Leader-following Case Research Articles

Model-free adaptive consensus design for a class of unknown heterogeneous nonlinear multi-agent systems with packet dropouts

This paper studies the consensus problem for a class of unknown heterogeneous nonlinear multi-agent systems via a network with random packet dropouts. Based on the dynamic linearization technique, novel model-free adaptive consensus protocols with the data compensation mechanism are designed for both leaderless and leader-following cases. The advantage of this approach is that only neighborhood input and output data of the agents are required in the protocol design. For the stability analysis, a new Squeeze Theorem based method is developed to derive the theoretic results instead of the traditional contraction mapping principle used in model-free adaptive control. It is shown that the consensus can be achieved for both leaderless and leader-following cases if the communication topology is strongly connected. Finally, numerical simulations verifying the correctness of the theoretical results are given.

Optimal distributed time-varying formation control for second-order multiagent systems: LQR-based method

The optimal leaderless and leader-following time-varying formation (TVF) control problems for second-order multiagent systems (MASs) are investigated, where two optimal TVF control protocols are proposed to achieve the desired formations as well as minimize the comprehensive optimization function that contain the cooperative performance index and the control energy index. For leaderless case, the optimal formation control problem is reformulated as an infinite-time state regulator problem by employing the state space decomposition method, which is subject to specified constraints on energy and performance indices, and the analytic criterion for optimal TVF achievability is subsequently proposed. Then, the results of optimal leaderless TVF control are extended to the leader-following case with switching topologies, where the main challenge is changed to find the optimal controller rather than the optimal gain matrix, and the optimal value of the comprehensive index is accurately determined. Finally, two simulation cases are proposed to validate the effectiveness of the theoretical results, and comparisons with previous works are presented to expound the optimality of the proposed formation control method.

Event-triggered global consensus of second-order multi-agent systems with asymmetric input saturation

This paper addresses the event-triggered global consensus issue of second-order multi-agent systems (MASs) with asymmetric input saturation, where the zero saturation bounds are allowed. First, for the leaderless situation, we propose an event-triggered mechanism and give the criterion for realizing global consensus. Different from the traditional event-triggered strategy in an effort to exclude the Zeno behavior, a preset minimum triggering interval is introduced. That is, the control input will not be updated within this interval after the latest trigger time, and the event-triggered condition is activated after this interval. Moreover, the above results are extended to the leader–follower case. Finally, some numerical examples illustrate the effectiveness of the developed schemes.

Edge-based adaptive secure consensus for nonlinear multiagent systems with communication link attacks

Fully distributed secure consensus control of nonlinear multiagent systems under communication link attacks is achieved, where the design criteria are independent of the Laplacian matrix related to the communication topology and its corresponding eigenvalues. Firstly, this article proposes an edge-based fully distributed adaptive protocol for leaderless nonlinear multiagent systems with communication link attacks to achieve secure consensus control, where the interaction strengths between neighboring agents are adaptively adjusted on the foundation of the transmitted relative states to counteract influences of communication link attacks. Then, the problem of secure consensus control for leaderless nonlinear multiagent systems with communication link attacks is transformed into the stability of secure consensus error systems, and sufficient conditions for leaderless nonlinear multiagent systems achieving fully distributed secure consensus control are given. Furthermore, main results for leaderless nonlinear multiagent systems are extended to leader-following cases. Finally, theoretical results are verified by two numerical examples.

Distributed adaptive fault-tolerant consensus control for multi-agent systems with event-triggered communication

ABSTRACT In this paper, the distributed fault-tolerant consensus control problem is studied for multi-agent systems with event-triggered communication. Unknown time-varying actuator faults including partial loss of effectiveness and bias are taken into consideration. For the sake of fault compensations, a novel distributed event-triggered control law is put forward via the adaptive fault-tolerant technique in the leaderless network. Then, two event-triggered mechanisms are constructed, and a positive function introduced therein is greatly useful for scheduling the information transmission as well as excluding the Zeno behavior. Under the proposed protocol, the consensus errors are proved to converge to zero asymptotically in a scalable and fully distributed way. Furthermore, the results obtained in the leaderless network are extended to the leader-following case. Finally, simulation examples are conducted to confirm the validity of the presented results.

