Sufficient Conditions For Consensus Research Articles

A resilient consensus algorithm with inputs for the distributed monitoringof cyber-physical systems

Recent advancements in multi-agent systems (MASs) have led to the development of numerous algorithms for achieving specific objectives, such as consensus. However, security remains a major challenge in MAS consensus, particularly addressing the adversarial behavior of malicious agents. This paper explores the extension of Mean-Subsequence-Reduced (MSR) algorithm-type mechanisms for resilient dynamic consensus in the presence of input reference signals. We provide necessary and sufficient conditions for resilient dynamic consensus without relying on the presence of trusted agents. Additionally, we experimentally validate the proposed algorithm and related conditions over a small cyber–physical system used for temperature monitoring. Furthermore, we propose and experimentally validate a fault-detection and recovery algorithm to achieve a resilient dynamic average consensus of regular agents.

Consensus for discrete-time second-order multi-agent systems in the presence of noises and semi-Markovian switching topologies

In this paper, we focus on the control problem of mean square consensus for second-order continuous-time multi-agent systems with multiplicative noises under Markovian switching topologies. A new Lyapunov function based on the Laplacian matrix of the corresponding union topology of all possible topologies is designed for the stochastic stability analysis of consensus. Applying matrix theory and stochastic stability for stochastic differential equations, we can analyze the consensus problem of the considered systems with the designed Lyapunov function. In addition, we present the sufficient conditions of the mean square consensus exponentially for the considered stochastic systems. Finally, we give an simulation example to numerically validate our theoretical results.

Dynamic event-triggered mean-square consensus of positive multi-agent systems via impulsive control under false data injection attacks

This paper investigates the mean-square impulsive consensus problem of positive multi-agent systems (MASs) under stochastic sensor false data injection attacks (FDIA). False data injection attacks are mortal to a positive system since the system positivity could be destroyed with ease (by tampering with the sampled positive state value to a negative one, for instance). To deal with this issue, a data compensator is proposed which preprocesses deliberately distorted state values to reduce their adverse impacts on the positivity of the positive MASs. On the other hand, a novel sampled-data-based dynamic event-triggered mechanism (SDB-DETM) is tailored to generate impulsive control time sequences, save control costs, and promise a desired control performance. A maximum event-trigger time interval is introduced as a substitute for the assumption of the average time interval when considering the randomness of FDIA. Furthermore, the dynamics of the auxiliary dynamic variable are improved to adapt the novel SDB-DETM with mixed signals. A sufficient and necessary condition of the positivity of the positive MASs under FDIA is presented. The commonly used positive constraints on the error system are removed. By constructing a quadratic Lyapunov function, a sufficient condition of the mean-square consensus of the positive MASs is derived. Two numerical examples are provided to illustrate the effectiveness of theoretical results.

Asynchronous impulsive consensus of discrete-time nonlinear multi-agent systems with time-varying delays

This paper addresses the asynchronous impulsive consensus of discrete-time nonlinear multi-agent systems with time-varying delays. Moreover, leader-following relationship is considered for the presented multi-agent systems, in which cooperation and competition exist simultaneously. By using the linear matrix inequality (LMI) method and the stability theory for delayed discrete-time impulsive systems, a set of sufficient conditions for consensus are obtained to realize asynchronous exponential impulsive consensus with controllers acting at different time sequences for different agents. Mainly formulated by the topology matrices, impulsive intervals, and gain coefficients, these criteria are easily implemented and have lower energy consumption compared with traditional impulsive control methods. Finally, several numerical simulations are shown to display the effectiveness of the derived theoretical results.

Pinning Group Consensus of Multi-agent Systems Under DoS Attacks

In this paper, group consensus is investigated for a class of nonlinear multi-agent systems suffered from the DoS attacks. Firstly, a first-order nonlinear multi-agent system is constructed, which is divided into M subsystems and each subsystem has an unique leader. Then a protocol is proposed and a Lyapunov function candidate is chosen. By means of the stability theory, a sufficient criterion, which involves the duration of DoS attacks, coupling strength and control gain, is obtained for achieving group consensus in first-order system. That is, the nodes in each subsystem can track the leader of that group. Furthermore, the result is extended to nonlinear second-order multi-agent systems and the controller is also improved to obtain sufficient conditions for group consensus. Additionally, the lower bounds of the coupling strength and average interval of DoS attacks can be determined from the obtained sufficient conditions. Finally, several numerical simulations are presented to explain the effectiveness of the proposed controllers and the derived theoretical results.

Leader-Following Consensus of Discrete-Time Nonlinear Multi-Agent Systems with Asymmetric Saturation Impulsive Control

Impulsive control is an effective approach for coordinating multi-agent systems in practical environments due to its high robustness and low cost. However, impulsive control exhibits characteristics such as high amplitude and rapid variation, potentially presenting threats to the equipment. Additionally, multi-agent systems are constrained by input saturation due to limitations in physical controller structures and information-processing capabilities. These saturation constraints may be asymmetrical. Therefore, it is necessary to consider the saturation constraint when implementing impulsive control, as it can also mitigate the threats posed by the impulse to agents. This paper investigates the leader-following consensus for a class of discrete-time nonlinear multi-agent systems, proposing an asymmetric saturation impulsive control protocol to reduce the energy consumption and damage to the equipment. Regarding the handle of asymmetric saturation, an approach is proposed that eliminates the need for transformation from the asymmetric case to the symmetric case, which retains the saturation function and directly introduces the sector condition to deal with saturation nonlinearity. Furthermore, based on Lyapunov stability theory and matrix theory, sufficient conditions for leader-following consensus in discrete-time nonlinear multi-agent systems under asymmetric saturation impulsive control are established, and the admissible region of the system is estimated. Finally, numerical simulations are provided to verify the validity of the theoretical results.

