Leader-following consensus for multi-agent systems with actuator faults via adaptive event-triggered control

In this paper, the leader-following consensus problem is investigated by event-triggered control for multi-agent systems subject to time-varying actuator faults. Firstly, for a case of the leader without control input, a distributed event-triggered fault-tolerant protocol is proposed with the help of adaptive gains. Secondly, the proposed protocol is developed by an auxiliary nonlinear function to compensate the effect of the leader’s unknown bounded input. It is shown that under the both obtained protocols the tracking errors converge to an adjustable neighborhood around the origin, meanwhile the Zeno behavior is avoided. Moreover, the protocols are fully distributed in sense that any global information associated with the network is no longer utilized. Finally, numerical examples are presented to show the validity of the obtained protocols.     

Leader-following consensus control of multiple nonholomomic mobile robots: An iterative learning adaptive control scheme

In this paper, the distributed iterative learning control for nonholonomic mobile robots with a time-varying reference is investigated, in which the mobile robots are with parametric uncertainties and are not fully actuated. Besides, the control gains of mobile robots are unknown. The leader is with a time-varying reference trajectory, and there is no need to assume that the time-varying reference is linearly parameterized by a set of known functions. A distributed control scheme is designed for each mobile robot based on a set of local compensatory filters designed by its neighborhood information. Stability analysis is established through a set of composite energy function. The uniform convergence of the consensus errors can be guaranteed. An example is given to show that our designed control law is effective.     

Interventional bipartite consensus on coopetition networks with unknown dynamics

In this paper, an interventional bipartite consensus problem is considered for a high-order multi-agent system with unknown disturbance dynamics. The interactions among the agents are cooperative and competitive simultaneously and thus the interaction network (just called coopetition network in sequel for simplicity) is conveniently modeled by a signed graph. When the coopetition network is structurally balanced, all the agents are split into two competitive subgroups. An exogenous system (called leader for simplicity) is introduced to intervene the two competitive subgroups such that they can reach a bipartite consensus. The unknown disturbance dynamics are assumed to have linear parametric models. With the help of the notation of a disagreement state variable, decentralized adaptive laws are proposed to estimate the unknown disturbances and a dynamic output-feedback consensus control is designed for each agent in a fully distributed fashion, respectively. The controller design guarantees that the state matrix of the closed-loop system can be an arbitrary predefined Hurwitz matrix. Under the assumption that the coopetition network is structurally balanced and the leader is a root of the spanning tree in an augmented graph, the bipartite consensus and the parameter estimation are analyzed by invoking a common Lyapunov function method when the coopetition network is time-varying according to a piecewise constant switching signal. Finally, simulation results are given to demonstrate the effectiveness of the proposed control strategy.     

Distributed observer-based consensus tracking for nonlinear MASs with nonuniform input delays and disturbances

In this paper, we investigate the consensus tracking problem of nonlinear MASs with nonuniform time-varying input delays and external disturbances. For each follower, the composited disturbance observer and the state observer are employed to estimate bounded composited disturbances and unmeasured states, and a distributed observer based on output-feedback is proposed to approximate the leader’s states approachably. Sequentially, the consensus tracking control is converted into a stability control problem for the nonlinear MASs with nonuniform time-varying input delays. Subsequently, a distributed controller based on the truncated prediction approach is presented, which only depends on the boundary value of time-varying input delays. The distributed controller can render each follower synchronically stable via the Lyapunov stability theory. Finally, a group of single-link manipulators is used as an example to verify the effectiveness of the theoretical results.     

Distributed control for output-constrained nonlinear multi-agent systems with completely unknown non-identical control directions

This paper studies the consensus problem for a class of nonlinear multi-agent systems with asymmetric time-varying output constraints and completely unknown non-identical control directions. Firstly, in order to deal with the problem of asymmetric time-varying output constraints, the original output-constrained multi-agent systems are transformed into new unconstrained multi-agent systems by constructing the state transformation for each agent. Secondly, the emergence of multiple Nussbaum-type function terms is avoided by introducing novel sliding-mode-esque auxiliary variables and consensus estimate variables, which allows the control directions to be completely unknown non-identical. Thirdly, a novel control strategy is proposed by combining novel variables with state transformation method for the first time, which makes the design of distributed consensus protocol more concise. Through Lyapunov stability analysis, the proposed distributed protocol ensures that the output constraints are never violated and the consensus can be achieved asymptotically. Finally, a practical simulation example is given to demonstrate the effectiveness of the proposed distributed consensus protocol.     

