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This paper addresses the problem of containment control for second-order multi-agent systems with position constraints, time delays, and switching graphs. The approach involves treating position constraints with a scaling factor and transforming the system into a new one through model transformations. Based on the analysis of Lyapunov function, it is demonstrated that all followers will eventually enter the convex hull formed by the leaders, as long as there exists at least a directed path to one of the leaders for all followers in the union of the communication graphs. Finally, numerical results are presented to validate the effectiveness of the algorithm.

In the study of multi-agent distributed control, the distributed containment control is an important problem, which aims to make all the following agents enter the convex hull formed by the leader agents. It has a wide application prospect in UAV information collection and robust control. In the practical application of distributed containment control, agents usually experience unknown or uncertain working environment and are needed to suppress or even eliminate the adverse effects of external disturbances. In this paper, we study the robust containment control problem for second-order multi-agent systems with fixed topology. Based on the second-order dynamics model, the distributed algorithm is designed, and introduce the model transformation factor, and then transform the model. Based on Lyapunov stability theory, we analyze the stability of multi-agent system by solving differential equations combined with the comparison theorem. Then we minimize the maximum of the output multi-agent system under the external disturbance, and improve the anti-interference performance of the system. Finally, we implement a simulation example to illustrate theoretical results.

This article studies the observer-based event-triggered containment control problem for linear multiagent systems (MASs) under denial-of-service (DoS) attacks. In order to deal with situations where MASs states are unmeasurable, an improved separation method-based observer design method with less conservativeness is proposed to estimate MASs states. To save communication resources and achieve the containment control objective, a novel observer-based event-triggered containment controller design method based on observer states is proposed for MASs under the influence of DoS attacks, which can make the MASs resilient to DoS attacks. In addition, the Zeno behavior can be eliminated effectively by introducing a positive constant into the designed event-triggered mechanism. Finally, a practical example is presented to illustrate the effectiveness of the designed observer and the event-triggered containment controller. [ABSTRACT FROM AUTHOR]

This article proposes a secure containment control of multi-agent systems under cyber attacks. Multiple Unmanned Aerial Vehicle Systems (UAVs) are considered in this article. The suggested approach considers denial of service (DoS) attacks, containment control of multiple UAVs, and designs a strong steering approach as well as a secure middleware for data sharing and exchange. A combination of graph theory and L1 adaptive control is utilized to ensure efficient steering and cooperation. The data distribution services (DDS) middleware handles data transfer among all the UAVs, which solves the interoperability challenge when interacting with several UAVs from various platforms and can be regarded as an enhanced security strategy depending on its quality of service (QoS). The L1 controller is used to stabilize the dynamic model of each UAV, while the graph method is used for the containment of multi UAVs. The linear matrix inequalities (LMIs) control is designed as a robust level of security to handle the influence of the DoS attack. Simulation results are utilized to validate and demonstrate the suggested technique’s performance under the criteria mentioned before.

Time-varying group formation-containment tracking problems for general linear multiagent systems with unknown control input are investigated. Agents are classified into tracking leaders, formation leaders, and followers and assigned in groups. Tracking leaders with unknown control inputs provide unpredictable trajectories as macroscopic moving references. Formation leaders accomplish desired subformations while following the trails of tracking leaders. At the same time, followers converge into different convex hulls spanned by formation leaders. First, formation-containment tracking protocols are designed with neighboring relative information and effects of unknown input of tracking leaders. Then, the design of group division is analyzed by adjusting the properties in Laplacian matrices, which represent interaction relationships. An algorithm to determine the parameters in control protocols is proposed, and the formation tracking feasible constraint is presented. Next, it is proved that the general linear multiagent system can achieve time-varying group formation-containment control effectively with errors uniformly asymptotically converging to zero under designed protocols. Finally, a numerical simulation is given to verify the effectiveness of obtained theoretical results. [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 article investigates the containment control problem of nonlinear multiagent systems subject to actuator nonlinearity, unmeasured states, and unknown external disturbances. The predictor technique is employed for each subsystem, and the prediction error is utilized to update the adaptive law. The problem of actuator nonlinearity with dead zone and saturation input is solved by introducing an auxiliary control signal. Incorporating the state observer and disturbance ones, an extended state observer is proposed to compensate the effect of unmeasurable and unknown disturbances, simultaneously. Based on Lyapunov theory and graph theory, it is shown that the devised control scheme guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Moreover, the followers can enter the dynamic convex hull spanned by the dynamic leaders. A simulation example with comparison analysis is provided to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, the output containment control problem of heterogeneous linear multiagent systems (MASs) with unbounded distributed transmission delays is considered. A key technical lemma is first established to show that the distributed observers under unbounded distributed transmission delays can be utilized to estimate the convex combination of the states of multiple leaders. Then, a novel distributed output feedback control law is proposed based on those distributed observers. It is shown that under our proposed control law, the output of each follower converges to the convex hull spanned by the outputs of the leaders. In addition, our results include relevant results on output containment control of MASs with bounded distributed or constant transmission delays as special cases. Finally, the effectiveness of the proposed control law is demonstrated by a simulation example. [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 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]

