Formation-containment Problem Research Articles

Output Formation Containment for Multiagent Systems Under Multipoint Multipattern FDI Attacks: A Resilient Impulsive Compensation Control Approach.

The increasing number of devices and frequent interactions of agents from networked multiagent systems (MASs) exacerbate the risks of potential cyber attacks, especially the different point attacks and multiple pattern attacks. This article considers the output formation-containment problem for MASs under multipoint multipattern false data injection (FDI) attacks. The multipoint describes the attacks simultaneously occurring on the sensors, actuators, and communication channels; the multipattern captures that sensor and actuator attack signals are both continuous deterministic variables, and the communication channel attack signals are intermittent random variables, obeying the Bernoulli distribution. For such compromised MASs, a novel hybrid protocol is proposed, which integrates a state observer, an attack estimator, an impulsive interactor and a compensation controller. Thereinto, the state observer and the attack estimator are constructed to recover the unmeasured system states and the unknown FDI attack signals, respectively; the impulsive interactor is designed to guarantee that the neighbor's signals are transmitted only at impulsive instants, and meanwhile the channel attacks are randomly launched; using the recovered signals, the compensation controller is devised to alleviate the effect of attacks. A sufficient condition is identified, under which the output formation containment is achieved with cooperative uniform ultimate boundedness (UUB). Finally, simulation results are carried out to validate the effectiveness and advantages of the proposed approach.

Adaptive Event-Triggered Time-Varying Output Bipartite Formation Containment of Multiagent Systems Under Directed Graphs.

The time-varying output bipartite formation containment (TVOBFC) problem for linear multiagent systems (MASs) under directed graphs is an important problem. However, the methods in existing works rely on the global information of the MASs or do not use event-triggered communication. This article investigates two kinds of TVOBFC problems for heterogeneous linear MASs under signed digraphs by event-triggered communication. For the first case where leaders have the same dynamics, the innovative fully distributed event-triggered protocol for the follower is proposed. In this case, the followers form the preset formation shape. For the second case where leaders have different dynamics, the leaders are divided into two groups. One group can directly obtain the output information of the virtual leader, while the other group cannot. In order to make leaders achieve the formation shape and track the virtual leader, two kinds of innovative observers are designed for two kinds of leaders to estimate the state of the virtual leader, and the control protocol is designed for each leader based on the designed observers. Then, the control law for each follower is designed to solve the formation containment problem. Finally, two examples are introduced to illustrate the main results.

Anti-disturbance fault-tolerant formation containment control for multiple autonomous underwater vehicles with actuator faults

This paper investigates the time-varying formation containment problem for multiple autonomous underwater vehicles (MAUVs) system subject to actuator faults in three-dimensional space. The leader AUVs are required to track the virtual leader AUV with time-varying offset vectors, and at the same time the follower AUVs are demanded to converge into the convex hull formed by the leader AUVs. The extended state observers (ESOs) are designed to estimate the external disturbances and unknown nonlinearities of MAUVs system in real time, hence ensuring the anti-disturbance ability of MAUVs system. The tracking differentiators (TDs) are developed so as to avoid the differential explosion issues caused by the derivatives of the virtual control laws. The distributed formation containment control laws are put forward for compensating the impacts of unknown bounded actuator bias fault and loss of actuator effectiveness fault based on adaptive control strategy. Furthermore, the stability of MAUVs system is demonstrated by means of Lyapunov stability theory. At last, a numerical simulation is presented to confirm the effectiveness of the proposed method.

Formation–containment control of multi-agent systems with communication delays

This paper designs formation–containment control algorithms for a class of second-order nonlinear multi-agent systems governed by Euler–Lagrange dynamics with communication delays. The formation–containment problem consists of leader agents’ formation control and follower agents’ containment control. Firstly, to make the leaders form a desired formation and move collectively with a constant velocity, a coordinated formation control algorithm is designed and the variable-gain technique is used to eliminate the effect of communication delays on the leaders’ formation control. Secondly, considering that only the leaders have access to the desired moving velocity, we propose distributed velocity estimators for followers in which the communication delays also exist in the followers’ information interaction. By using the estimated velocity information, coordinated containment control laws are designed for the followers to drive them asymptotically converge to the convex hull spanned by all leaders. Furthermore, to increase the system robustness against uncertainties and external disturbances, the adaptive updating laws are designed for all agents. Finally, simulations are given to demonstrate these obtained results.