Bipartite time-varying formation group containment control for multi-agent systems based on multi-layer network and semi-signed directed graph

The bipartite time-varying formation group containment tracking control problem of multi-agent systems with unknown input leader on semi-signed digraph is studied. In this paper, the multi-agent system is divided into three layers: the leader layer with unknown input, the formation layer with cooperative-competitive relationship, and the containment layer without competitive relationship. First, the formation members in formation layer track the state of the leader in the leader layer, to achieve bipartite time-varying formation and form two convex hull. Then, by assuming two subgroups of the containment layer exist a well-informed individual (which can receive corresponding convex hull of all the formation members of communication), respectively, the followers of the two subgroups can not only converge to respectively two convex hulls formed by formation layer, also can make the followers of the same subgroup converge to a common value, this provides a prerequisite for the formation control of the followers in the containment layer. Next, different control protocols are designed for formation layer and containment layer respectively based on neighbor information, and Lyapunov function is constructed to provide stability proof for the realization of the problem. Finally, several simulation results are given to verify the validity of the theory.     

Distributed consensus control of periodically time-varying multi-agent systems using neural networks and fourier series expansion

This paper studies the consensus of nonlinear multi-agent systems with periodic disturbances and uncertain dynamics based on matrix theory, adaptive control, neural networks and fourier series expansion. Firstly, fourier series expansion and neural networks are used to describe the unknown periodic time-varying parameter and uncertain nonlinear dynamic, respectively. Secondly, based on adaptive control technology and reparameterization method, two new fully distributed control protocols are designed based on symbolic function and smooth hyperbolic tangent function, respectively, so that all agents can reach asymptotic consensus. Thirdly, a new positive integral bounded function is introduced to compensate for the approximation error caused by the smooth hyperbolic tangent function instead of the symbolic function, so that all network nodes achieve the same consensus effect. Finally, a simulation example is given to verify the effectiveness of the two algorithms and to illustrate their advantages and disadvantages.     

Practical time-varying output formation tracking for high-order multi-agent systems with collision avoidance,obstacle dodging and connectivity maintenance

Practical time-varying output formation tracking problems with collision avoidance, obstacle dodging and connectivity maintenance for high-order multi-agent systems are investigated, and the practical time-varying output formation tracking error is controlled within an arbitrarily small bound. The outputs of followers are designed to track the output of the leader with unknown control input while retaining the predefined time-varying formation. Uncertainties are considered in the dynamics of the followers and the leader. Firstly, distributed extended state observers are developed to estimate the uncertainties and the leader’s unknown control input. A strategy of obstacle dodging is given by designing an ideal secure position for the followers which are in the threatened area of the obstacles. By constructing collision avoidance, obstacle dodging and connectivity maintenance artificial potential functions, corresponding negative gradient terms are calculated to achieve the safety guarantee. Secondly, a practical time-varying output formation tracking protocol is proposed by using distributed extended state observers and the negative gradient terms. Additionally, an approach is presented to determine the gain parameters in the protocol. The stability of the closed-loop multi-agent system with the protocol is analyzed by using Lyapunov stability theory. Finally, a simulation experiment is provided to illustrate the effectiveness of the obtained methods.     

Distributed state estimator-based consensus tracking of multi-agent systems with exogenous disturbance

The consensus tacking problem for multi-agent systems with a leader of none control input and unknown control input is studied in this paper. By virtue of the relative state information of neighboring agents, state estimator and disturbance estimator are designed for each follower to estimate the system states and exogenous disturbance, respectively. Meanwhile, a novel control protocol based on two estimators is designed to make tracking error eventually converge to zero. Furthermore, the obtained results are further extended to the leader with unknown control input. A novel state estimator with adaptive time-varying gain is proposed such that consensus tracking condition is independent of the Laplacian matrix with regard to the communication topology. Finally, two examples are presented to verify the feasibility of the proposed control protocol.     