In this article, we study the dynamic resilient containment control problem for continuous-time multirobot systems (MRSs), i.e., the problem of designing a local interaction protocol that drives a set of robots, namely the followers, toward a region delimited by the positions of another set of robots, namely the leaders, under the presence of adversarial robots in the network. In our setting, all robots are anonymous, i.e., they do not recognize the identity or class of other robots. We consider as adversarial all those robots that intentionally or accidentally try to disrupt the objective of the MRS, e.g., robots that are being hijacked by a cyber–physical attack or have experienced a fault. Under specific topological conditions defined by the notion of (r,s)-robustness, our control strategy is proven to be successful in driving the followers toward the target region, namely a hypercube, in finite time. It is also proven that the followers cannot escape the moving containment area despite the persistent influence of anonymous adversarial robots. Numerical results with a team of 44 robots are provided to corroborate the theoretical findings. [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 problem of distributed hierarchical fault-tolerant containment control for heterogeneous linear multiagent systems (MASs) is investigated. In most of the existing distributed methods for MASs with system failures, each agent broadcasts its state, or output, or the estimation of state to neighbors. Once an agent is subjected system failures, faults affect the dynamics of other agents over the network, that is, the influence of faults on the agent will propagate with the network. In order to overcome this drawback, a fault-tolerant hierarchical containment control protocol is developed, which includes two layers: 1) the upper layer and 2) the lower layer. The upper layer consists of a virtual system and a cooperative controller to achieve a virtual containment objective. The lower layer consists of an actual system and a fault-tolerant controller to track the upper layer virtual system. Compared with the existing results, the phenomenon of fault propagation can be avoided by introducing the hierarchical design approach, that is, the fault of agent $i$ only affects the dynamics of itself, and does not affect the dynamics of other agents through the network. It is shown that each follower converges asymptotically to a convex hull spanned by leaders with external input. Finally, the developed method is demonstrated by simulation results. [ABSTRACT FROM AUTHOR]

This brief investigates the fixed-time containment control (FTCC) of second-order disturbed nonlinear multi-agent systems (MASs). A new nonsingular terminal sliding mode (NTSM) control protocol is devised to ensure the FTCC for disturbed nonlinear MASs. A novel NTSM surface is correspondingly proposed to ensure the fixed-time convergence of the considered systems. The explicit estimation of settling time is given as well, which is irrespective of system initial values. Finally, one numerical example is presented to demonstrate the correctness of the proposed results. [ABSTRACT FROM AUTHOR]

The containment control problem in fractional-order multiagent systems over a directed graph is studied in this article. Two distributed control protocols with or without time delays are designed by utilizing the sampled position and velocity data. Then, based on the knowledge of the matrix theory and Laplace transform, some necessary and sufficient conditions to reach containment are derived. For the protocol with time delays, similar sufficient and necessary conditions are obtained. Finally, some simulation examples are designed to verify that the theorems are correct. [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]

This article is concerned with the containment control of multiple manipulators with uncertain parameters. A novel distributed adaptive backstepping strategy is given in the finite-time control framework. The finite-time command filters (FTCFs) used in the strategy can avoid the explosion of complexity problem for conventional backstepping. To further improve the control performance, the filtering errors caused by the used FTCFs are removed by using the error compensation mechanism (ECM). The proposed virtual control signal, the control torque, and the adaptive updating law can guarantee the set tracking errors converge to an adjustable neighborhood of the origin in finite time in the presence of uncertain parameters. Because the virtual control signal and ECM only use the local information, the established method is completely distributed. Two simulation examples are given to show the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Cooperative control of multirobot systems (MRSs) has earned significant research interest over the past two decades due to its potential applications in multidisciplinary engineering problems. In contrast to a single specialized robot, the MRS can be designed to offer flexibility, reconfigurability, robustness to faults, and cost-effectiveness in solving complex and challenging tasks. In this article, we aim to develop a unified cluster formation containment coordination framework for networked robots that can be decomposed into two layers containing the leaders and the followers. According to the proposed methodology, the leader robots are first distributed into a set of distinct and nonoverlapping clusters depending on the positions and priorities of the targets exploiting a game-theoretic rule. Then, they are steered to attain the desired formations around the corresponding targets. Subsequently, the follower robots are made to converge into the convex hull spanned by the leaders of the individual clusters. A prototype search and rescue operation is considered to highlight the usefulness of the proposed coordination framework. Furthermore, real-time hardware experiments were conducted on miniature mobile robots to validate the feasibility of the theoretical results. [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]

