Robust formation control for uncertain multi-agent systems

Robust formation problems for linear multi-agent systems with uncertainties and external disturbances are investigated in this paper. The model of each agent can be described by a nominal linear system combined with external disturbances and uncertainties which include parameter perturbations and nonlinear uncertainties. A more general bound of uncertainties is introduced. A robust formation controller, which consists of a nominal controller and a robust compensator, is proposed to achieve the desired state formation and restrain the influence of uncertainties and disturbances. Furthermore, sufficient conditions for time-varying formation feasibility are introduced and proved. Finally, a numerical example is provided to demonstrate the theoretical results.     

Network-based leader-following formation control of second-order autonomous unmanned systems

This article investigates two kinds of leader-following formation control problems of second-order autonomous unmanned systems under directed topology, that are, the cases with constant velocity and time-varying velocity for the leader. First, the kinematical equation of autonomous unmanned systems is established according to some real scenarios. Second, by assuming the velocity of the leader is constant, a sufficient condition ensuring the formation control of autonomous unmanned systems is derived and some control parameters are suitably designed. Third, it is assumed that the velocity of leader is time-varying, and the formation controller with two parts is designed. The first part is intended to form the desired formation of all followers and the second part aims to reach the consensus of velocity. Some simulation examples are finally presented to verify the effectiveness of the obtained theoretical results.     

Distributed sensor fault diagnosis for a formation of multi-vehicle systems

In the paper, a distributed sensor fault detection and isolation scheme is presented for a network of second-order integrators. A new distributed control law is developed to achieve formation of the system. By using the integration information of distributed formation errors, the control law improves the robustness of the formation. A distributed observer is then designed in each vehicle based on the closed-loop dynamic model of the vehicle. Each vehicle updates the states of the distributed observer by employing the measurements of itself and the transmitted state estimations from its neighbors. Based on the distributed observer, a distributed fault detection observer and a distributed fault isolation observer are designed. The presented distributed fault detection observer in each vehicle is able to be sensitive to the faults of all vehicles in the system. By using the distributed fault isolation observers, each vehicle is able to be sensitive to the faults of itself, its neighbors and its neighbors’ neighbors and to be robust to the faults of other vehicles. Although the fault isolation of the proposed scheme is simple, computation loads of the scheme are lower than the current ones since only the model of the individual vehicle is used. Finally, the effectiveness of the control law and the fault diagnosis scheme is demonstrated by simulations and real-time experiments carried out based on a formation of three quadrotors.     

Scale-based cluster formation for multi-agent systems with mismatched disturbances

This paper studies scale-based cluster formation problem of multi-agent system (MASs) under mismatched disturbances. A distributed sliding mode control with a disturbance observer is proposed to solve the aforementioned problem in the leaderless and leader-follower cases. The proposed control strategy provides satisfactory robust performance under mismatched disturbances and is thus more applicable to complicated formation control tasks. Finally, simulation results are provided to justify the validity of the proposed method.     

Limited-energy output formation for multiagent systems with intermittent interactions

Limited-energy output formation design and analysis problems are addressed for multiagent systems with intermittent interactions. Firstly, a new dynamic output feedback formation control protocol with the limited energy supply is proposed, which contains two independent parts associated with the interactive interval and the non-interactive interval. Then, sufficient conditions for leaderless limited-energy output formation are proposed by a new two-step design approach, which can make two gain matrices of the formation control protocol be designed independently. Meanwhile, the output formation reference function is determined to describe the absolute motion of all agents as a whole. Moreover, by constructing two transformation matrices with specific structures, the main conclusions for leaderless multiagent systems are extended into leader-follower ones. Finally, two numerical simulations are shown to demonstrate theoretical results.     

Event-triggered time-varying formation control for general linear multi-agent systems

This paper investigates event-triggered formation control problems for general linear multi-agent systems. The time-varying formation this paper studied can be described by a bounded piecewise differentiable vector-valued function. Firstly, a time-varying formation control protocol based on event-triggered scheme is constructed by the states of the neighboring agents. Each agent broadcasts its state information to neighbor nodes if the triggering condition is satisfied, and the communication load is decreased significantly. Then, an algorithm consisting of three steps is proposed to design the event-triggered formation control protocol. Moreover, it is proven that under the designed event-triggered formation protocol, the multi-agent systems can achieve the desired time-varying formation which belongs to the feasible formation set with the bounded formation error and the closed systems do not exhibit Zeno behavior. Finally, simulation results are given to demonstrate the effectiveness of the theoretical analysis.     

