Distributed Adaptive Consensus Disturbance Rejection for Multi-Agent Systems on Directed Graphs

This paper addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph, which however is global information. In this paper, based on only the agent dynamics and the relative states of neighboring agents, a distributed adaptive consensus protocol is designed to achieve leader-follower consensus for any communication graph containing a directed spanning tree with the leader as the root node. The proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed. Extensions to the case with multiple leaders are further studied.

This paper considers the consensus control problem of heterogeneous linear multiagent systems. A distributed proportional-integral (PI) protocol is presented to ensure consensus of heterogeneous linear multiagent systems with directed communication graphs. Sufficient conditions for the choice of control parameters are derived. For the case that the agents are subject to the external time-varying but bounded disturbances, the proposed distributed PI protocol can assure uniformly ultimate boundedness of the consensus error. The effectiveness of the results is illustrated both theoretically and numerically.

Robust finite-time containment control of general linear multi-agent systems under directed communication graphs

ABSTRACTThis paper addresses the distributed consensus protocol design problem for linear multi-agent systems with directed graphs and external unmatched disturbances. Novel distributed adaptive consensus protocols are proposed to achieve leader–follower consensus for any directed graph containing a directed spanning tree with the leader as the root node and leaderless consensus for strongly connected directed graphs. It is pointed out that the adaptive protocols involve undesirable parameter drift phenomenon when bounded external disturbances exist. By using the σ modification technique, distributed robust adaptive consensus protocols are designed to guarantee the ultimate boundedness of both the consensus error and the adaptive coupling weights in the presence of external disturbances. All the adaptive protocols in this paper are fully distributed, relying on only the agent dynamics and the relative states of neighbouring agents.

This paper investigates the consensus disturbance rejection problem for general linear multi-agent systems in the presence of matched disturbances under the directed communication topology. Firstly, based on the local output information among agents, the disturbance observer is proposed to estimate the disturbances and compensate for their influences on the multi-agent systems. Secondly, the fully distributed output feedback consensus protocol is designed to guarantee that all agents can reach an agreement value. Finally, a simulation example is presented to illustrate the effectiveness of the results.

This paper addresses the time-varying formation-containment (FC) problem for general linear multi-agent systems based on an observer viewpoint under the directed communication graph which contains a spanning tree. A new format of time-varying formation shapes with the properties of translation, scalability and rotation is proposed. Then the time-varying formation tracking problem where the real leader's input is unknown to all other agents is solved independently. After that, the time-varying FC problem where the challenge is how to deal with the formation-achieving agents' unknown nonzero inputs for containment-achieving agents, is firstly addressed. All the designed controllers, which need no eigenvalue information of the whole graph, are fully distributed and so can be applied to large-scale systems. The influence of communication graph structure to the control convergence rate is further analysed. The above theoretical results are verified by multiple nonholonomic vehicles in simulations.

This paper studies the adaptive consensus tracking problem for multi-agent systems modeled as high-order integrators with uncertain nonlinear dynamics under directed communication graphs. By parameterizing the unknown dynamics of the agents and the unknown input of the leader, two decentralized tracking control laws are designed using the state information and only the output information, respectively. With state information, globally uniformly ultimately bounded consensus tracking with arbitrarily small tracking errors can be achieved and when only output information is available, based on high-gain observers, semi-global result can be obtained. Numerical examples are provided to illustrate the effectiveness of the controllers.

This paper presents an event‐triggered distributed control protocol designed for scenarios involving Denial‐of‐Service (DoS) attacks within directed communication graphs. We address the consensus problem of uncertain systems by employing neural networks to approximate nonlinear components. Compared with traditional neural network observers, the proposed method incorporates damping terms to ensure the boundedness of neural network estimators. Initially, an auxiliary system was constructed to decouple the consensus problem under a directed communication graph framework. It is demonstrated that the uncertain nonlinear system can achieve consensus through the utilization of information exchanged among neighboring agents. Subsequently, to curtail the consumption of communication resources, we introduce an event‐triggered control protocol based on the aforementioned approach, incorporating an effective event‐triggering function. Building upon the proposed control protocol, we further develop a control strategy tailored for systems under DoS attacks. Furthermore, the event‐triggered mechanism without using global information in trigger condition not only curtails superfluous information exchange among agents but also precludes the occurrence of Zeno behavior (i.e., infinite triggering within a finite time interval). Finally, numerical simulations are carried out to validate the efficacy of the proposed control protocol.