This article is concerned with the containment control problem for a class of multiagent systems (MASs) based on event-triggered output feedback. For homogeneous MASs, a distributed observer-based containment control protocol and a distributed hybrid event-triggered scheme are proposed. The observers, containment controllers, and event-triggered conditions are designed simultaneously by means of the matrix transformation technique. The proposed event-triggered mechanism includes not only the traditional triggering function but also a running time upper bound, which saves the communication workload and improves system performance. Furthermore, based on the output regulation framework, a hybrid distributed event-triggered scheme and a distributed containment control protocol for heterogeneous MASs are developed, where the dynamics of the followers vary. Multiply unmanned aerial vehicles are modeled as a linear MAS to verify the effectiveness of the presented algorithm. [ABSTRACT FROM AUTHOR]

This article addresses the containment control problem of multiagent systems under directed topologies, where the model of each agent is an unknown nonlinear nonaffine pure-feedback dynamic, and at the same time, the outputs and their derivatives of the leaders are unknown. To avoid the complex design process with the recursive methods (i.e., backstepping and dynamic surface), each unknown higher order nonlinear dynamic is transformed into a simple high-order integral model with unknown affine nonlinear terms in the last-order dynamic at first. Then, the fuzzy logic systems and the fuzzy state observers are constructed to approximate the unknown affine nonlinear terms and the unknown transformed states. Finally, a novel fully distributed fuzzy adaptive containment control law is generated according to the state observers and the supervised control. The stability of the closed-loop system is analyzed in the Lyapunov sense and the containment errors converge to a small neighborhood of the origin. Simulation results show the feasibility and effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This article addresses a filter-driven-approximation (FDA)-based design problem for the distributed containment control of multi-input–multi-output pure-feedback multiagent systems with completely unknown nonlinearities. Local filter-driven approximators are designed to compensate for unknown nonaffine nonlinear functions lumped in the local controller design procedure where the first-order filtered signals of the error surfaces, state variables, and control inputs are linearly combined for the design of the filter-driven approximators. A containment control scheme using the filter-driven function approximators is recursively constructed to ensure that the outputs of the followers converge to the convex hull spanned by multiple time-varying leaders. Compared with existing containment control results using adaptive neural-network-based or fuzzy-based approximators, the proposed FDA-based containment control scheme depends only on the relative output information among agents and does not require any adaptive techniques. Thus, the proposed control structure can be simplified. It is shown that the closed-loop signals, including approximation errors are semi-globally uniformly ultimately bounded. Simulation examples are provided to validate the effectiveness of the proposed theoretical 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]

In this paper, the intermittent containment control problem of second-order multi-agent systems with sampled position data is investigated. Under the case that the velocity measurements are inaccurate or unavailable, a novel intermittent containment control protocol is designed based on both the current and delayed sampled position datum. A necessary and sufficient condition depending upon the coupling strengths, the spectrum of the Laplacian matrix, the communication width, the sampling period and the time delay, is derived for achieving second-order intermittent containment control. Finally, numerical simulations are presented to demonstrate the efficiency of theoretical results.

In order to investigate coordinated orbit control problem for large-scale cluster flight spacecraft, a distributed orbital containment control algorithm is proposed for spacecraft cluster flight system with multiple leaders. At first, a general distributed orbital containment control strategy for large-scale cluster spacecraft system is given, so that all followers are driven to the convex hull formed by leaders. Then the constraints of convergence and convergence rate of cluster spacecraft system on control gains and information topology are investigated. Specifically, the control gains which achieve maximal convergence rate are analyzed. Furthermore, two kinds of cell partitions from graph theory are employed to investigate the influence of information topology on steady states of followers, which provides theoretical basis for collision avoidance design. Finally, simulation results show that the designed information topology could meet the requirements of large-scale cluster system, and followers belonging to the same cell have the same steady states.

