Bipartite Consensus Tracking Research Articles

Quantized model-free adaptive iterative learning bipartite consensus tracking for unknown nonlinear multi-agent systems

This paper considers the data quantization problem for a class of unknown nonaffine nonlinear discrete-time multi-agent systems (MASs) under repetitive operations to achieve bipartite consensus tracking. Here, a quantized distributed model-free adaptive iterative learning bipartite consensus control (QDMFAILBC) approach is proposed based on the dynamic linearization technology, algebraic graph theory, and sector-bound methods. The proposed approach doesn’t require each agent’s dynamics knowledge and only uses the input/output data of MASs, where the data is coded by the logarithmic quantizer before being transmitted. Moreover, we consider both cooperative and competitive relationships among agents. We rigorously prove the stability of the proposed scheme and analyze the effects of data quantization. Meanwhile, we demonstrate that data quantization does not affect the stability of MASs, and bipartite consensus tracking errors can converge to zero with the processing of the proposed scheme, although the data quantization slows the convergence rate. Furthermore, the results are extended to switching topologies, and three simulation studies further validate the effectiveness of the designed method.

Sampled-data-based event-triggered secure bipartite tracking consensus of linear multi-agent systems under DoS attacks

This paper investigates secure bipartite consensus tracking of linear multi-agent systems under denial-of-service(DoS) attacks by using event-triggered control mechanism with data sampling. Both bipartite leader-following and containment tracking consensus are considered in this paper. The event-triggered control protocol using sampled-data information is designed to save limited resources. The communication channels are interrupted by intermittent DoS attacks. Sufficient conditions on the sampling periods, attack frequency and attack duration are obtained to ensure secure bipartite tracking consensus of the multi-agent systems. Finally, simulation example is provided to illustrate the effectiveness of the theoretical results.

Bipartite Consensus Tracking for Second-Order Multiagent Systems: A Time-Varying Function-Based Preset-Time Approach

This article is concerned with bipartite consensus tracking for second-order multiagent systems with signed directed graphs. A time-varying function-based preset-time approach is proposed to realize the convergence in predetermined time. First, a class of time-varying functions with generalized properties are presented. Second, two time-varying function-based auxiliaries and a corresponding manifold are constructed. Under a structurally balanced and strongly connected graph, a time-varying function-based controller considering the neighboring state is proposed to guarantee that the system trajectory is constrained on the manifold such that bipartite consensus tracking is achieved in preset-time. Third, for first-order multiagent systems, a preset-time controller is further developed with simplified design. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed controllers.

Distributed Bipartite Adaptive Event-Triggered Fault-Tolerant Consensus Tracking for Linear Multiagent Systems Under Actuator Faults.

This article considers the distributed bipartite adaptive event-triggered fault-tolerant consensus tracking issue for linear multiagent systems in the presence of actuator faults based on the output feedback control protocol. Both time-varying additive and multiplicative actuator faults are taken into account in the meantime. And the upper/lower bounds of actuator faults are not required to be known. First, the state observer is designed to settle the occurrence of unmeasurable system states. Two kinds of event-triggered mechanisms are then developed to schedule the interagent communication and controller updates. Next, with the developed event-triggered mechanisms, a novel observer-based bipartite adaptive control strategy is proposed such that the fault-tolerant control problem can be addressed. Compared with some related works on this topic, our control scheme can achieve the intermittent communication and intermittent controller updates, and the more general actuator faults and network topology are considered. It is proved that the exclusion of Zeno behavior can be realized. Finally, three illustrative examples are given to demonstrate the feasibility of the main theoretical findings.

H ∞ bipartite consensus of nonlinear multi-agent systems over a directed signed graph with a leader of non-zero input

This paper examines the bipartite tracking consensus for nonlinear multi-agents over a directed signed graph under bounded disturbances and a non-zero bounded input of the leader. For dealing with disturbances, the control theory has been adopted to develop a robust bipartite tracking consensus protocol. An additional switching control action is proposed to counteract the bounded matching input of the leader. The proposed control ensures the asymptotic convergence of the consensus error for known matching bounded input at the leader without disturbances, and an performance criterion from bounded disturbances to the consensus error has been provided. Contrary to the traditional consensus frameworks, our approach considers the nonlinear agents to resolve the bipartite consensus, disturbances for a robust distributed control, directed signed graphs, and bounded non-zero input at the leader for dealing with a realistic consensus scenario. Two simulation examples are provided for illustration.