Distributed multiple-bipartite consensus in networked Lagrangian systems with cooperative–competitive interactions

In combination with the collective behavior evolution of bipartite consensus and cluster/group consensus, this paper proposes the notion of multiple-bipartite consensus in networked Lagrangian systems (NLSs), effectively integrating the above emergent collective behaviors in cooperative–competitive networks. The problems of leaderless multiple-bipartite consensus and leader-following multiple-bipartite tracking consensus are solved via deploying the designed distributed adaptive torque controllers for uncertain NLSs. Compared with the traditional bipartite consensus framework, antagonistic interactions can exist in the same subnetwork. By introducing an acyclic partition and adding the integral item in the distributed adaptive torque control protocols, the explicit expressions of the final states are eventually obtained in the leaderless case. Moreover, the leader-following case can be realized in finite time resorting to two predefined estimators embedded in the scheme. The effectiveness of two scenarios has been illustrated through numerical simulations with ten heterogeneous mechanical manipulators.

Consensus of multi-agent systems with both input amplitude and input rate constraints

In this paper, the consensus problem is considered for multi-agent systems with input constraint under directed graphs, including leaderless and leader-following cases. Different from existing related works, the distinct feature of this paper is that both the amplitude and rate of the agents’ input are ensured in the given ranges. For the leaderless case, the saturation control strategy is designed and employed for multi-agent systems consensus with the aid of a novel saturation function. For the leader-following case, the saturation-function-based distributed observer as well as the observer-based saturation controller are proposed to achieve consensus. Finally, simulation results show the effectiveness of the designed methods.

Finite-time consensus of nonlinear multi-agent systems via impulsive time window theory: a two-stage control strategy

This paper concentrates on the finite-time consensus problem faced by nonlinear multi-agent systems (MASs) via impulsive time window theory with a two-stage control (TSC) strategy. The TSC strategy divides the whole control period into two parts: a variable impulsive control stage and a finite-time consensus control stage. Different from general single-stage control, TSC can dynamically adjust the time periods of impulsive control and finite-time control according to practical application requirements. Variable impulsive control is also discussed in this paper. Compared with the sampling based on traditional fixed impulsive theory, impulsive sampling in the TSC strategy occurs randomly within an impulsive time window and provides much more flexibility. In addition, a switching topology scheme is introduced in this paper to strengthen the stability of MASs. Finally, two numerical simulation examples (one leaderless case and one leader-following case) are used for the theoretical analysis.

Observer-Based Consensus Control for Heterogeneous Multi-Agent Systems with Output Saturations

This paper studies the consensus problem for heterogeneous multi-agent systems with output saturations. We consider the agents to have different dynamics and assume that the agents are neutrally stable and that the communication graph is undirected. The goal of this paper is to achieve the consensus for leaderless and leader-following cases. To solve this problem, we propose the observer-based distributed consensus algorithms, which consists of three parts: the nonlinear observer, the reference generator, and the regulator. Then, we analyze the consensus based on the Lasalle’s Invariance Principle and the input-to-state stability. Finally, we provide numerical examples to demonstrate the validity of the proposed algorithms.

Synchronization control for networked mobile robot systems based on Udwadia–Kalaba approach

This paper addresses the problem of synchronization control for networked multi-mobile robot systems from the perspective of analytical mechanics. By reformulating the task requirement as a constrained motion problem, a unified synchronization algorithm for networked multi-mobile robot systems with or without leaders is proposed in combination with algebraic graph theory and the Udwadia–Kalaba approach. With the proposed algorithm, the networked mobile robot system can achieve synchronization from arbitrary initial conditions for the leaderless case and realize accurate trajectory tracking with explicitly given reference trajectories for the leader-following case. Numerical simulations of a networked wheeled mobile robot system are performed under different network structures and various trajectory requirements to show the performance of the proposed control algorithm.

