthermore, a corollary about the leader-follower synchronization with a leader for coupled RDNNs with directed communication topology is given. In the end, two numerical examples are provided to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper introduces a distributed containment control strategy for multiple unmanned surface vehicles (USVs) under the unknown external disturbances. The communication network of the USVs is a fixed, directed topology and only a part of the follower USVs can read the states of leader USVs. To guarantee the transient and steady-state performance of the system, the tracking errors are converted into new error functions. By utilizing the disturbance observer, the external disturbances are effectively estimated. According to the new group of errors, a distributed containment controller is proposed with the estimated external disturbances. Furthermore, using graph theory and Lyapunov approach, it is proved that all variables of the multiple USV systems are bounded and the tracking errors can be confined within the specified performance ranges. Finally, simulation results illustrate the effectiveness of the designed distributed containment controller. • A control scheme is proposed for with multiple leader in a distributed network. • A specific performance controller is proposed by changing the synchronization error. • A distributed controller for multi-USVs based on disturbance observer is designed. [ABSTRACT FROM AUTHOR]

This work investigates the fixed-time distributed coordination control for multiple Euler–Lagrange systems and, in particular, addresses containment control with stationary/dynamic leaders as well as leaderless synchronization control. For the containment control scenario with stationary leaders, the subgraph associated with followers is directed. When dynamic leaders are involved, the information transfer between neighboring followers is bidirectional, for which a novel distributed estimator is developed. For the leaderless synchronization control scenario, the communication network among agents is unidirectional. Three fixed-time distributed control schemes are designed for the aforementioned three cases by applying the fixed-time stability theory. The convergence of the coordination control objectives can be achieved in a fixed time that does not depend on any initial conditions of agents’ states, and the settling times are also explicitly derived. Finally, numerical simulations are presented to demonstrate the feasibility of the developed control strategies. [ABSTRACT FROM AUTHOR]

This article is concerned with the problem of distributed adaptive fuzzy fault-tolerant containment control (FTCC) for a class of heterogeneous nonlinear multiagent systems with actuator faults and external disturbances. Two FTCC strategies are proposed for two different cases, i.e., leader’s input can be obtained by its neighboring follower agents and the input of the leader is not available by any followers, respectively. In the first case, a distributed observer-based adaptive FTCC protocol is presented to achieve the containment control objective. In the second case, a distributed adaptive FTCC method which is independent of global information about the communication topology and upper bounds of the leader’s input is developed using the local containment error. An auxiliary controller gain is proposed to solve the problem of partial loss of effectiveness faults, and the potential singularity brought by the auxiliary controller gain to the controller can be avoided by introducing a projection operator. It is shown that each follower converges asymptotically to a convex hull spanned by the leaders with external input. Finally, the developed method is demonstrated by simulation results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this article, the containment control problem of multiagent systems (MASs) with active leaders under a directed communication graph is addressed. A novel pull-based event-triggered protocol combined with aperiodic sampled-data mechanism is first presented, where each agent merely updates controller at its own triggering instants. Under the proposed control protocols, the information is only exchanged and calculated at the aperiodic sampling instants, therefore, it can reduce communication congestion and save computing resources. Furthermore, the Zeno behavior is naturally excluded because the trigger instants are in the set of aperiodic sampled instants. By virtue of the algebraic graph theory and Lyapunov stability analysis, it is shown that the active leaders can reach their desired states predefined arbitrarily and all followers are driven to the convex hull formed by the leaders. Finally, an illustrative example is given to validate the theoretical results and emphasize the advantages of the proposed protocols. [ABSTRACT FROM AUTHOR]

A new event-triggered iterative learning control method is proposed for handling the distributed containment control problem of model-free multiagent systems under a fixed directed graph. The designed controller merely uses the input and output signals, controlled model information is not required. At first, the unknown dynamic is transformed into the linearization model upon the base of pseudo partial derivative. Secondly, the novel distributed containment controller is proposed for each follower by use of iterative learning algorithm. Moreover, a new trigger mechanism is designed to save energy of the systems, such that the updating number of the proposed controller can be reduced greatly. Mathematical deduction shows that the controller can render the outputs of the followers converge to a convex hull formed by the outputs of leaders. Finally, simulation examples are given for verifying the significance of proposed method. [ABSTRACT FROM AUTHOR]