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]

This paper addresses the output feedback distributed containment control problem for a class of nonlinear stochastic multiagent systems under a fixed directed graph. Existing works usually design the containment control protocol using backstepping design method based on a conservative Lipschitz condition on nonlinear functions, which has a tedious control design procedure. In this paper, a new output feedback distributed containment control algorithm is proposed based on a novel dynamic compensator, which can not only simplify the control design procedure but also relax the condition on nonlinear terms. The proposed distributed containment protocol for each agent depends only on the agent output and the relative outputs of its neighbor agents, and can reduce the communication burden between the agents. Based on the Lyapunov stability theory, it is proved that the outputs of the followers are driven into the convex hull spanned by the outputs of the leaders with the proposed linear controller. Finally, the effectiveness of the theoretical results is illustrated by simulation examples. [ABSTRACT FROM AUTHOR]

This article investigates the event-triggered containment control problem for stochastic nonlinear multiagent systems with unknown Bouc–Wen hysteresis input. Based on the backstepping technique, an adaptive fuzzy event-triggered containment control scheme is proposed, which is conditionally updated only at the sampled instants. Fuzzy logic systems are used to approximate the unknown nonlinear functions. In addition, a Nussbaum function is utilized to eliminate the effect of unknown hysteresis. Moreover, an event-triggered mechanism is introduced to reduce the communication burden. By using stochastic Lyapunov stability theory and graph theory, it is proved that all signals in the closed-loop system are semiglobally uniformly ultimately bounded. Meanwhile, all the followers’ outputs converge to the dynamic convex hull spanned by the dynamic leaders. Finally, the effectiveness of the proposed control scheme is illustrated by some simulation results. [ABSTRACT FROM AUTHOR]

In this brief, the output feedback based finite-time attitude containment control problem for multiple spacecrafts is investigated. A novel finite-time command filtered backstepping containment control scheme is proposed for attitude systems with unmeasurable states, inertia uncertainties, external disturbances and input saturations, which can not only guarantee the containment control errors converge to the sufficient small neighborhood of the origin in finite-time, but also overcome the computation complexity problem in traditional backstepping. The simulation results show the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive finite-time attitude containment control for multiple spacecrafts with unknown external disturbances in spacecraft formation flying is investigated. A distributed control strategy combined with finite-time command filtered backstepping (FTCFB) and an adaptive technique is proposed, which can guarantee the containment errors of attitudes between leader spacecrafts and follower spacecrafts reaching the desired neighborhood in finite time. Moreover, the applied second-order sliding mode differentiator in FTCFB can make the output of the command filter fast approximate the derivative of the virtual signal at the second step of backstepping, which can further improve the control quality. A simulation example is given to show the effectiveness of the new designed technique presented. [ABSTRACT FROM AUTHOR]

In this paper, a containment problem is investigated for sampled-data agent networks subject to switching topologies and information delays. A nonlinear algorithm is introduced to ensure that the agents move into a convex area formed by some static leaders. The analytical approaches include the model transformation, the convexity analysis, and the Lyapunov approach. It proves that the containment problem can be achieved for sampled-data agent networks with bounded information delays and switching topologies if the union of the communication graphs has spanning trees. A numerical example is employed to demonstrate the validity of the theoretical results.

In this paper, the containment control problem of the second-order multi-agent systems (MASs) with general noise over directed topology is investigated. General noise, which may be the mixture of colored and white noise, is introduced to model the perturbation of MASs. Since constructing an anti-perturbed distributed controller for concerned MASs is difficult, we attend to use the perturbation tolerant character of the convex hull spanned by multiple leaders in the containment control problems of MASs. To this end, the hierarchical topology structure of MASs is used, which can largely reduce the communication loads and computational complexity. It is shown that the MASs are noise-to-state stable and the state of the MASs has an asymptotic gain in the mean square based on random differential equations (RDEs) theorem framework. Moreover, the relative hierarchical topology reconfiguration algorithm is given based on which the system can withstand stronger noise and all followers gradually converge to the convex hull formed by the leaders of the respective level. Finally, the numerical simulation is carried out to substantiate the feasibility of the proposed control theory.

This work deals with the containment control problem of multi-agent networks with different fractional-order dynamics under bounded communication delays. Unlike most existing work, we analyze this problem from a positive system viewpoint. For the case where the communication delays are the same constant, we investigate the entry-wise monotonicity of the solution of the corresponding error system. Then, by bounding the solution of the time-varying delay system by its corresponding system with constant delay, it is shown that as long as every follower can obtain information at worst from one leader directly or indirectly, the followers will finally arrive at the convex hull spanned by the stationary leaders. Our results reveal that the communication delay independence in containment control of fractional-order multi-agent networks has a strong connection with the delay-insensitive stability of positive systems. An example is also employed to illustrate the obtained theoretical findings.

