Bipartite Consensus Problem Research Articles

Output Bipartite Consensus for Second-Order Heterogeneous Uncertain Agents With State-Dependent Cooperation-Competition Interactions

For state-dependent cooperation-competition networks, the output bipartite consensus problem of heterogeneous uncertain agents is studied in this paper. In our framework, all the agents are described by second-order continuous-time nonlinear systems with different intrinsic dynamics, and the agents' uncertainties are characterized by unknown parameters in the intrinsic term. Then, the edge evolution rules with hysteresis coefficients are proposed via the classification strategy. To solve this problem, the distributed Lyapunov-based redesign method with the potential function term is first applied to such second-order heterogeneous uncertain multi-agent system. Through the three-step correlation design, the explicit expressions of the distributed controllers and the unknown parameter estimators are obtained, and it is shown that the state-dependent cooperation-competition network is always connected and maintains structural balance for all time if an initial structurally balanced and connected network topology is provided. On this basis, it follows from the total Lyapunov function that output bipartite consensus can be achieved asymptotically for the heterogeneous uncertain multi-agent system. Finally, a numerical simulation is provided to validate the structural balance of state-dependent networks and output bipartite consensus of heterogeneous uncertain agents.

Data-Driven Bipartite Consensus Tracking for Nonlinear Multiagent Systems With Prescribed Performance

In this article, a data-driven control strategy with prescribed performance is proposed to address the distributed bipartite consensus problem for unknown nonlinear multiagent systems (MASs) undersigned directed graphs. The dynamics of the agents in each topology are completely unknown and the desired trajectory information is only communicated to a subset of agents. First, the unknown nonlinear dynamic of each agent is transformed into an equivalent time-varying linearized model by utilizing the dynamic linearization method. Then, by considering the prescribed performance, a strictly increasing function is given to transform the constrained tracking error condition of the nonlinear MASs into an equivalent unconstrained error condition. Meanwhile, a new control protocol that only uses the input and output data of the agents is designed in the case of fixed or switched topologies. The proposed method can not only guarantee the bipartite consensus but also ensure the bipartite tracking error always converges to the prescribed region. Moreover, the designed control parameters can be adjusted appropriately to obtain better tracking performance. Finally, the convergence of bipartite consensus tracking error is guaranteed through rigorous theoretical analysis. The control scheme is further verified by two examples.

Active disturbance rejection‐based event‐triggered bipartite consensus control for nonaffine nonlinear multiagent systems

AbstractThis article investigates the active disturbance rejection‐based distributed event‐triggered bipartite consensus problem of nonaffine nonlinear multiagent systems with input saturation. To reduce the update frequency of the control signal, an event‐triggered mechanism is employed for each follower. Additionally, the active disturbance rejection technology, as a combination of the extended state observer and the tracking differentiator, is introduced to estimate the uncertainties of the system and address the problem of explosion of complexity in the backstepping design process. Compared with the traditional distributed bipartite consensus schemes using neural networks/fuzzy logic systems, the design complexity of the control law is reduced in the proposed scheme. Meanwhile, the tracking error is maintained within a predefined range via the funnel function. Finally, the stability of the system is proved under the Lyapunov stability analysis theory, and the effectiveness of the proposed strategy is verified via simulation examples.

Fully Distributed Pull-Based Event-Triggered Bipartite Fixed-Time Output Control of Heterogeneous Systems With an Active Leader.

This article deals with the fully distributed pull-based event-triggered bipartite fixed-time output consensus problem of heterogeneous linear multiagent systems (HLMASs) with an active leader, whose information can be merely accessed by a small fraction of followers. First, a class of fully distributed fixed-time observers is proposed for each follower to estimate the leader's system matrices, position, and control input under the signed communication topology, respectively. Then, based on the estimations of leader's system matrices, two adaptive algorithms are given to solve the regulator equations. Furthermore, the fully distributed fixed-time observer-based controllers associated with state feedback and output feedback are, respectively, proposed by employing the pull-based event-triggered mechanism (ETM) where each agent merely updates controller at its own triggering instants. Correspondingly, some sufficient criteria and the rigorous proofs are provided to ensure the implementation of bipartite output consensus in fixed time by using the Lyapunov stability theory and fixed-time stability theory. Moreover, the strictly positive lower bounds of intervals between two adjacent event-triggered times are derived, which means the Zeno behavior is ruled out. Finally, numerical simulations are performed to demonstrate the theoretical analysis.