Bipartite consensus tracking for antagonistic topologies with leader's unknown input

AbstractIn this paper, the bipartite consensus tracking problem of linear multiagent systems on leader‐follower signed directed graph is studied, where the leader's unknown input is taken into consideration. Based on only local relative information of neighboring agents, discontinuous distributed adaptive protocols are proposed, where nonlinear function is introduced for each agent to tackle leader's unknown input. To avoid tremors phenomenon, continuous distributed protocols are further presented to achieve practical bipartite consensus. Both the state feedback and output feedback cases are investigated. Different from existing literature showing bipartite consensus achievement with gauge transformation, this paper reveals a novel property of the signed Laplacian matrix, which plays a key role in simplifying the bipartite consensus demonstration. Two practical examples on synchronization of Chua's circuits are presented to illustrate the effectiveness of the designed protocols.

Bipartite consensus of multi-agent systems with reduced-order observer-based distributed control protocols

This paper considers the bipartite consensus problem for multi-agent systems, in which both bipartite leaderless consensus and bipartite tracking problems are investigated under signed digraph. Two distributed output feedback control laws are proposed based on reduced-order observer design, respectively, for solving the bipartite leaderless consensus and bipartite tracking consensus problems. Some sufficient conditions are obtained for achieving the bipartite consensus of the multi-agent systems, by using the algebraic Riccati equation design and Jordan decomposition technique. Finally, two simulation examples are presented to illustrate the effectiveness of the obtained theoretical results.

Semi-global bipartite consensus tracking of singular multi-agent systems with input saturation

This paper investigates the problem of bipartite consensus tracking for a class of linear singular multi-agent systems under a signed graph topology, where the control input of each agent is subject to saturation. By exploiting a parametric algebraic Riccati equation (ARE)-based low-gain feedback approach, a static state feedback control protocol and a dynamic observer-based output feedback control protocol are developed utilizing local information. It is shown that under the presented protocols, semi-global bipartite consensus tracking can be achieved if the underlying signed communication graph is structurally balanced and contains a spanning tree rooted at the leader. A numerical example is finally given to illustrate the effectiveness of the theoretical results.

Bipartite tracking consensus for asynchronous second‐order multiagent systems with event‐triggered mechanism

SummaryThis article is concerned with event‐triggered bipartite tracking consensus under an asynchronous sampling setting, where the event‐triggering condition for each agent is allowed to be intermittently examined at its own sampling instants. First, a novel distributed protocol based on independent sampling period is presented, with which the bipartite tracking consensus issue can be transformed into the convergence problem of the augmented error system. Then, with the help of tools from graph theory and matrix analysis, a sufficient condition on the bipartite tracking consensus is derived. By appropriately choosing control parameters, it is shown that the bipartite tracking consensus can be achieved under the proposed protocol for the graph that contains a directed tree and the subgraph among followers is structurally balanced. Finally, numerical simulations are provided to verify the theoretical results.

Finite-Time and Fixed-Time Bipartite Consensus Tracking of Multi-Agent Systems With Weighted Antagonistic Interactions

This paper is concerned with the problem of bipartite consensus tracking for multi-agent systems with both cooperative and antagonistic interactions. These interactions among vertices in a signed digraph are first investigated with the signs of the weighted products of associated paths in their augmented undirected graph. To improve the convergence rate, a finite-time protocol and a fixed-time protocol are developed to solve the bipartite consensus tracking problem with a finite-time and a settling time independent of any initial states, respectively. Moreover, an M-matrix based method is well proposed to estimate all parameters in the constructed Lyapunov function, therefore, the upper bounds of the settling times for finite-time and fixed-time cases can be analytically determined. Finally, numerical examples are provided to demonstrate the effectiveness of proposed methods.

