Directed Interaction Topologies Research Articles

Distributed fixed-time output consensus for disturbed second-order multiagent systems with dead-zone input

This article investigates the fixed-time output consensus (FTOC) problem for second-order multiagent systems (MASs) with mismatched disturbance and dead-zone input under directed interaction topology. Firstly, a fixed-time disturbance observer is constructed for each agent to estimate the mismatched disturbance. Secondly, a new distributed control scheme based on the fixed-time stability theory and adding a power integrator approach is proposed, which solves the FTOC problem of the MASs. In addition, an explicit representation of the upper bound of settling time is also provided. Finally, two simulation examples demonstrate the feasibility and superiority of the devised control strategy.

Performance-Based Distributed Control of Multiagent Systems: A Dual Phase Approach.

In this article, we investigate the distributed tracking control problem for networked uncertain nonlinear strict-feedback systems with unknown time-varying gains under a directed interaction topology. A dual phase performance-guaranteed approach is established. In the first phase, a fully distributed robust filter is constructed for each agent to estimate the desired trajectory with prescribed performance such that the control directions of all agents are allowed to be nonidentical. In the second phase, by establishing a novel lemma regarding Nussbaum function, a new adaptive control protocol is developed for each agent based on backstepping technique, which not only steers the output to track the corresponding estimated signal asymptotically with arbitrarily prescribed transient response but also extends the application scope of the proposed control scheme largely since the unknown control gains are allowed to be time-varying and even state-dependent. In such a way, the underlying problem is tackled with the output tracking error converging into an arbitrarily preassigned residual set exhibiting an arbitrarily predefined convergence rate. Besides, all the internal signals are ensured to be semi-globally ultimately uniformly bounded (SGUUB). Finally, two examples are provided to illustrate the effectiveness of the co-designed scheme.

Fixed-time leader–follower consensus for second-order multi-agent systems: Variable exponent sliding mode control approach

This paper investigates the fixed-time leader–follower consensus (LFC) problem of second-order multi-agent systems (MASs) with bounded disturbance under directed interaction topology. First, a sliding mode manifold (SMM) with consensus errors–dependent variable exponential coefficient is given. Then, two sliding mode control (SMC) protocols are proposed. The proposed control protocols can eliminate the singularity, while guaranteeing the fixed-time reachability of the consensus errors to the sliding mode surface (SMS) and the fixed-time convergence of the consensus errors toward the origin along the SMS. Finally, the validity of the obtained methodology is confirmed by two simulation examples.

Estimator-based multi-target tracking of networked robotic systems via predefined-time hierarchical control method

In this paper, we study the multi-target tracking problem of networked robotic systems (NRSs) within predefined time under a directed interaction topology considering disturbances and physical parameter uncertainties. On the basis of non-singular sliding-mode surface, a new predefined-time estimator-based hierarchical control algorithm is put forward so as to address the tracking problem under the case of multiple moving targets. Using the time base generator (TBG), a distributed estimator algorithm is designed to ensure that the followers can estimate different target states within a predefined-time. Certain sufficient conditions of predefined-time multi-target tracking of NRSs are presented using the Lyapunov stability and neighbor information interaction principle. In the end, numerical simulation experiments are offered to indicate the availability and correctness of the theoretical results.

Privacy-Preserving Adaptive Resilient Consensus for Multiagent Systems Under Cyberattacks

This article investigates the secure and privacy-preserving consensus problem of multi-agent systems (MASs) with directed interaction topologies under multiple cyber attacks, which contain deception attacks and DoS attacks. First, a unified attack model is introduced to characterize such a multiple attack phenomenon. Besides, considering the existence of eavesdroppers who can intercept the data transmitted on the links, a fully distributed agent value reconstruction method based on the idea of state decomposition is designed to prevent the leakage of the agent's initial information. Then, a novel privacy-preserving adaptive resilient consensus algorithm (PPARCA) with certain graph robustness condition for MASs under the multiple cyber attacks is proposed. The algorithm adaptively takes different countermeasures in the face of different cyber attacks. PPARCA uses the reconstructed agents' states and combines with the modified Secure Acceptance and Broadcast Algorithm (SABA). Theoretical analysis shows that the proposed algorithm can effectively protect the privacy of the initial state of the agents, and reach resilient consensus in the face of cyber attacks. Finally, numerical simulations and Raspberry Pi MASs practical application experiments demonstrate the effectiveness of the proposed results.