The formation of concern for face and its impact on knowledge sharing intention in knowledge management systems

Previous empirical studies have shown that in Chinese culture face is critical for the success of knowledge sharing in knowledge management systems (KMS). However, much less is known about the factors shaping the concern for face and the way they impact on the individual's knowledge sharing intention in KMS. Using data drawn from professionals’ knowledge sharing practices in Taiwanese organizations, this study focuses on a detailed investigation of the concern for face and how it impedes individuals’ knowledge sharing intention in the KMS context. The research findings show that the perfection of authentic self and the scrutiny of others (referred to as others’ watch) together explain 27.7% of the variance in face in relation to public self. In turn, face related to public self explains 20.7% of subjective norms. Finally, face related to public self and subjective norms together account for 41.2% of the variance in knowledge sharing intention. The research findings have important theoretical and managerial implications.     

Cascade design for formation control of nonholonomic systems in chained form

This paper presents a constructive method to design a cooperative state and output feedback to steer a group of nonholonomic mobile robots in chained form to form a desired geometric formation shape. The control methodology divides the resulting tracking error dynamics into a cascaded of linear and time-varying subsystems. A basic consensus algorithm is first applied to the linear subsystem which makes the states synchronize exponentially to zero. Once this first linear subsystem has converged, the second cascade can be treated as a linear time-varying subsystem perturbed by a vanishing term from its cascade. A dynamic state and output feedback is constructed to achieve synchronization of the rest of the states. The proof of stability is given using a result from cascade systems. Since time delay appears in many interconnection networks and particularly in cooperative control, its effect on the stability of the closed-loop system is analyzed using Razumikhim theorem. It is shown that the established cooperative controller work well even in the presence of time delay. Numerical simulations are performed on models of car-like mobile robots to show the effectiveness of the proposed cooperative state and output-feedback controllers.     

Finite-time formation control of nonaffine nonlinear systems under directed communication interactions

This paper studies the problem of finite-time formation tracking control for networked nonaffine nonlinear systems with unmeasured dynamics and unknown uncertainties/disturbances under directed topology. A unified distributed control framework is proposed by integrating adaptive backstepping control, dynamic gain control and dynamic surface control based on finite-time theory and consensus theory. Auxiliary dynamics are designed to construct control gains with non-Lipschitz dynamics so as to guarantee finite-time convergence of formation errors. Adaptive control is used to compensate for uncertain control efforts of the transformed systems derived from original nonaffine systems. It is shown that formation tracking is achieved during a finite-time period via the proposed controller, where fractional power terms are only associated with auxiliary dynamics instead of interacted information among the networked nonlinear systems in comparison with most existing finite-time cooperative controllers. Moreover, the continuity of the proposed controller is guaranteed by setting the exponents of fractional powers to an appropriate interval. It is also shown that the improved dynamic surface control method could guarantee finite-time convergence of formation errors, which could not be accomplished by conventional dynamic surface control. Finally, simulation results show the effectiveness of the proposed control scheme.     

Time-varying formation control for nonlinear multi-agent systems against actuator attacks

The formation control problem with time-varying characteristics is investigated for the time-delayed nonlinear multi-agent systems against actuator attacks. A neural-network-based adaptive control method is constructed to achieve the desired control objective, which is outputs of the followers can complete the desired transformation of formation configuration. To eliminate the influence of malicious attacks on the actuators, an actuator attacks defense strategy is proposed to resist false data injection attacks occurred in the actuator. The uncertainty of the dynamics caused by nonlinear functions is resolved by the neural-network approximate method. The problem of the time delay is handled by an improved Lyapunov-Krasovskii functional approach, which can also avoid the singularity problem that may occur during the construction of the control method. Based on the Lyapunov stability theory, it is proved that all signals of closed-loop systems are semi-globally stable and the formation error can converge to a small neighborhood of the origin. Finally, the results of simulations are provided to verify the feasibility of the theoretical analysis and the effectiveness of the proposed control method.     

Affine formation control for multi-agent systems with prescribed convergence time

In this paper, the affine formation control problem for multi-agent systems with prescribed convergence time is investigated. Firstly, on the basis of a time-varying scaling function, a distributed continuous control algorithm is designed, under which a stationary affine formation of the nominal configuration is able to be achieved within a prescribed time. Secondly, to track a time-varying formation within the prescribed time, a distributed control protocol is proposed by employing a leader–follower control strategy. Furthermore, the boundary layer technique is adopted to avoid chattering effect. Finally, simulation examples are provided to demonstrated the effectiveness of the proposed design.     

Specified-time bearing-based formation control of multi-agent systems via a dynamic gain approach

In this paper, the specified-time bearing-based formation control problem is investigated via a dynamic gain approach. Both the leader-follower and leaderless cases for single- and double-integral multi-agent systems are considered with bearing measurement, respectively. By considering the communication graph as bearing rigid, distributed bearing-based controllers with a time-varying gain are designed. By using time transformation method and Lyapunov stability theory, the close-loop systems under the proposed protocols can achieve the target formation within the specified time. Comparing with some existing results, the proposed approaches can make multi-agent systems converge to the desired formation within any preset time without dependence on the initial conditions or system parameters. Finally, some simulations and experiments are presented to demonstrate the effectiveness of the proposed algorithms.     