一类具有动态领导者和时滞的多主体系统的一致性

研究了一类具有动态领导者并且存在时变耦合时滞的多主体系统的一致性问题．在所考虑的模型中,领导者的速度不能被精确量测．为了跟踪这样一个领导者主体,将对每个跟随者主体构造分散式状态估计器以及设计基于邻居的控制器;同时,由于耦合时滞的存在,基于邻居的控制器和状态估计器均包含了时变时滞的作用．当多主体系统的耦合拓扑是固定的或切换的有向图时,跟随者与领导者之间的跟踪误差得到了估计．特别地,可以证明,当动态领导者的速度可以被精确量测时,每一个跟随者都能够跟踪上领导者．     

Adaptive observer-based event-triggered finite time formation tracking for multi-agent systems with a non-cooperative leader

The event-triggered time-varying formation tracking for a class of second-order multi-agent systems (MASs) subject to a non-cooperative leader is investigated in this paper. First, in the presence of the unknown input of the leader and external disturbances, a distributed observer with adaptive parameters is put forward for followers to estimate the velocity tracking error. Then, based on the estimated tracking error and an auxiliary variable, a finite time formation controller is further constructed, which is updated depending on a pre-designed event-triggered mechanism. As a result, the desired time-varying formation configuration can be realized in finite time with less communication resource consumption. It’s noted that the constructed formation strategy doesn’t rely on any global information and thus is fully distributed. The stability of the controlled multi-agent system is proved rigorously and it’s verified that event-triggered intervals are with a positive lower bound. At last, simulations are carried out to illustrate the effectiveness of the presented algorithm.     

Distributed control of cluster lag consensus for first-order multi-agent systems on QUAD vector fields

This paper addresses the problem of cluster lag consensus for first-order multi-agent systems which can be formulated as moving agents in a capacity-limited network. A distributed control protocol is developed based on local information, and the robustness of the protocol is analyzed by using tools of Frobenius norm, Lyapunov functional and matrix theory. It is shown that when the root agents of the clusters are influenced by the active leader and the intra-coupling among agents is stronger enough, the multi-agent system will reach cluster lag consensus. Moreover, cluster lag consensus for multi-agent systems with a time-varying communication topology and heterogeneous multi-agent systems with a directed topology are studied. Finally, the effectiveness of the proposed protocol is demonstrated by some numerical simulations.     

Leader-following successive lag consensus of nonlinear multi-agent systems via observer-based event-triggered control

This article investigates the leader-following successive lag consensus (SLC) for nonlinear multi-agent systems (NMASs) via the observer-based event-triggered control (OBETC), in which two scenarios including constant consensus delay and time-varying consensus delay are considered. Since the system states might not be directly available in actual scenes, the state estimation method is utilized for followers to track their full information. Based on the relative state, a class of distributed event-triggered control protocols is constructed, where the event-triggered strategy is introduced such that each follower can determine the broadcasting time to its neighbors. Obviously, these designed control protocols considerably lessen the expense over communication networks and the frequency of protocol updates. Furthermore, with the aid of the Lyapunov function method, a series of sufficient conditions for guaranteeing the leader-following SLC of NMASs is obtained. Meanwhile, it is proved that no Zeno behavior is exhibited. Finally, several numerical examples are given to illustrate the validity of our theoretical results.     