Bearing-only Formation Maneuvering for UAV Swarm over Directed Interaction Topologies

Bearing-only Formation Maneuvering for UAV Swarm over Directed Interaction Topologies

Robust Linear-Velocity-Free Formation Tracking of Multiple Quadrotors With Unknown Disturbances

This article addresses the problem of quadrotor formation control with inaccessible linear velocity and the unknown disturbances under directed interaction topologies. Considering the unknown disturbances act in both the translational and rotational motions of each underactuated quadrotor, a hierarchical distributed disturbance rejection controller is developed for the quadrotor formation. In the outer loop, an observerbased translational controller is designed to achieve the desired formation over directed interaction topologies. To estimate the inaccessible linear velocity measurements, a uniform differentiator is designed for each quadrotor using only the position information. In the inner loop, a robust geometric attitude controller is developed based on a super-twisting algorithm (STA). The proposed controllers can reach disturbance rejections in the whole frequency domain as much as desired and achieve asymptotic formation tracking within the appointed time. The stability analysis is presented using Lyapunov stability theory on cascaded systems, and the effectiveness of the proposed control strategy is demonstrated through numerical simulations

Cooperative learning event‐triggered control for discrete‐time nonlinear multi‐agent systems by internal and external interaction topology

AbstractThis paper investigates distributed cooperative learning event‐triggered control for discrete‐time strict‐feedback nonlinear multi‐agent systems with an identical system structure and different recurrent reference orbits. A clever system decomposition method is firstly proposed to divide every ‐order agent system into first‐order subsystems, which makes it possible to solve the tough problem that every estimated neural weight cannot converge to an unique ideal value based on the existing control scheme. By constructing two interaction typologies, a novel distributed cooperative weight updating law is designed by the introduction of the internal interaction terms between subsystems of every agent, the external interaction terms between agents, and the triggering mechanism between agents. With the combination of the graph multiplication operation, the consensus theory and the matrix null space property, the proposed cooperative event‐triggered control scheme guarantees that every agent can track their corresponding recurrent reference trajectories. And further the exponential convergence of all agents' neural estimated weights to a close vicinity around their mutual and unique ideal weights is verified under the condition that the directed interaction topology between agents is strongly connected and balanced. Such a weight convergence makes the proposed scheme has some significant advantages including the small data storage space, the convenient knowledge reuse, the good generalization ability, and the low communication burden. By reinvoking the saved constant weights, a static learning controller is presented for the high‐performance control of similar diversified tracking tasks. Simulation studies and some comparisons are given to show the advantages and effectiveness of the presented scheme.

Dynamic gain scheduling control design for linear multiagent systems subject to input saturation

This paper considers the finite-time bipartite consensus problem governed by linear multiagent systems subject to input saturation under directed interaction topology. Due to the existence of input saturation, the dynamic performance of linear multiagent systems degrades significantly. For the improvement of the dynamic performance of systems, a dynamic gain scheduling control approach is proposed to design a dynamic Laplacian-like feedback controller, which can be obtained from the analytical solution of a parametric Lyapunov equation. Suppose that each agent is asymptotically null controllable with bounded control, and that the corresponding interaction topology of the signed directed graph with a spanning tree is structurally balanced. Then the dynamic Laplacian-like feedback control can ensure that linear multiagent systems will achieve the finite time bipartite consensus. The dynamic gain scheduling control can better improve the bipartite consensus performance of the linear multiagent systems than the static gain scheduling control. Finally, two examples are provided to show the effectiveness of the proposed control design method.

Aggressive Formation Tracking for Multiple Quadrotors Without Velocity Measurements Over Directed Topologies

This paper addresses the aggressive formation tracking problem of quadrotors without velocity measurements over directed interaction topologies. A distributed formation control scheme is proposed for a multiple quadrotors system, which includes an outer-loop position controller to achieve the desired formation and an inner-loop attitude controller to regulate the attitudes. First, a second-order auxiliary system is designed to overcome the unmeasurable linear velocity. Next, the posotion controller is presented using only the position information under the directed topologies. Then, the geometric attitude controller is developed to carry out aggressive rotation maneuvers. Furthermore, an auxiliary system based on Lie algebra is proposed to eliminate the unreliable angular velocity feedback caused by disturbances and bias perturbations. Using Lyapunov stability theory on a cascaded system, it is rigorously proven that the proposed formation controller is asymptotically stable. Finally, the applicability and performance of the proposed control scheme are demonstrated by the numerical simulations.