In this paper, we introduce a fast row-stochastic decentralized algorithm, referred to as FRSD, to solve consensus optimization problems over directed communication graphs. The proposed algorithm only utilizes row-stochastic weights, leading to certain practical advantages in broadcast communication settings over those requiring column-stochastic weights. Under the assumption that each node-specific function is smooth and strongly convex, we show that the FRSD iterate sequence converges with a linear rate to the optimal consensus solution. In contrast to the existing methods for directed networks, FRSD enjoys linear convergence without employing a gradient tracking (GT) technique explicitly, rather it implements GT implicitly with the use of a novel momentum term, which leads to a significant reduction in communication and storage overhead for each node when FRSD is implemented for solving high-dimensional problems over small-to-medium scale networks. In the numerical tests, we compare FRSD with other state-of-the-art methods, which use row-stochastic and/or column-stochastic weights.

This paper deals with a cooperative control problem of a team of double-integrator agents moving along a set of given curves with a nominated formation. A projection-tracking design method is proposed for designing the path-following control and the formation protocol, which guarantee formation motion of the multi-agent system under a directed communication graph. Necessary and sufficient conditions of the control gains for solving the coordinated problem are obtained when the directed communication graph has a globally reachable node. Simulation results of formation motion among three agents demonstrate the effectiveness of the proposed approach.

By applying iterative learning control approach, the consensus is studied for multi‐agent systems (MASs) with one‐sided Lipschitz (OSL) nonlinearity. Firstly, the P‐type and D‐type learning schemes with initial state learning are introduced for such MASs. Then, utilizing the OSL and the quadratically inner‐bounded constraints, the convergence conditions of the consensus algorithms are presented and analyzed under a directed communication graph. We show that both algorithms, on a fixed finite‐time interval, can achieve perfect consensus tracking. Finally, the correctness of the obtained results is illustrated with simulation examples.

This paper focuses on the control of a team of agents designated either as leaders or followers and exchanging information over a directed communication network. The goal is to drive each follower to a target position that depends on its neighbors. To this purpose, we propose a decentralized control scheme based on sliding-mode techniques and study the position error propagation within the network using the notion of Input-to-State Stability (ISS). In particular, we derive sufficient conditions on the control parameters for guaranteeing that the error dynamics is ISS with respect to the leaders' velocities. Moreover, we show that, under suitable assumptions, the sliding-mode part of the control law is capable of steering the position errors to zero in finite time. The theoretical results are backed up by numerical simulations.

This study applies a design method called linear quadratic regulator to tackle the containment control problem of discrete-time linear multi-agent systems over directed graphs. By solving an algebraic Riccati equation, the study establishes both necessary and sufficient conditions required to achieve consensus. The researchers introduce an innovative distributed control law for information transmission between leaders and followers. This control law allows the following agents to move within the convex hull formed by the navigation agent, and effectively enables them to converge quickly and then follow again by introducing position error adjustment parameters. The effectiveness of the proposed algorithms is demonstrated through a simulation example.

In this article, we investigate the event-triggered consensus problem for general linear multiagent systems with bounded communication network delay. To reduce the communication frequency, we propose some dynamic periodic event-triggering strategies, under which an auxiliary dynamic variable and a weighting parameter are introduced for each agent to build its event-triggering condition. Then, a distributed adaptive consensus protocol, which includes a time-varying coupling weight for each edge, is designed based on the proposed event-triggering strategies. With the well-designed updating laws of dynamic variables, coupling weights and weighting parameters, we can theoretically guarantee the consensus of the concerned multiagent systems. Our event-triggering strategies do not require agents to continuously verify the event-triggering conditions or read their neighbors’ real-time state information. Moreover, Zeno behavior is inherently excluded as the interevent intervals are bounded from below by one period in the periodic event-triggering framework. Two numerical examples are provided to verify the effectiveness of the proposed event-triggered consensus protocols.

In this article, the containment control problem of multiagent systems (MASs) with active leaders under a directed communication graph is addressed. A novel pull-based event-triggered protocol combined with aperiodic sampled-data mechanism is first presented, where each agent merely updates controller at its own triggering instants. Under the proposed control protocols, the information is only exchanged and calculated at the aperiodic sampling instants, therefore, it can reduce communication congestion and save computing resources. Furthermore, the Zeno behavior is naturally excluded because the trigger instants are in the set of aperiodic sampled instants. By virtue of the algebraic graph theory and Lyapunov stability analysis, it is shown that the active leaders can reach their desired states predefined arbitrarily and all followers are driven to the convex hull formed by the leaders. Finally, an illustrative example is given to validate the theoretical results and emphasize the advantages of the proposed protocols.