Bipartite Consensus Control for a Swarm of Robots

Abstract This paper studies the bipartite consensus problem of a swarm of robots whose dynamics are formulated by Lagrangian equations. Two distributed bipartite consensus control protocols are proposed for a swarm of robots without a leader or with a virtual leader. For the nonleader case, the networked Lagrangian system can reach static bipartite consensus under the control protocol developed, and the final convergent states can be explicitly determined by the specific structure of the Laplacian matrix associated with the cooperative–competitive network topology. For the virtual leader case, all the followers can track the leader's state in a bipartite formation to realize bipartite tracking consensus. Finally, the simulation results are given to verify the theoretical results.

Bipartite tracking consensus of linear multi‐agent systems with a dynamic leader under signed digraph

This study is concerned with the bipartite tracking consensus problem for linear multi-agent system over signed digraph, in which the leader agent owns a bounded control input that is unavailable to the followers. Compared with existing related works, the communication topology under consideration is allowed to be directed. Two kinds of distributed control protocols are proposed based on the relative states of neighbouring agents. By applying the graph theory, Lyapunov theory and adaptive control, some sufficient conditions for the bipartite tracking consensus are obtained. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed design methodology.

Distributed Model-Free Bipartite Consensus Tracking for Unknown Heterogeneous Multi-Agent Systems with Switching Topology.

This paper proposes a distributed model-free adaptive bipartite consensus tracking (DMFABCT) scheme. The proposed scheme is independent of a precise mathematical model, but can achieve both bipartite time-invariant and time-varying trajectory tracking for unknown dynamic discrete-time heterogeneous multi-agent systems (MASs) with switching topology and coopetition networks. The main innovation of this algorithm is to estimate an equivalent dynamic linearization data model by the pseudo partial derivative (PPD) approach, where only the input–output (I/O) data of each agent is required, and the cooperative interactions among agents are investigated. The rigorous proof of the convergent property is given for DMFABCT, which reveals that the trajectories error can be reduced. Finally, three simulations results show that the novel DMFABCT scheme is effective and robust for unknown heterogeneous discrete-time MASs with switching topologies to complete bipartite consensus tracking tasks.

Distributed Control of Time-Varying Signed Networks: Theories and Applications.

Signed networks admitting antagonistic interactions among agents may polarize, cluster, or fluctuate in the presence of time-varying communication topologies. Whether and how signed networks can be stabilized regardless of their sign patterns is one of the fundamental problems in the network system control areas. To address this problem, this paper targets at presenting a self-appraisal mechanism in the protocol of each agent, for which a notion of diagonal dominance degree is proposed to represent the dominant role of agent's self-appraisal over external impacts from all other agents. Selection conditions on diagonal dominance degrees are explored such that signed networks in the presence of directed time-varying topologies can be ensured to achieve the uniform asymptotic stability despite any sign patterns. Further, the established stability results can be applied to achieve bipartite consensus tracking of time-varying signed networks and realize state-feedback stabilization of time-varying systems. Simulations are implemented to verify our uniform asymptotic stability results for directed time-varying signed networks.

Event-triggered Pinning Bipartite Tracking Consensus of the Multi-agent System Subject to Input Saturation

This paper focuses on the bipartite tracking consensus problem of the multi-agent system with cooperative-competitive interactions. In order to save resources, an event-triggered pinning scheme subjected to input saturation is designed. Suppose that the signed graph representing cooperative-competitive interactions is structurally balanced, and the initial states for the agents belong to the specified ellipsoid. By using Lyapunov theory and linear matrix inequality (LMI) techniques, some sufficient conditions are derived to ensure that the bipartite tracking consensus of the system under event-triggered pinning control can be achieved. Moreover, the bipartite tracking consensus of system with Lipschitz nonlinear dynamics is also investigated, and Zeno behavior can be excluded. Subsequently, numerical examples are provided to illustrate the effectiveness of the obtained results.