Intermittent Sampled Data Control for Time-Varying Formation-Containment of the Multiagent System with/without Time Delay

Time-varying formation-containment problems for a second-order multiagent system (SOMAS) are studied via pulse-modulated intermittent control (PMIC) in this paper. A distributed control framework utilizing the neighbors’ positions and velocities is designed so that leaders in the multiagent system form a formation, and followers move to the convex hull formed by each leader. Different from the traditional formation-containment problems, this paper applies the PMIC framework, which is more common and more in line with the actual control scenarios. Based on the knowledge of matrix theory, algebraic graph theory, and stability theory, some sufficient conditions are given for the time-varying formation-containment problem of the second-order multiagent system. Some numerical simulations are proposed to verify the effectiveness of the results presented in this paper.

Layered Formation-containment Control of Multi-agent Systems in Constrained Space

This paper addresses the layered formation-containment (LFC) problem for multiagents in the constrained space with a directed communication topology. The formation-containment problem is first defined using a layered framework, and a layered distributed finite-time estimator is proposed to acquire the target states for agents in each layer. Based on the proposed framework, the formation configuration and the mechanism of the information flow can be explored and designed naturally. To avoid collisions with borders, obstacles, as well as the other agents in the constrained space, an artificial potential function is designed based on the Dirac delta function. Further, a disturbance observer and adaptive neural networks (NNs) are applied to respectively tackle the external disturbance and the model uncertainties. The desired formation of each layer can be achieved while no collision occurs in the constrained space. The semi-global uniform ultimate boundedness of closed-loop errors is guaranteed by Lyapunov stability theory. Simulation results are given to show the effectiveness of the proposed approaches.

Time-Varying Output Formation Containment of General Linear Homogeneous and Heterogeneous Multiagent Systems

This paper investigates the time-varying output formation-containment control of general linear homogeneous and heterogeneous multiagent systems (MAS). This control aims at making each follower's output reach an agreement on the time-varying formation reference, namely, the centroid of the multiple leaders’ outputs, and keep a predefined time-varying offset with respect to it. Distributed static output-feedback (OPFB) and dynamic OPFB control protocols are first constructed for homogeneous and heterogeneous MAS, respectively, using only neighboring relative output information and a time-varying formation compensation signal. It is proved that the time-varying output formation-containment problem is solved by making certain output formation-containment errors go to zero asymptotically. Then, local sufficient conditions and explicit local design procedures are provided for both homogeneous and heterogeneous MAS. It is shown that the state/output consensus problems, the state/output containment problems, the state/output formation control problems, the time-varying state/output formation-tracking problems with a single leader, and target enclosing problems of homogeneous/heterogeneous MAS can all be treated as special cases of this paper. Finally, numerical simulations validate the effectiveness of the proposed control protocols.

Output formation-containment of interacted heterogeneous linear systems by distributed hybrid active control

This paper investigates the output formation-containment problem of interacted heterogeneous linear systems, where each heterogeneous system, whether the leader or the follower, has different dimensions and dynamics. Different from existing literature, discrete-time communication manner is deployed to reduce the communication consumption. By the impulsive control method, a distributed hybrid active controller is designed using the discrete-time information of neighbors. It achieves the output formation-containment of heterogeneous systems if two related conditions are satisfied, namely, local linear matrix inequalities (LMIs) and a bounded constraint on the average interacted interval. Moreover, the controller parameter design is further simplified by replacing the LMI condition with a Hurwitz condition, which can be easily guaranteed by solving a Riccati equation. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical result.

Distributed Three‐Dimensional Formation Containment Control of Multiple Unmanned Aerial Vehicle Systems

AbstractThis 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.

Distributed Adaptive Finite-Time Approach for Formation-Containment Control of Networked Nonlinear Systems Under Directed Topology.

This paper presents a distributed adaptive finite-time control solution to the formation-containment problem for multiple networked systems with uncertain nonlinear dynamics and directed communication constraints. By integrating the special topology feature of the new constructed symmetrical matrix, the technical difficulty in finite-time formation-containment control arising from the asymmetrical Laplacian matrix under single-way directed communication is circumvented. Based upon fractional power feedback of the local error, an adaptive distributed control scheme is established to drive the leaders into the prespecified formation configuration in finite time. Meanwhile, a distributed adaptive control scheme, independent of the unavailable inputs of the leaders, is designed to keep the followers within a bounded distance from the moving leaders and then to make the followers enter the convex hull shaped by the formation of the leaders in finite time. The effectiveness of the proposed control scheme is confirmed by the simulation.