Containment control is an important issue in the consensus problem of multiagent systems (MASs). This article presents an output-based containment control strategy for a class of nonaffine nonlinear MASs with uncertainies and directed topology. With the help of differential homeomorphism transform and the idea of active disturbance rejection control (ADRC), a nonaffine nonlinear MAS is transformed into an affine one with uncertainties. Two filters with extended states in each follower are designed with the idea of extended state observer to reconstruct the states of the transformed MAS. Then, uncertainties of the MAS are compensated with the help of the estimations of the extended states. Moreover, the derivative of the virtual control signal in the backstepping technique is replaced by a tracking differentiator (TD), overcoming the so-called “explosion of complexity” problem. By means of Lyapunov theory, the containment errors of the followers are proven to converge to a small neighborhood around the origin via an appropriate choice of parameters. Simulation examples are provided to demonstrate the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this paper, the containment problem with nonconvex velocity constraints is studied for second-order discrete-time multiagent systems. A distributed projection-based algorithm is proposed for all followers to be gathered in the convex area formed by multiple stationary leaders. It is revealed that the algorithm can solve the velocity-constrained containment problem with communication delays and switching networks provided that each follower has at least a directed path from some leaders to itself in the union of graphs. The main analysis approaches include model transformation techniques, Lyapunov function, and convexity analysis. A simulation example is also included to elucidate the obtained result. [ABSTRACT FROM AUTHOR]

This article is concerned with the problem of the containment control with respect to continuous-time semi-Markovian multiagent systems with semi-Markovian switching topologies. Two kinds of classical control schemes, which are dynamic containment control and static containment control schemes, are utilized to address the proposed synthesis problem. Based on the linear matrix inequality (LMI) method, the dynamic containment controller and static containment controller are designed to plunge into the studied semi-Markovian multiagent systems, respectively. Moreover, the random switching topologies with the semi-Markovian process, the partly unknown transition rates, and the generally uncertain transition rates are taken into account, which can be applicable to more practical situations. Finally, the simulation results are provided to illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In the practical application, such as military, logistics or drone control, in order to meet the mission needs, the scale of multi-agent systems is constantly expanding, and the number of leaders required to implement control is increasing. In containment control, it has some difficulties in forming convex hulls by traditional control methods to achieve ideal control purposes. We propose a method that is more suitable and effective for large-scale networks to achieve containment control here. In this paper, a controllable containment control algorithm based on hierarchical clustering for multi-agent systems is proposed by combining the topology optimisation theory and complex network controllability theory. First, the multi-agent network is divided into several communities according to the hierarchical clustering algorithm. Then the maximum matching algorithm of bipartite graph is used to determine the minimum leader set satisfying the network controllability. Second, the corresponding control protocols are designed for the agents, and a position adjustment control force is introduced to adjust the motion of individuals that are located outside the convex hull in the process of containment among the communities. Therefore, when achieving and maintaining the controllable containment control within the community, the controllable containment control among the communities can be achieved effectively through the proposed algorithm. Finally, some simulation examples are presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

An observer-based containment control issue is addressed for a class of uncertain nonlinear multiagent systems with a directed topology via the active disturbance rejection control and backstepping techniques. A kind of nonlinear extended state observers (ESOs) based on fractional power functions is developed, and the estimations of extended states are utilized to compensate uncertain dynamics in real time. Compared with linear ESOs, the advantages of the ESOs in this paper lie in peaking reduction and better tolerance of measurement noise for the closed-loop system. Moreover, tracking differentiators are employed to avoid the explosion of complexity caused by repeated differentiations of nonlinear functions. It is proven that the containment errors of the followers converge to small neighborhoods of the origin and they are adjustable by suitable choice of parameters. Finally, two simulation examples, both practical and numerical ones, are shown to demonstrate the effectiveness of the proposed control approach. [ABSTRACT FROM AUTHOR]