A continuous-time consensus algorithm using neurodynamic system for distributed time-varying optimization with inequality constraints

In this paper, a distributed time-varying convex optimization problem with inequality constraints is discussed based on neurodynamic system. The goal is to minimize the sum of agents’ local time-varying objective functions subject to some time-varying inequality constraints, each of which is known only to an individual agent. Here, the optimal solution is time-varying instead of constant. Under an undirected and connected graph, a distributed continuous-time consensus algorithm is designed by using neurodynamic system, signum functions and log-barrier penalty functions. The proposed algorithm can be understood through two parts: one part is used to reach consensus and the other is used to achieve gradient descent to track the optimal solution. Theoretical studies indicate that all agents will achieve consensus and the proposed algorithm can track the optimal solution of the time-varying convex problem. Two numerical examples are provided to validate the theoretical results.     

Time-varying formation tracking for high-order multi-agent systems with switching topologies and a leader of bounded unknown input

Time-varying formation tracking problems for high-order multi-agent systems with switching topologies are investigated. Different from the previous work, the states of the followers form a predefined time-varying formation while tracking the state of the leader with bounded unknown control input. Besides, the communication topology can be switching, and the dynamics of each agent can have nonlinearities. Firstly, a nonlinear time-varying formation tracking control protocol is presented which is constructed using only local neighboring information. Secondly, an algorithm with four steps is proposed to design the time-varying formation tracking protocol, where the time-varying formation tracking feasibility condition is introduced. Thirdly, by using the Lyapunov theory, the stability of the proposed algorithm is proven. It is proved that the high-order multi-agent system with switching topologies achieves the time-varying formation tracking if the feasibility condition holds and the dwell time is larger than a positive constant. Finally, a numerical example with six followers and one leader is given to demonstrate the effectiveness of the obtained results.     

Bipartite consensus of multi-agent systems with matched uncertainty via fully distributed edge-based event-triggered mechanism

The leader-following bipartite consensus of multi-agent systems (MASs) with matched uncertainty is investigated by using the fully distributed asynchronous edge-based event-triggered mechanism. Firstly, event-triggered mechanisms are constructed for each edge and the leader to decrease the consumption of system resources. The state feedback and output feedback control protocols are proposed, which do not depend on the global values of the communication graph. Secondly, sufficient conditions for the bipartite consensus of MASs are obtained by Lyapunov stability theory. Thirdly, the feasibility of the proposed event-triggered mechanisms is further verified by exclusion of Zeno phenomenon. Finally, the effectiveness of control protocol is illustrated by simulation.     

Distributed data driven control for multi-agent consensus with unknown system dynamics

This study investigates the consensus tracking problem for unknown multi-agent systems (MASs) with time-varying communication topology by using the methods of data-driven control and model predictive control. Under the proposed distributed iterative protocol, sufficient conditions for reducing tracking error are analyzed for both time invariable and time varying desired trajectories. The main feature of the proposed protocol is that the dynamics of the multi-agent systems are not required to be known and only local input-output data are utilized for each agent. Numerical simulations are presented to illustrate the effectiveness of the derived consensus conditions.     

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.     

Mean-square consensus of heterogeneous multi-agent systems with communication noises

This paper addresses the mean-square consensus problems of continuous-time heterogeneous multi-agent systems with communication noises. First, in order to attenuate the communication noises, time-varying consensus gains are applied in the consensus algorithm. Then, by using the tools of algebraic graph theory and stochastic analysis, sufficient conditions for the mean-square consensus are given for the cases with and without a leader. Finally, simulations are provided to demonstrate the effectiveness of the proposed algorithms.     

Consensus tracking control for nonlinear multiagent systems with asymmetric state constraints and input delays

In this paper, the consensus tracking problem is studied for a group of nonlinear heterogeneous multiagent systems with asymmetric state constraints and input delays. Different from the existing works, both input delays and asymmetric state constraints are assumed to be nonuniform and time-varying. By introducing a nonlinear mapping to handle the problem caused by state constraints, not only the feasibility condition is removed, but also the restriction on the constraint boundary functions is relaxed. The time-varying input delays are compensated by developing an auxiliary system. Furthermore, by utilizing the dynamic surface control method, neural network technology and the designed finite-time observer, the distributed adaptive control scheme is developed, which can achieve the synchronization between the followers’ output and the leader without the violation of full-state constraints. Finally, a numerical simulation is provided to verify the effectiveness of the proposed control protocol.