Finite-time scaled consensus tracking of a class of high-order nonlinear multi-agent systems with unstable linearization

In this paper, we consider the finite-time scaled consensus tracking of a class of high-order nonlinear multiagent systems(MASs)who owns unstable modes in its Jacobian linearized system. The presence of unstable linearization makes the high-order MASs in question essentially different from those in the existing works. Under a directed interaction topology, to overcome the difficulties caused by the asymmetry property of Laplacian matrix, the finite-time scaled consensus control scheme is developed by the modified addition of a power integrator method. Based on finite-time Lyapunov stability theorem and algebra graph theory, for high-order MASs with unstable linearization even in the presence of non-lipschitz nonlinear dynamic, all system states are bounded and the output tracking errors are finite-time uniformly ultimately bounded(FUUB). Finally, a numerical example is given to demonstrate the effectiveness of the theoretical results.

Finite-Time Containment Control for Nonlinear Second-Order Multiagent System Under Directed Topology

This article investigates the finite-time containment control for a class of second-order multiagent systems with nonlinear dynamics and external disturbances under fixed directed interaction topology. Due to the existence of nonlinear dynamics and unknown but bounded external disturbances, there is an underlying technical difficulty for the design of containment controller. Furthermore, it is a challenge for the theoretical analysis of finite-time containment control problem due to the asymmetric Laplacian matrix arising from the constraint of one-way directed communication among the agents. In response to the above-mentioned challenges, a finite-time containment control algorithm is proposed. First, the multiagent system is considered with inherent nonlinear dynamics and unknown but bounded external disturbances. Second, the desired containment control protocol is presented under a directed interaction topology. Furthermore, by adding a power-integrator technique and Lyapunov function theory, the sufficient conditions are derived for the existence of the finite-time containment controller of a class of second-order multiagent systems. Finally, a numerical example is given to verify the usefulness of the proposed finite-time containment control protocol.

Distributed event-triggered affine formation control for multiple underactuated marine surface vehicles

This article focuses on the distributed event-triggered affine formation control problem for multiple underactuated marine surface vehicles (UMSVs) considering affine transformation and communication energy consumption under a directed interaction topology. Firstly, the affine transformation mechanism is adopted to improve the flexibility and maneuverability of the formation. The proposed technique allows a rich collection of collective motions such as translation, rotation, scaling, and the combination of these transformations. Then, unlike the event-triggered control of a single marine vehicle, this paper considers reducing communication frequency between vehicles. Thus, an event-triggered mechanism is proposed, which can save computation resources compared with traditional ones while excluding the Zeno behavior. Subsequently, it is proved that all signals in the closed-loop system are ultimately uniformly bounded (UUB), meanwhile, all tracking errors converge to a small compact set under the proposed control strategy. Finally, numerical simulations illustrate the effectiveness of the proposed formation controller.

A Scalable Adaptive Approach to Multi-Vehicle Formation Control with Obstacle Avoidance

This paper deals with the problem of distributed formation tracking control and obstacle avoidance of multi-vehicle systems (MVSs) in complex obstacle-laden environments. The MVS under consideration consists of a leader vehicle with an unknown control input and a group of follower vehicles, connected via a directed interaction topology, subject to simultaneous unknown heterogeneous nonlinearities and external disturbances. The central aim is to achieve effective and collision-free formation tracking control for the nonlinear and uncertain MVS with obstacles encountered in formation maneuvering, while not demanding global information of the interaction topology. Toward this goal, a radial basis function neural network is used to model the unknown nonlinearity of vehicle dynamics in each vehicle and repulsive potentials are employed for obstacle avoidance. Furthermore, a scalable distributed adaptive formation tracking control protocol with a built-in obstacle avoidance mechanism is developed. It is proved that, with the proposed protocol, the resulting formation tracking errors are uniformly ultimately bounded and obstacle collision avoidance is guaranteed. Comprehensive simulation results are elaborated to substantiate the effectiveness and the promising collision avoidance performance of the proposed scalable adaptive formation control approach.