Limited-Budget Consensus Design and Analysis for Multiagent Systems With Switching Topologies and Intermittent Communications

This paper investigates limited-budget consensus design and analysis problems of general high-order multiagent systems with intermittent communications and switching topologies. The main contribution of this paper is that the tradeoff design between the energy consumption and the consensus performance can be realized while achieving leaderless or leader-following consensus, under constraints of limited budgets and intermittent communications. Firstly, a new intermittent limited-budget consensus control protocol with a practical trade-off design index is proposed, where the total budget of the whole multiagent system is limited. Then, leaderless limited-budget consensus design and analysis criteria are derived, in which the matrix variables of linear matrix inequalities are determined according to the total budget and the practical trade-off design parameters. Meanwhile, an explicit formulation of the consensus function is derived to describe the consensus state trajectory of the whole system. Moreover, a new two-stage transformation strategy is utilized for leader-following cases, by which the dynamics decomposition of leaderless and leader-following cases can be converted into a unified framework, and sufficient conditions of the leader-following limited-budget consensus design and analysis are determined via those of the leaderless cases. Finally, numerical simulations are given to illustrate theoretical results.

Leaderless and leader-following consensus of heterogeneous second-order multi-agent systems on time scales: an asynchronous impulsive approach

ABSTRACT Second-order asynchronous consensus of heterogeneous multi-agent systems on time scales is researched in this article. Compared with traditional continuous or discrete systems, this paper considers the dynamic equation on time scales. Heterogeneous systems composed of nonlinear and linear dynamic behaviour are put forward, and the dynamic behaviour of each agent is distinct from each other. Furthermore, we propose two asynchronous impulsive control schemes, which do not require the impulse to occur at the same time instant for each agent. Based on stability theorem and time scale theory, two criteria are put forward on time scales to solve leaderless and leader-following consensus. Especially, for the leader-following case, a pinning control strategy is introduced. The number of pinning impulsive nodes is different at disparate impulsive instants and the minimum proportion of pinned nodes can be derived. At last, two simulation results indicate the validity of theoretical analysis.

Intermittent Time-Varying Formation Control for High-Order Networked Agents Subject to Discontinuous Communications

This paper investigates the leaderless and leader-follower time-varying formation design and analysis problems for a group of networked agents subject to discontinuous communications. Firstly, a leaderless time-varying formation control protocol is proposed via the intermittent control strategy, where the control input of each agent is constructed by the distributed local state information and formation instructions in the communication time unit, but it is zero in the noncommunication time unit. Then, an explicit formulation of the formation center function is determined to describe the formation movement trajectory of the whole networked agents. Leaderless time-varying formation design and analysis with discontinuous communications are given in the form of linear matrix inequalities. Moreover, the main results of the leaderless cases are extended to the leader-follower cases. Finally, two numerical examples are provided to illustrate the theoretical results of leaderless and leader-follower cases, respectively.

Quantised scaled consensus of linear multiagent systems on faulty networks

In this paper, the practical mean-square scaled-consensus problem of multiagent systems is studied. Higher-order general linear dynamics is investigated, where all agents are subject to faults or denial of service attacks (DoS). The considered network comprises agents taking quantised states under undirected communication channels. Different from the existing works, no strict conditions have been imposed on the eigenvalues of the agents' state matrix. First, we propose a distributed scaled-consensus protocol that utilises a probabilistic quantisation algorithm. Second, scaled-disagreement analysis is provided via mean-square stability methodology. Finally, sufficient conditions in terms of linear matrix inequalities are presented in order to obtain scaled-consensus gain for both leaderless and leader–follower cases. The presented theoretical results are examined through two simulation examples.

Distributed Time-Varying Output Formation Tracking Control for General Linear Multi-Agent Systems With Multiple Leaders and Relative Output-Feedback

In this paper, a unified distributed swarm intelligence algorithm is developed to study time-varying output formation (TVOF) for a general linear multi-agent system (MAS) with a directed network. New adaptive output-feedback formation protocols are proposed to achieve TVOF stabilization for leaderless directed networks and TVOF tracking for leader-follower networks. For the leaderless case, only agents’ outputs are required to achieve the desired time-varying formation. An adaptive observer-type formation protocol is constructed via relative outputs of neighboring agents. No global information of the directed network is used to determine the protocol. A distributed algorithm is developed to solve the TVOF stabilization problem after the observability decomposition. For the leader-follower case, only partial agents have knowledge of the leaders’ information. An adaptive formation tracking protocol is constructed using dynamic relative output-feedback for neighboring followers. Based on the distributed algorithm, it is proved that the TVOF tracking problem with multiple leaders can be solved in a fully distributed manner.