This paper investigates the containment control problem of multi-agent systems with semi-Markovian switching topologies. Different from the related works, this paper considers a more general case that the control inputs of leaders are nonzero, the sojourn time distributions of the semi-Markovian switching topologies are mode transition-dependent, and the states of agents are not measurable. Reduced-order observer-based control protocols are proposed, respectively, for two cases that the transition rates are completely known and partially unknown, which ensures that the containment of the multi-agent systems can be achieved in the mean square sense. Finally, simulation examples are given to illustrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we investigate the event-triggered containment control problem for a class of multiagent systems, where agents are described by higher-order linear dynamics subject to stochastic disturbances. In event-triggered control scenarios, the control action is updated when a specified error reaches a given threshold. Due to the existence of stochastic factors, the given threshold may be reached in an any short time interval, which makes it hard to avoid Zeno behavior. In view of this, we propose two novel event-triggered containment control schemes for the underlying multiagent systems with stochastic disturbances. Using the stochastic control theory, graph theory, and Lyapunov functional method, it is proven that the followers' states can almost surely converge to the convex hull spanned by the leaders’ states. It is noted that the continuous communications among agents are not required and each agent's inter-event intervals are lower-bounded by a positive constant. As such, the proposed control schemes are both practical and implementable. Finally, a numerical example is presented to illustrate the developed schemes’ effectiveness. [ABSTRACT FROM AUTHOR]

This article investigates distributed coordinated tracking problems of networked heterogeneous systems. Based on asynchronous sampling information, distributed sampled-data protocols are employed to realize leader-following synchronization and containment tracking in networked heterogeneous systems. In asynchronous sampled-data protocols, each node has different sampling instants with other nodes and only samples itself information at its own sampling instants. By utilizing the input-delay approach and Lyapunove–Krasovskii functional approach, some sufficient conditions for guaranteeing the coordinated tracking are presented. First, quasi-synchronization criteria are obtained for networked heterogeneous oscillator systems with a dynamic leader over the directed graph. Second, in the presence of multiple heterogeneous leaders for networked heterogeneous systems, sufficient conditions of quasi-containment tracking are derived. In a word, all followers can converge into a bounded level of convex hull spanned by the leader(s). The upper bounds of tracking errors are estimated for both quasi-synchronization and quasi-containment tracking. Finally, two numerical examples are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the problem of containment control for a class of nonlinear multi-agent system. The local dynamics under consideration is governed by a nonlinear system with time delays and white Gaussian noise. The multi-agent system consists of both leaders and followers, and the containment control protocol proposed is an interaction between the leaders and followers characterised by time-varying delays and switching topology. Under a certain assumption on the connectivity of the whole network, by constructing a Lyapunov–Krasovskii functional, and using the average dwell time approach and some new analytical techniques, the sufficient conditions are established to ensure that each follower converges in mean square to the convex hull spanned by the leaders. A numerical example is presented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Summary: In this study, we consider the problem of distributed H∞ containment control for multiagent systems over switching communication topologies. There exists a constant time‐delay and the energy‐bounded communication disturbances in the information transmission process, which are considered. Using the relative output, we develop an observer‐based containment control scheme such that the followers asymptotically converge to the convex hull formed by the leaders with a guaranteed H∞ performance level. By constructing a Lyapunov functional and using the inequality technique, sufficient conditions for the existence of such dynamic controllers are obtained in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed control protocol. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed containment control problem for a class of general second-order multiagent systems with switched dynamics, which is composed of a continuous-time (CT) subsystem and a discrete-time (DT) subsystem. For this switched multiagent system under fixed directed topology, a distributed containment control protocol is proposed for each follower based on the relative local measurements of neighboring followers and leaders. Some necessary and sufficient conditions are derived under the condition that the network topology contains a directed spanning forest, and these conditions ensure that the general second-order containment control problem can be solved under arbitrary CT–DT switching. If the general second-order system is reduced to the double integrator system, some simpler containment conditions are presented. Furthermore, the similar results are also obtained under switching directed topology. Finally, some simulation examples are presented to show the efficiency of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies a containment problem with communication delays and switching topologies. A nonlinear projection containment control algorithm for followers with single-integrator discrete-time dynamics is proposed. The main approach is to use the convexity of the convex hull spanned by multiple stationary leaders to show the nonincreasing monotonicity of the largest distance from the agents to the convex hull. It is shown that the nonlinear projection containment control algorithm is robust to arbitrarily bounded communication delays as long as each follower jointly has a path from some leaders to itself. Finally, a numerical example is implemented to show the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Summary: The containment control of stochastic multiagent systems with semi‐Markov switching topologies is investigated in this paper. The general case that the distribution function of the sojourn time is dependent on both the current system mode and the target mode is considered. Taking state multiplicative noise into account and using stochastic techniques, sufficient conditions to achieve the containment control in the asymptotic mean square sense are obtained in a form of linear matrix inequalities and the controller design condition is given. Finally, a simulation is given to demonstrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