Leaderless and Leader-Following Bipartite Consensus of Multiagent Systems With Sampled and Delayed Information.

This article proposes a hybrid systems approach to address the sampled-data leaderless and leader-following bipartite consensus problems of multiagent systems (MAS) with communication delays. First, distributed asynchronous sampled-data bipartite consensus protocols are proposed based on estimators. Then, by introducing appropriate intermediate variables and internal auxiliary variables, a unified hybrid model, consisting of flow dynamics and jump dynamics, is constructed to describe the closed-loop dynamics of both leaderless and leader-following MAS. Based on this model, the leaderless and leader-following bipartite consensus is equivalent to stability of a hybrid system, and Lyapunov-based stability results are then developed under hybrid systems framework. With the proposed method, explicit upper bounds of sampling periods and communication delays can be calculated. Finally, simulation examples are given to show the effectiveness.

Learning-Based Robust Bipartite Consensus Control for a Class of Multiagent Systems

This article studies the robust bipartite consensus problems for heterogeneous nonlinear nonaffine discrete-time multiagent systems (MASs) with fixed and switching topologies against data dropout and unknown disturbances. The controlled system’s virtual linear data model is first developed by employing the pseudopartial derivative technique, and a distributed combined measurement error function is established utilizing a signed graph theory. Then, an input gain compensation scheme is formulated to mitigate the effects of data dropout in both feedback and forward channels. Moreover, a data-driven learning-based robust bipartite consensus control (LRBCC) scheme based on a radial basis function neural network observer is proposed to estimate the unknown disturbance, using the online input/output data without requiring any information on the mathematical dynamics. The stability analysis of the proposed LRBCC approach is given. Finally, simulation and hardware testing results further demonstrate the designed method’s correctness and effectiveness.

Event-triggered bipartite consensus for nonlinear multi-agent systems under switching topologies: A time-varying gain method

In this paper, the event-triggered bipartite consensus problem is investigated for nonlinear multi-agent systems under switching topologies, only part of topologies contain directed spanning tree rooted at the leader. First, a dynamic bipartite compensator is constructed based on relative output information to provide control signal. Then, the time-varying gain method is adopted to propose a compensator-based event-triggered control protocol without Zeno behavior. Notably, the control protocol proposed achieves the bipartite consensus while reducing update frequency effectively. Moreover, a low conservative switching law is designed by the topology-dependent average dwell time strategy, which fully considers the differences among topologies and provides an independent average dwell time for each topology. As an extension, the nonlinear multi-agent systems with non-zero input of leader are further studied. Finally, a practical example is presented to demonstrate the feasibility of proposed control protocol.

Dynamic Event-Triggered Bipartite Output Consensus for Heterogeneous Multi-Agent Systems Under Signed Digraphs

In this brief, the bipartite output consensus (BOC) problem is studied by dynamic event-triggered control for heterogeneous multi-agent systems under signed digraphs. A novel fully distributed control protocol, containing an observer-based adaptive controller and a Zeno-free dynamic event-triggered mechanism (ETM), is provided to guarantee the asymptotic convergence of BOC errors. Notably, an internal dynamic variable is introduced in the ETM to prolong interevent time intervals, which further reduces consumption on transmission. In addition, it is worth pointing out that the provided protocol remains valid even if global information about signed digraphs is unavailable. Finally, a numerical example is taken to demonstrate the effectiveness of protocol.

Event-Triggered Asymmetric Bipartite Consensus Tracking for Nonlinear Multi-Agent Systems Based on Model-Free Adaptive Control

In this paper, an asymmetric bipartite consensus problem for the nonlinear multi-agent systems with cooperative and antagonistic interactions is studied under the event-triggered mechanism. For the agents described by a structurally balanced signed digraph, the asymmetric bipartite consensus objective is firstly defined, assigning the agents' output to different signs and module values. Considering with the completely unknown dynamics of the agents, a novel event-triggered model-free adaptive bipartite control protocol is designed based on the agents' triggered outputs and an equivalent compact form data model. By utilizing the Lyapunov analysis method, the threshold of the triggering condition is obtained. Subsequently, the asymptotic convergence of the tracking error is deduced and a sufficient condition is obtained based on the contraction mapping principle. Finally, the simulation example further demonstrates the effectiveness of the protocol.