Adaptive neural finite-time bipartite consensus tracking of nonstrict feedback nonlinear coopetition multi-agent systems with input saturation

This paper concentrates on the adaptive neural finite-time bipartite consensus tracking of nonstrict feedback nonlinear coopetition multi-agent systems with input saturation. A novel consensus tracking method combined the adaptive neural control with the finite-time command filtered backstepping is proposed. During each backstepping process, the Radical Basis Function Neural Network (RBF NN) is used to approximate the unknown nonlinear dynamics and the finite-time sliding mode differentiator (FTSMD) is used to obtain intermediate signals and their derivative. Moreover, the filtering errors are eliminated by using error compensation signals. By using the finite-time Lyapunov stability theory, it can be proved that the bipartite consensus tracking errors can converge to a sufficient small region of the origin in finite-time and all signals in the closed-loop systems are bounded in finite-time although there exists the input saturation. The effectiveness of the proposed method is shown by simulation results.

Distributed bipartite tracking consensus of nonlinear multi-agent systems with quantized communication

This paper mainly tends to address distributed bipartite tracking consensus problem for nonlinear multi-agent systems subject to logarithmic quantization. Based on appropriate quantized criterion, a distributed protocol with static coupling gain is developed. By employing Lyapunov technique and other mathematical analysis, the results show that distributed bipartite tracking consensus of multi-agent systems can be ensured with quantized relative state measurements, if some conditions are met. Additionally, compared with distributed protocol, the fully distributed protocol with dynamic coupling gain is further designed and analyzed via adaptive control, which is independent of any global information. Finally, simulations are exploited to support our theoretical analysis.

Bipartite Tracking Consensus of Generic Linear Agents With Discrete-Time Dynamics Over Cooperation-Competition Networks.

This article addresses the bipartite tracking consensus for a set of mobile autonomous agents over directed cooperation-competition networks. Here, cooperative and competitive interactions among the agents are described by positive and negative edges of the directed network topology, respectively. Both fixed and switching network topologies are considered. For the case with fixed network topology, the matrix product technique is utilized to derive the convergence result. For the case with switching network topologies, some key results related to the composition of binary relations are the main technical tools of analyzing the error system. In addition, the upper bound for the spectral radius of the system matrix is given to ensure the convergence of the system even if the single uncoupled system is strictly unstable. The applicability of the derived results is verified through two simulation experiments.

Data Driven Distributed Bipartite Consensus Tracking for Nonlinear Multiagent Systems via Iterative Learning Control

This article explores a data-driven distributed bipartite consensus tracking (DBCT) problem for discrete-time multi-agent systems (MASs) with coopetition networks under repeatable operations. To solve this problem, a time-varying linearization model along the iteration axis is first established by using the measurement input and output (I/O) data of agents. Then a data-driven distributed bipartite consensus iterative learning control (DBCILC) algorithm is proposed considering both fixed and switching topologies. Compared with existing bipartite consensus, the main characteristic is to construct the proposed control protocol without requiring any explicit or implicit information of MASs' mathematical model. The difference from existing iterative learning control (ILC) approaches is that both the cooperative interactions and antagonistic interactions, and time-varying switching topologies are considered. Furthermore, through rigorous theoretical analysis, the proposed DBCILC approach can guarantee the bipartite consensus reducing tracking errors in the limited iteration steps. Moreover, although not all agents can receive information from the virtual leader directly, the proposed distributed scheme can maintain the performance and reduce the costs of communication. The results of three examples further illustrate the correctness, effectiveness, and applicability of the proposed algorithm.

Distributed bipartite leader-following consensus of linear multi-agent systems with input time delay based on event-triggered transmission mechanism

This study focuses on the distributed bipartite consensus tracking for linear multi-agent systems with input time delay based upon event-triggered transmission mechanism. Both cooperative interaction and antagonistic interaction between neighbor agents are considered. A novel distributed bipartite control technique with event-triggered mechanism is raised to address this consensus issue. Different from the existing methods, our control technique does not need continuous communication among agents, is capable of addressing the case of input delay, and is applicable for the signed communication topology. Moreover, to avoid continuous monitoring of one’s own state, a self-triggered control strategy is further proposed. And when the system states cannot be measured, the observer-based bipartite control technique with event-triggered mechanism is thus put forward. Furthermore, the results in leader-following consensus are extended to containment control. It is proven that the proposed controllers fulfill the exclusion of Zeno behavior in two consensus problems. Finally, simulation experiments are used to test the practicability of the theoretical analysis.