One typical reflection of our understanding on multiagent systems (MASs) is our ability to design the emergence mechanism responsible for their various cooperative behaviors. This paper is concerned with the cooperative robust containment control problem of multileader MASs subject to unknown nonlinear dynamics and external disturbances. Specifically, quasi-containment and asymptotic containment problems are, respectively, considered by using tools from neural network (NN) approximation theory and Lyapunov stability theory of nonsmooth systems. A new kind of containment controllers consisting of a linear local information-based feedback term, a neuro-adaptive approximation term and a nonsmooth feedback term are designed to complete the goal of quasi-containment. Under the assumption that the subgraph depicting the coupling configuration among followers is detail-balanced and each follower can be influenced by at least one leader, it is proven that the containment error vector of the closed-loop MASs will be uniformly ultimately bounded if the control parameters of the proposed containment controllers are suitably designed. By introducing a pseudo ideal weighting matrix for NN approximator embedded at each follower, a novel class of containment controllers are further designed to precisely achieve asymptotic containment in the considered MASs where the Euclidean norm of containment error vector asymptotically converges to zero. At last, numerical simulations are given to verify the validity of these derived theoretical results. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the containment control problem for second‐order multiagent systems with intermittent communications and time‐varying delays. Under the common assumption that each follower can only communicate with its neighbors over some disconnected time intervals, some distributed controllers are designed such that all the followers can converge to convex hull formed by the leaders. Firstly, a distributed intermittent control protocol without considering time delays is proposed for second‐order containment control with intermittent communications. Then, under delayed and intermittent communication, a kind of distributed containment control algorithm is derived for second‐order multiagent systems with time‐varying delays. Based on the Lyapunov function technology and the intermittent control method, some sufficient conditions are presented to guarantee that the second‐order multiagent systems can achieve intermittent containment control under fixed topology. As an extension, similar results are obtained for containment control under switching topology. Finally, numerical simulations are presented to demonstrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper addresses containment control of multi-agent systems with multiple interactive leaders. The containment control objective is two-fold: the leaders converge to a desired formation, and the followers move into the convex hull spanned by the leaders’ final positions. Some sampled-data based protocols are proposed, which are effective when the communication environment suffers from intermittent information, switching topology and time-delays. For the leaders, the convergence analysis can be easily obtained by using the properties of the SIA matrices. The geometric configuration of the desired formation is not affected by the switching topology or time-delays. For the followers, the convergence analysis is much complicated since the properties of the SIA matrices cannot be used. Based on the relationship between the topology and matrices, it is proved that the followers will move into the convex hull of the desired formation, and then change their positions in the convex hull as the time evolves under the switching topology; however, the final states of the followers are not affected by the time-delays. Finally, the theoretical results are illustrated by some simulations. [ABSTRACT FROM AUTHOR]

This paper concentrates the distributed formation containment problems for multiple unmanned aerial vehicle (UAV) systems under both fixed directed and switching directed topologies. The objective is to introduce the formation control into the containment control research, where master UAVs should exchange information with each other to achieve and maintain a desired formation. Then, two different control protocols are proposed for the master UAVs and slave UAVs, respectively. Utilizing the algebraic graph theory and stability theory, some sufficient conditions are derived to guarantee the master UAVs complete a prespecified formation, while the states of the slave UAVs converge to a convex hull formed by those of the master UAVs. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Containment control problems for high‐order linear Markov jump swarm systems with a dynamic output feedback under directed interaction topologies are investigated. A necessary and sufficient condition for Markov jump swarm systems to guarantee output containment is proposed. A sufficient condition is further presented to ensure the scalability of the criteria. Finally, numerical simulations show that the swarm system achieves output containment under the sufficient condition. [ABSTRACT FROM AUTHOR]

The cooperative containment control for multiagent systems with high-order linear dynamics under a directed graph is studied. A follower-based observer based on relative outputs of neighboring agents is developed to estimate the relative states of neighbors which avoid designing the observer for the leaders in the existing literature. A matrix transformation is introduced to eliminate the coupling terms resulting from the simultaneous design of observers and controllers. A feasible condition on devising observers and controllers is obtained. Furthermore, the result is extended to deal with the case with transmission time delay. The effectiveness of the proposed design method is verified by providing two simulation examples. [ABSTRACT FROM AUTHOR]