Resilient Bipartite Consensus of Second-Order Multiagent Systems With Event-Triggered Communication

This article investigates the resilient bipartite consensus problem for continuous-time second-order multiagent systems in the presence of totally bounded malicious nodes under signed digraphs. An event-based resilient impulsive algorithm is employed, which cannot only mitigate the malicious nodes’ influence on the convergence of normal ones but also reduce the communication loads of agents. A necessary and sufficient condition related to the network topology is established for solving resilient bipartite consensus by using system transformation. A numerical simulation illustrates the effectiveness of the result.

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.

Stochastic Bipartite Consensus for Second-Order Multi-Agent Systems with Communication Noise and Antagonistic Information

In this paper, the bipartite consensus problem for second-order multi-agent systems with no leader, one leader and multiple leaders are investigated, where the information exchange is disturbed by measurement noise and antagonistic information. In order to attenuate the effect of communication noise, a time-varying gain c(t) is utilized and the stochastic approximation bipartite control protocol is proposed. It is given that the underlying protocol can solve the bipartite consensus problem for MASs with no leader/one leader/multiple leaders if the communication topology is strongly connected/has a spanning tree/has a spanning forest and the c(t) satisfies some mild condition. Meanwhile, for system with these three cases, a series of sufficient and necessary conditions are given. Especially, for the case with no leader, we obtain that the final state of agent is related with the initial position and initial velocity of each agent. For the case with one leader, we can get that the followers in one group can follow up the state of one leader, and the followers in another group tend to the opposite value. Additionally, for the case with multiple leaders, the containment control can be achieved where followers’ states in one group can converge to the quai-convex hull of leaders’ state and the ones in another group converge to the opposite convex hull. Finally, some numerical examples are given to support our new results.

Prescribed Performance Bipartite Consensus Control for Stochastic Nonlinear Multiagent Systems Under Event-Triggered Strategy.

In this article, the event-triggered bipartite consensus problem for stochastic nonlinear multiagent systems (MASs) with unknown dead-zone input under the prescribed performance is studied. To surmount the influence of the dead-zone input, the dead-zone model is transformed into a linear term and a disturbance term. Meanwhile, the prescribed tracking performance is realized by developing a speed function, which means that all tracking errors of MASs can converge to a predefined set in a given finite time. Moreover, the unknown nonlinear dynamics are approximated by fuzzy-logic systems. By combining the dynamic surface approach and the Lyapunov stability theory, we design an adaptive event-triggered control algorithm, such that the bipartite consensus problem of stochastic nonlinear MASs can be achieved, and all signals are semiglobally uniformly ultimately bounded in probability of the closed-loop systems. Finally, simulation examples are proposed to verify the feasibility of the algorithm.

Dynamic Leader-Following Bipartite Consensus of Multiple Uncertain Euler-Lagrange Systems Under Deception Attacks

In this brief, we mainly focus on the problem of leader-following (LF) bipartite consensus of multiple uncertain Euler-Lagrange systems (ELSs) under the influence of deception attacks. In contrast to existing results, we consider the exosystem with an auxiliary system in this brief, of which auxiliary system is dynamic, and both exosystem and auxiliary system can greatly enrich the reference signal and make our control scheme more flexible. However, due to the presence of deception attacks and the dynamic auxiliary system, we are confronted with the question of whether the system can properly achieve LF bipartite consensus despite the effects of both previously mentioned. To solve this problem, we define a so-called dynamic leader-following problem, where the tracking error is bounded and decays to zero in a dynamic manner. Finally, we design an adaptive distributed control law with a filter to remove the effect of deception attacks, which is combined with the existing results to solve the LF bipartite consensus problem.

Sampled‐data bipartite consensus control of nonlinear multi‐agent systems under denial‐of‐service attacks

SummaryThis article concentrates on the sampled‐data secure bipartite consensus problem for a class of nonlinear multiagent systems under intermittent denial‐of‐service attacks. The network communication channels are destroyed when the attacks occur, which causes all the system states to be unavailable. A novel distributed sampled‐data output feedback control protocol is developed by using the discontinuous sensor data. It is proved by the Lyapunov stability analysis that the considered nonlinear multiagent systems can achieve bipartite consensus exponentially in light of the designed control protocol. Then, the control algorithm is extended to systems with both state and input delay. Finally, a simulation example is presented to verify the effectiveness of the proposed control protocol.