In this paper, the containment control was studied for high-order discrete-time multi-agent systems. A distributed 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 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. Finally, a simulation is also given to show the theoretical result.

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]

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]

This article focuses on the containment control problem for nonlinear multiagent systems (MASs) with unknown disturbance and prescribed performance in the presence of dead-zone output. The fuzzy-logic systems (FLSs) are used to approximate the unknown nonlinear function, and a nonlinear disturbance observer is used to estimate unknown external disturbances. Meanwhile, a new distributed containment control scheme is developed by utilizing the adaptive compensation technique without assumption of the boundary value of unknown disturbance. Furthermore, a Nussbaum function is utilized to cope with the unknown control coefficient, which is caused by the nonlinearity in the output mechanism. Moreover, a second-order tracking differentiator (TD) is introduced to avoid the repeated differentiation of the virtual controller. The outputs of the followers converge to the convex hull spanned by the multiple dynamic leaders. It is shown that all the signals are semiglobally uniformly ultimately bounded (SGUUB), and the local neighborhood containment errors can converge into the prescribed boundary. Finally, the effectiveness of the approach proposed in this article is illustrated by simulation results. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive fuzzy event-triggered containment control problem is addressed for uncertain nonlinear strict-feedback systems guided by multiple leaders. A novel distributed adaptive fuzzy event-triggered containment control is designed only using the information of the individual follower and its neighbors. Moreover, a distributed event-trigger condition with an adjustable threshold is developed simultaneously. The designed containment control law is updated in an aperiodic manner, only when event-triggered errors exceed tolerable thresholds. It is proved that the uniformly ultimately bounded containment control can be achieved, and there is no Zeno behavior exhibited by applying the proposed control scheme. Simulation studies are outlined to illustrate the effectiveness of the theoretical results and the advantages of the event-triggered containment control proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper considers the containment control problem for multiple Euler–Lagrange systems with unknown nonlinear dynamics, where the dynamics of the leaders are different from those of the followers. In addition, some followers cannot obtain information of the leaders owing to the limited communication range. We first adopt an event-based observer to estimate a trajectory inside the convex hull spanned by states of the leaders, in which continuous communication can be avoided as well. Then, we further utilize the fuzzy logic systems to approximate the unknown nonlinear dynamics and propose an adaptive control scheme. Under the proposed scheme, we can ensure that the states of the followers can converge to the convex hull formed by these states of the leaders. Finally, a simulation example is given to validate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this contribution, we propose and investigate the containment control issue for general linear multiagent systems (MASs) under the asynchronous setting, where the network topology is not subjected to any structural restrictions and the roles of the leaders and the followers are entirely determined by the network topology. It is assumed that the interaction time instants of each agent, at which this agent interacts with its neighbors, are independent of the other agents’ and can be unevenly distributed. An asynchronous distributed algorithm is proposed to implement the control strategy of linear MASs. The non-negative matrix theory and the composition of binary relations are utilized to handle the asynchronous containment control issue. It is shown that the leaders in each closed and strongly connected component of the network topology will reach a common state and the followers will gradually enter the dynamic convex hull constructed by the leaders. Moreover, it is also proved that the system matrix can be strictly unstable, and the upper bound of the system matrix’s spectral radius is explicitly stated. Finally, two simulation examples are also provided to verify the efficacy of our theoretical results. [ABSTRACT FROM AUTHOR]

In this brief, we aim to solve the containment problem for a class of discrete-time linear multi-agent systems (MASs) with multiple interaction leaders. Agents in the considered MASs will communicate with their neighbors through a signed digraph, i.e., the relationships between neighboring agents in the present MASs model may be cooperative or antagonistic, which differ from most previous research on containment of linear MASs. To achieve containment in such an MAS model, reduced-order observer-type containment controllers using the relative outputs of neighboring agents are developed. By utilizing stability theory of discrete-time linear systems, it is proved that the state trajectories of followers can enter eventually the convex hull formed by the trajectories of leaders and their symmetric trajectories provided that the inherent linear dynamics of each agent are stabilizable and detectable, and each follower could receive information directly or indirectly from at least one leader. Finally, a numerical example is presented to verify the achievement of containment under the proposed controllers. [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]