This paper studies the containment control of multiagent systems (MASs) with multiple dynamic leaders in both continuous-time domain and discrete-time domain. The leaders’ motions are described by the n th-order polynomial trajectories. This setting makes practical sense because given some critical points, the leaders’ trajectories are usually planned by the polynomial interpolations. In order to drive all followers into the convex hull spanned by the leaders, a PI $^{{n}} -type containment algorithm is proposed ( P and I are short for proportional and integral, respectively; I ^n implies that the algorithm includes up to the n th-order integral terms). It is theoretically proved that the PI $^{{n}}$ -type containment algorithm is able to solve the containment problem of MASs where the followers are described by any order integral dynamics. Compared to the previous results on the MASs with dynamic leaders, the distinguished features of this paper are that: 1) the containment problem is studied not only in the continuous-time domain but also in the discrete-time domain while most existing results only work in the continuous-time domain; 2) to deal with the leaders with the {n}{+} 1)th-order integral while the followers considered in this paper can be described by any-order integral dynamics; 3) the “sign” function is not employed in the proposed algorithm, which avoids the chattering phenomenon; and 4) both disturbance and measurement noise are taken into account. Finally, some simulation examples are given to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

This paper considers both semi-global and global containment control for a second-order multi-agent system that is composed by a network of identical harmonic oscillators or double integrators with multiple leaders and input saturation. A distributed low gain feedback algorithm is proposed to solve the semi-global containment control problem for the network whose topology is directed and initial condition is taken from any a priori given bounded set. In particular, by using a parametric Lyapunov equation approach, M-matrix properties and algebraic graph theory, an upper bound of the low gain parameter is estimated such that the low gain feedback matrix can be analytically determined without involving numerical computation. Furthermore, under the assumption that the induced subgraph formed by the followers is strongly connected and detail balanced, two linear feedback protocols are designed for coupled harmonic oscillators and coupled double integrators, respectively, to asymptotically achieve the global containment control of the network with any initial condition. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The event-based broadcasting containment control problem for both first-order and second-order multi-agent systems under directed topology is investigated. Based on certain event, each agent decides when to transmit its current states to its neighbours and the agents’ distributed control algorithms are based on these sampled state measurements, which can significantly decrease the number of the controllers’ updates. All the agents are divided into two groups, namely, the leaders and the followers. The formation control is introduced. The leaders exchange their information to converge to a formation. The followers utilise the information from both their leader neighbours and their follower neighbours and are driven to the convex hull of the leaders using the proposed control algorithms. Numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM PUBLISHER]

It is typical in containment control problems to assume that there is no conflict of interest among leaders. In this paper, we consider the situation where there is conflict between leaders; namely, the leaders compete to attract followers. The strategies of each leader are defined by choosing at most k followers to propagate their information. Then, we formulate a standard two-player zero-sum game by using graph theory and matrix theory. We further prove that each player will choose exactly k followers when the game achieves a Nash equilibrium. It is noteworthy that the interaction graph here is generated from the conflict between leaders and then the Nash equilibrium point of the game corresponds to the equilibrium topology. For the case of choosing one follower, a necessary and sufficient condition for an interaction graph to be the equilibrium topology is derived. Moreover, we can obtain the equilibrium topology directly if followers’ interaction graph is a circulant graph or a graph with a center vertex. Simulation examples are provided to validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the intermittent containment control problem for second-order multi-agent systems under directed communication topologies. In order to reduce energy consumption and overcome the difficulty of velocity measurement in engineering applications, an intermittent containment control protocol utilizing the present time-varying position data and sampled position data is proposed. Under the assumption on the existence of the directed spanning forest, a necessary and sufficient condition for the stability of the multi-agent system is obtained, which is derived by the coupling coefficients, the eigenvalues of the Laplacian matrix, the period length and the communication width. Finally, the correctness of the theoretical results is validated by experimental simulations. • A containment controller is provided for multi-agent systems with directed networks. • A necessary and sufficient condition for containment control is concluded. • A simpler condition is derived for the case of undirected topologies. [ABSTRACT FROM AUTHOR]

Containment analysis and design problems for general high-order linear time-invariant multi-agent systems with time-varying delays are studied, where the interaction topology is directed. Using the state information of each agent and neighboring agents, a protocol with time-varying delays is constructed, where the motion modes of the leaders can be specified. Based on Lyapunov–Krasovskii stability theory, sufficient conditions for general linear multi-agent systems with time-varying delays to achieve containment are proposed which only include four linear matrix inequalities independent of the number of agents. Moreover, an approach to determine the gain matrices in the protocol is presented. Finally, a numerical example is given to demonstrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]