A Coordination Law for Multiple Air Vehicles in Distributed Communication Scenarios

This paper proposes a consensus-based guidance methodology for multiple air vehicles to arrive at the same spot cooperatively. First, based on the Lyapunov stability theory, a guidance law with only one control parameter is proposed, and the exact expression of total flight time can be obtained with a control parameter equal to one. Then, a two-step guidance scheme, which can achieve a finite-time consensus of the flight time, is built upon the Lyapunov-based guidance law. In the first step, on account of the information exchange between the air vehicles through an undirected and connected communication topology, a time-varying control parameter is designed to reduce the disparities of the flight time. After the consensus of the flight time, the control parameter will remain constant at one, and simultaneous arrival can be achieved. Besides, the guidance strategy is applied in a leader-follower case that one of the vehicles cannot receive information from the others and acts as the leader. The effectiveness of the proposed method is demonstrated with simulations.

Consensus control of higher‐order Lipschitz non‐linear multi‐agent systems based on backstepping method

The consensus problem of higher-order Lipschitz non-linear multi-agent systems is studied. For the leaderless case, by using the backstepping method, a distributed recursive linear control scheme is proposed. In the recursive control design, based on feedback domination method, the Lipschitz conditions of the unknown non-linearities are organically used in the virtual controller design. The proposed recursive controllers guarantee that the leaderless multi-agent systems reach global consensus asymptotically. For the leader-follower case, first, baseline distributed recursive controllers are designed via backstepping method and feedback domination technique. Then with the baseline recursive controllers, a kind of linear sliding-mode surface and the corresponding sliding-mode controllers are proposed for the consensus tracking error system. Under the proposed sliding-mode controllers, the leader-follower multi-agent systems reach global consensus asymptotically. Besides, simulations verify the validity of the proposed distributed control algorithms for both cases.

Distributed time-varying group formation control for generic linear systems with observer-based protocols

In this paper, the time-varying group formation control for linear multi-agent systems under directed communication topology is investigated from an observer viewpoint. Different from the existing works on the time-varying group formation, the groups herein could have a cyclic partition, which is more common in real applications than the topology with the acyclic groups. The leaderless time-varying group formation problem is studied first. An observer-based distributed protocol is presented for each agent, where the observer is used to estimate the unmeasurable state utilizing the output information. Then, to broaden the scope of applications, we further study the leader-following case, in which there exists a leader with nonzero and bounded input for each subgroup. To tackle this problem, we take the input of the leader as a disturbance, and develop the new forms of control protocols with nonlinear functions. Furthermore, for both cases, it is shown that under the formation feasible conditions, the desired time-varying group formation can be achieved if the strong enough intra-group coupling is selected and the corresponding digraph of each subgraph contains a directed spanning tree. Finally, two simulation examples are given.

Composite sliding‐mode consensus algorithms for higher‐order multi‐agent systems subject to disturbances

Consensus problems for both leaderless and leader-follower disturbed higher-order multi-agent systems are investigated in this study. Based on the combination of integral sliding-mode control and disturbance observer techniques, composite sliding-mode consensus protocols are proposed for leaderless and leader-follower disturbed multi-agent systems, respectively. First, for the leaderless case, composite sliding-mode consensus protocols are designed to make the agents achieve asymptotic consensus. Second, for the leader-follower case, finite-time composite sliding-mode consensus protocols are presented to make the followers achieve consensus with the leader in finite time. Then based on the consensus algorithms proposed in this study, a consensus control strategy is given to realise the velocity and altitude finite-time consensus for a class of leader-follower multi-hypersonic vehicle systems. Finally, the numerical simulations are conducted to validate the efficiency of the proposed consensus algorithms.

Consensus control of linear systems with optimal performance on directed topologies

This paper studies the consensus control of linear multi-agent systems with optimal performance index on directed communication topologies. The consensus control protocols relying on the relative information between the agent and its neighbours are presented, and both the leaderless and leader-following cases are investigated. The global optimization of performance index is achieved with the presented control protocols by solving the algebraic Riccati equation (ARE), and the ARE can be solved without knowing the global information of communication topologies. The numerical examples are finally reported to illustrate the efficiency of the proposed protocols.