Bipartite Consensus for Second-Order Multiagent Systems With Matrix-Weighted Signed Network

The second-order scalar-weighted consensus problem of multiagent systems has been well explored. However, in some practical antagonistic interaction networks, the interdependencies of multidimensional states of the agents must be described by matrix coupling. In order to highlight the influence of matrix coupling in the antagonistic interaction network, we investigate the second-order matrix-weighted bipartite consensus problem on undirected structurally balanced signed networks. Under the proposed bipartite consensus protocol, an algebraic condition is obtained for achieving second-order bipartite consensus via utilizing matrix-valued Gauge transformation and stability theory. Then, using the obtained criteria, a more direct algebraic graph condition is given for reaching bipartite consensus. Besides, because of the existence of negative (positive) semidefinite connections, the matrix-weighted network may have clustering phenomena, which means that matrix weights play a critical role in achieving consensus. An algebraic graph condition for admitting cluster bipartite consensus is provided. By designing matrix weights in practical scenarios, the required number of clusters can be obtained. Finally, the theoretical results are verified by five simulation examples.

Observer-Based Secure Event-Triggered Bipartite Consensus Control of Linear Multiagent Systems Subject to Denial-of-Service Attacks

This brief deals with the secure bipartite consensus problem for linear multi-agent systems (MASs) with Denial-of-Service (DoS) attacks subject to an observer-based dynamic event-triggered strategy (OBDES). Two event-triggered strategies involved with dynamic threshold are developed in controller and observer channels. Based on the connected structurally balanced signed graph, a new observer-based secure control protocol integrated of OBDES and relative output measurements of neighboring agents is proposed. The control strategy with dynamic coupling gains is fully distributed, which only requires to obtain the observer information from neighboring agents. Then, some criteria for secure bipartite consensus under DoS attacks are established. In addition, it is demonstrated that the Zeno behavior cannot not occur. At last, a numerical simulation is provided to verify the effectiveness of the proposed controller.

Robust bipartite tracking consensus of multi-agent systems via neural network combined with extended high-gain observer

In this paper, the robust bipartite tracking consensus problem for second-order multi-agent systems has been addressed in the presence of lumped disturbances and unknown velocity information. The leader’s dynamics are modeled by uncertain fractional-order equality based on the neural network (NN), and the followers can only obtain the position information of the leader under the signed networks. A novel robust bipartite tracking consensus control scheme is developed by combining the NN approximators, the continuous sliding mode control (SMC) strategy, and the improved extended high-gain observer (EHGO). The improved EHGO is used to compensate for and estimate each agent’s lumped disturbances and unknown velocity information in the controller design process. Moreover, NN is constructed to approximate the velocity and acceleration of the uncertain leader’s dynamics for generating the feedforward signal of controllers, and the adaptive update laws of estimation parameters are generated online based on the Lyapunov function. Finally, the effectiveness of the proposed control strategy is verified by some numerical simulations.

Adaptive event‐triggered bipartite consensus control for multi‐agent systems under signed digraphs

AbstractIn this paper, the bipartite consensus problem is addressed via adaptive event‐triggered control for multi‐agent systems in directed communication networks, where cooperative and competitive interactions are considered simultaneously. Under a strongly connected digraph, a novel fully distributed control protocol is first put forward, which consists of an adaptive controller and two event‐triggered mechanisms. The protocol is flexible and capable of achieving bipartite consensus without employing global information. Meanwhile, the Zeno behavior cannot occur by embedding functions in the event‐triggered mechanisms. Furthermore, a general digraph with a spanning tree is investigated, and it is shown that the proposed protocol is still effective in bipartite consensus including the leader–follower one as a special case. It is worth noting that there is no need for the protocol to continuously update the controller, nor to maintain the uninterrupted communication with neighbors. Finally, the validity of the presented results is confirmed by simulations.

Special issue on PID control in the information age: Theoretical advances and applications

Special issue on PID control in the information age: Theoretical advances and applications