Collectively Rotating Formation and Containment Deployment of Multiagent Systems: A Polar Coordinate-Based Finite Time Approach.

This paper investigates the problem of achieving rotating formation and containment simultaneously via finite time control schemes for multiagent systems. It is nontrivial to maintain rotating formation where the desired formation structure is time-varying and only neighboring information is available. The underlying problem becomes even more complicated if containment is imposed yet finite time convergence is required at the same time. To tackle this problem, a polar coordinate-based approach is exploited in this paper. Finite time control protocols are established for leader agents and follower agents, respectively, such that three goals are achieved in finite time concurrently: 1) all the agents maintain a stable rotating motion around a common circular center with a common (possibly time-varying) angular velocity; 2) the leader agents form and maintain a prespecified rotating formation structure; and 3) the follower agents converge to the shifting convex hull shaped by the dynamically moving (circling) leaders. It is the polar coordinate expression that simplifies the formulation of the rotating formation-containment problem and facilitates the finite time control design process. The effectiveness of the proposed control scheme is illustrated via both formative mathematical analysis and numerical simulation.

Output formation-containment of coupled heterogeneous linear systems under intermittent communication

This paper investigates the output formation-containment problem of the coupled heterogeneous linear systems under intermittent communication. The systems considered in this paper are more general in the sense that each system, whether a leader or a follower, has different dimension and different dynamic. Besides, each system only communicates with its neighbors intermittently. Based on the intermittent information, both the state-feedback and the output-feedback distributed control protocols are designed and a criterion is derived to calculate the lower bound of the communication ratio. Furthermore, a heuristic algorithm based on the Fireworks Algorithm is developed to obtain an optimized communication ratio, which greatly reduces the communication burden. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Formation-containment control for second-order multi-agent systems with time-varying delays

In this paper, formation-containment control problems for multi-agent systems with second-order dynamics and time-varying delays are studied. The states of leaders are designed to achieve the time-varying formation and the states of followers are required to converge to the convex hull spanned by those of leaders simultaneously, which differs from conventional formation control or containment control problems. Using the neighboring positions and velocities, formation-containment protocols with time-varying delays are constructed. By exploiting the space decomposition approach, formation-containment problems are transformed into the asymptotically stable problems. Sufficient conditions for second-order multi-agent systems with time-varying delays to realize formation-containment are presented. A method to obtain the unknown gain matrices in the protocols is proposed. Numerical simulations are shown to illustrate the effectiveness of the theoretical results.

Output formation-containment analysis and design for general linear time-invariant multi-agent systems

Output formation-containment control problems for general linear time-invariant multi-agent systems with directed topologies are dealt with. Output formation-containment means that the outputs of leaders achieve the predefined formation, and at the same time the outputs of followers converge to the convex hull formed by the outputs of leaders. Firstly, static output protocols are presented for leaders and followers respectively. Then output formation-containment problems of multi-agent systems are transformed into asymptotic stability problems. Sufficient conditions with less computation complexity are proposed for multi-agent systems to achieve the output formation-containment. An explicit expression for the time-varying output formation reference function is derived to describe the macroscopic movement of the whole output formation-containment. Explicit expressions to describe the relationship among the outputs of followers, the time-varying output formation for the leaders and the output formation reference are derived. It is proven that the outputs of followers not only converge to the convex hull formed by those of leaders but also achieve certain time-varying formation specified by the convex combination of the desired output formation for the leaders. Moreover, an approach to determine the gain matrices in the protocols is given for multi-agent systems to achieve the output formation-containment. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

Formation-containment control for high-order linear time-invariant multi-agent systems with time delays

Formation-containment analysis and design problems for time-delayed high-order linear time-invariant multi-agent systems with directed interaction topologies are studied. Firstly, protocols with time delays are presented for leaders and followers, where the formation for leaders can be time-varying. Then formation-containment problems for time-delayed multi-agent systems are transformed into asymptotic stability problems of time-delayed systems. Sufficient conditions for multi-agent systems to achieve formation-containment are proposed, which include eight linear matrix inequalities independent of the number of leaders and followers. Furthermore, an explicit expression of the formation reference function for leaders is derived, where the motion modes of formation reference can be specified. An approach to determine the gain matrices in the protocols is given using the method of changing variables. Finally, numerical simulations are provided to demonstrate theoretical results.