Collision-free formation-containment control for a group of UAVs with unknown disturbances

This paper focuses on the formation-containment control problem for a group of fixed-wing unmanned aerial vehicles (UAVs) subjected to unknown disturbances. To solve this problem, a two-layer control framework is developed by decoupling the problem into a trajectory generation problem at the group level and a trajectory tracking problem at the individual level. Firstly, based on the directed interaction topology and the required configuration of the UAVs, two types of finite-time estimators are constructed to generate the desired trajectories of the leading UAVs and the following UAVs, respectively. Meanwhile, to guarantee the safety of each UAV, the smooth collision avoidance potential function and obstacle avoidance potential function are designed. After that, using the dynamic surface control (DSC) technique and combined with the established potential functions, a distributed control law with the ability of collision avoidance is presented for each UAV to track the generated trajectory without any collision, where the homogeneous extended state observer (HESO) is developed to compensate for the mismatched and matched disturbances. The stability of the whole closed-loop system is provided using the Lyapunov theorem. Finally, simulation results demonstrate the effectiveness of the proposed control algorithm.

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.

Distributed Prescribed-Time Consensus Observer for High-Order Integrator Multi-Agent Systems on Directed Graphs

This brief deals with the distributed consensus observer design problem for high-order integrator multi-agent systems on directed graphs, which intends to estimate the leader states accurately in a prescribed time interval. A new kind of distributed prescribed-time observers (DPTO) on directed graphs is first formulated for the followers, which is implemented in a cascading manner. Then, the prescribed-time zero-error estimation performance of the above DPTO is guaranteed for both time-invariant and time-varying directed interaction topologies, based on strictly Lyapunov stability analysis and mathematical induction method. Finally, the practicability and validity of this new distributed observer are illustrated via a numerical simulation example.

Guaranteed‐performance consensus for nonlinear singular multiagent systems with directed topologies

AbstractThe guaranteed‐performance consensus problems for nonlinear singular multiagent systems with directed topologies in both leader‐following case and leaderless case are investigated, where the directed interaction topologies contain a directed spanning tree. For situations with and without the leader, two different quadratic performance functions are proposed based on state errors. The state errors in the leader‐following case are the state differences between the followers and the leader while in the leaderless case are the state differences between agents with adjacent numbers. First, by exploiting state transformation, the consensus problems are transformed into the stability problems of the corresponding error systems. Second, on the basis of singular systems theory, Laplacian matrix properties, and linear matrix inequality techniques, sufficient conditions for guaranteed‐performance consensus are derived for both leader‐following and leaderless cases. Third, the explicit expressions of the guaranteed‐performance cost are obtained. Finally, two numerical examples are presented to illustrate the effectiveness of the theoretical results.

Finite-time multi-target tracking of networked Euler–Lagrange systems via hierarchical active disturbance rejection control

This paper investigates the finite-time multi-target tracking problem of networked Euler–Lagrange systems (NELSs) with a directed interaction topology, parametric uncertainties and external disturbances. A novel finite-time hierarchical active disturbance rejection control (ADRC) algorithm is designed to handle such a challenging problem without velocity measurement. To be specific, a nonsingular distributed estimator algorithm is newly designed to respectively estimate the states of the targets in a finite time. Based on the extended state observer (ESO), we present a finite-time local control scheme to obtain satisfactory tracking performance of the NELSs. Besides, sufficient conditions for deriving the finite-time stability of the cascade closed-loop systems are presented based on the Lyapunov argument. Finally, numerical simulations are performed to show the control performance and feasibility of the main results.

A New Fixed-Time Consensus Tracking Approach for Second-Order Multiagent Systems Under Directed Communication Topology

This paper considers fixed-time consensus tracking of second-order multiagent systems (MASs) under directed interaction topology. A novel distributed observer is presented to estimate the leader's states within a fixed time, which overcomes the difficulties caused by the asymmetry of the Laplacian matrix. A sliding surface is designed and a nonsingular terminal sliding mode consensus protocol is developed to achieve fixed-time convergence of the tracking error to the origin. It is shown that each follower can track the leader's trajectory within a fixed time. Particularly, the gain of the presented consensus protocol is directly related to the prescribed time, which makes it convenient to determine and tune the gain according to the requirement of convergence time. Moreover, the presented control protocol reduces the conservativeness of the convergence time estimation for sliding motion. The simulation results validate the effectiveness of the proposed consensus scheme.