Distributed rotating formation control of second-order leader-following multi-agent systems with nonuniform delays

In this paper, the leader-following rotating formation control problem is investigated for second-order multi-agent systems with nonuniform time-delays. We propose a distributed algorithm to drive all agents to achieve a desired formation and orbit around a common point. By a frequency domain analysis method, the upper bound of the maximum time-delay is obtained. Finally, a numerical simulation is given to illustrate the obtained results.     

Signal generator based finite-time formation control for disturbed heterogeneous multi-agent systems

This paper investigates finite-time formation control problems of heterogeneous multi-agent systems subject to mismatched and matched disturbances. The studied agents are modelled with both different orders and dimensions. To achieve the desired finite-time formation control goal, a novel signal generator based finite-time formation control scheme is proposed, which is composed of two parts. In the first part, a distributed finite-time signal generator is established to produce formation references for the agents in finite time. In the second part, based on finite-time observer technique and homogeneous systems theory, a kind of composite anti-disturbance controllers are constructed for the agents to track the formation references in finite time. In this way, the studied multi-agent system completes the desired finite-time formation control task. Compared with the existing results, the proposed control scheme solves the disturbed finite-time formation control problems with both different agents’ orders and dimensions, simplifies the formation controller design by using a modular design philosophy, and makes the agents have a plug and play feature. A simulation example is shown to validate the effectiveness of the proposed control scheme.     

Distributed adaptive optimization-based formation tracking with double parameter projections for multi-agent systems

In this paper, a distributed adaptive optimization-based formation tracking strategy with double parameter projections for multi-agent systems is addressed under a centralized task allocation and distributed task execution (CTA-DTE) framework. Since a pre-described formation strategy is unable to adapt to a complex and dynamic environment, an optimization-based approach is proposed to transfer the formation tracking problem into a time-varying optimization one, subject to some constraints with several time-varying parameters which determine the rule of formation configuration change adaptively. These parameters are computed by a centralized unit and allocated to each agent as a global mission. Furthermore, each agent cooperates with others to execute this mission under a distributed optimization-based strategy, which combines a geometric center observer technology and a novel double parameter projections technology. The former ensures accurate tracking of a continuous reference trajectory. The latter guarantees that all agents enter into a time-varying security region and never escape from it, and meanwhile, all agents are attracted towards the best time-varying formation configuration via a gradient descent with a compensation. Finally, some simulation results are illustrated to verify the effectiveness of the strategy.     

Distributed formation control of double-integrator fractional-order multi-agent systems with relative damping and nonuniform time-delays

In this paper, distributed formation control problems are studied for double-integrator fractional-order multi-agent systems (DIFOMASs) with relative damping and nonuniform time-delays. The required state deviations of a group of multi-agent systems are achieved through a local state information interaction, which means that this group of multi-agent systems achieves formation control. In the context of this paper, the dynamic model is first established and the formation control protocol is designed for distributed formation control of DIFOMASs with relative damping under symmetric time-delays and asymmetric time-delays. Then, some sufficient conditions for achieving distributed formation control of DIFOMASs are acquired with the help of graph theory, matrix theory, stability theory and frequency-domain theory. In the end, two simulation examples are performed to verify the efficacy of our proposed method.     

Distributed adaptive fault-tolerant formation control for heterogeneous multiagent systems under switching directed topologies

This paper studies the cooperative fault-tolerant formation control problem of tracking a dynamic leader for heterogeneous multiagent systems consisting of multipile unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) with actuator faults under switching directed interaction topologies. Based on local neighborhood formation information, the distributed fault-tolerant formation controllers are constructed to ensure that all follower UAVs and UGVs can accomplish the demanding formation configuration in the state space and track the dynamic leader’s trajectory. By incorporating the sliding mode control and adaptive control technique, the actuator faults and unknown parameters of follower agents can be compensated. Through the theoretical analysis, it is proved that the cooperatively semiglobally uniformly ultimately boundedness of the closed-loop system is guaranteed, and the formation tracking errors converge to a small adjustable neighborhood of the origin. A simulation example is introduced to show the validity of the proposed distributed fault-tolerant formation control algorithm.     

Droplet formation and shrinking in aqueous two-phase systems using a membrane emulsification method

Using a membrane emulsification method based on porous hollow-fiber membranes in combination with an aqueous two-phase system (ATPS), we are able to produce “water-in-water” droplets with narrow-dispersed size distributions. The equilibrium phases of the aqueous two-phase system polyethylene glycol-dipotassium hydrogen phosphate are used for this purpose. The droplet diameter of a given fluid system is determined by the flow rates of the continuous and disperse phase as well as the hollow fiber dimensions. When diluting the disperse phase and thus moving the ATPS system out of equilibrium, the droplet size can be further reduced in comparison to the equilibrium case. Generally, droplets formed with this method have diameters 20%–60% larger than the inner hollow fiber diameter. The new strategy of diluting the disperse phase allows the production of droplet diameter below the inner diameter of the membrane.