Event-Triggered Semi-Global Output Consensus of Discrete-Time Multi-Agent Systems With Input Saturation and External Disturbances

In this brief, the event-triggered semi-global output consensus is investigated for discrete-time multi-agent systems subject to input saturation and external disturbances. Under the assumption that the dynamics of all nodes are identical, based on output regulation, a protocol view is proposed by using relative state information. On the basis of Lyapunov stability theory, sufficient conditions for output consensus are obtained. Finally, a simulation result is given to illustrate the theoretical findings.

Reachable set estimation and H∞$H_\infty$ performance for delayed fuzzy multi‐agent systems under false data injection attacks

AbstractAddressed in this paper is the reachable set estimation (RSE) problem for fuzzy‐model‐based leader‐follower multi‐agent systems with time‐varying delays and false data injection attacks. First, the aperiodic sampled‐data control is designed for the follower agents with randomly occurring false data injection attacks. Then, using the Kronecker product, the error system between the leader and the follower is obtained in a compact general form. Next, a novel Lyapunov‐Krasovskii functional is constructed with the knowledge of sampling patterns and time‐varying delays. In the framework of linear matrix inequalities, sufficient consensus conditions are determined from the performance index and Lyapunov theory to guarantee that its reachable set is enclosed by an ellipsoid in the existence of bounded perturbations. In the end, the Duffing Van der Pol oscillator and the single‐link robot arm models are employed to validate the derived theoretical results.

Group consensus for competitive multiagent systems with input saturation and intermittent communication using current and outdated states

This paper investigates group consensus control for first-order multi-agent systems (MASs) with input saturation and intermittent communication. A novel class of distributed group consensus protocols is designed by combining current and outdated states of agents, which differs from the standard one using only current states. Sufficient conditions for group consensus are derived for MASs without two conservative assumptions required by previous literature. The proposed protocol can accelerate the convergence speed of MASs by choosing appropriate outdated states. Several examples are provided to illustrate the effectiveness of our results.

Delay Robustness of Consensus Algorithms: Continuous-Time Theory

Consensus among autonomous agents is a key problem in multi-agent control. In this paper, we consider averaging consensus policies over time-varying graphs in presence of unknown but bounded communication delays. It is known that consensus is established (no matter how large the delays are) if the graph is periodically, or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">uniformly</i> quasi-strongly connected (UQSC). The UQSC condition is often believed to be the weakest sufficient condition under which consensus can be proved. We show that the UQSC condition can actually be substantially relaxed and replaced by a condition that we call <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">aperiodic</i> quasi-strong connectivity (AQSC), which, in some sense, proves to be very close to the necessary condition (the so-called integral connectivity). Under the assumption of reciprocity of interactions (e.g., for undirected or type-symmetric graphs), a necessary and sufficient condition for consensus in presence of bounded communication delays is established; the relevant results have been previously proved only in the undelayed case.

Leader-following identical consensus for Markov jump nonlinear multi-agent systems subjected to attacks with impulse

The issue of leader-following identical consensus for nonlinear Markov jump multiagent systems (NMJMASs) under deception attacks (DAs) or denial-of-service (DoS) attacks is investigated in this paper. The Bernoulli random variable is introduced to describe whether the controller is injected with false data, that is, whether the systems are subjected to DAs. A connectivity recovery mechanism is constructed to maintain the connection among multi-agents when the systems are subjected to DoS attack. The impulsive control strategy is adopted to ensure that the systems can normally work under DAs or DoS attacks. Based on graph theory, Lyapunov stability theory, and impulsive theory, using the Lyapunov direct method and stochastic analysis method, the sufficient conditions of identical consensus for Markov jump multi-agent systems (MJMASs) under DAs or DoS are obtained, respectively. Finally, the correctness of the results and the effectiveness of the method are verified by two numerical examples.

Game-Based Consensus of Hybrid Multiagent Systems.

This article considers consensus of first-order/second-order hybrid multiagent systems (MASs) based on game modeling. In the first-order hybrid MAS (HMAS), a subset of agents select the Nash equilibrium of a multiplayer game as their states at each game time and the others update their states with first-order continuous-time (C-T) dynamics. By graph theory and matrix theory, we establish sufficient and necessary conditions for consensus of the first-order HMAS with two proposed protocols. The second-order HMAS is composed of agents whose states are determined by the Nash equilibrium of a multiplayer game and agents whose states are governed by second-order C-T dynamics. Similarly, sufficient and necessary conditions are given for consensus of the second-order HMAS with two proposed protocols. Several numerical simulations are provided to verify the effectiveness of our theoretical results.

Exponential Consensus of Multiagent Systems Based on Nonlinear Parabolic PDEs via Intermittent Boundary Control

The exponential consensus issue is investigated for leader-following multiagent systems (MASs) based on nonlinear parabolic partial differential equations (PDEs) on a directed graph via intermittent boundary control (IBC) methods. On the one hand, when the system’s state is accessible, an IBC protocol is designed based on the transfer information generated by the agent’s communication with its neighbors and the information coupling at the boundary <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x= l$</tex-math> </inline-formula> , and the sufficient conditions for exponential consensus of leader-following MASs are obtained. On the other hand, when the system’s state is not available completely, the agent’s state is estimated by the proposed observer, and the observer’s coupling information and the boundary coupling information of the agent are adopted to design an IBC protocol to solve the leader-following consensus issue. Finally, two numerical simulations are supplied to account for the obtained theoretical 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.

A distributed predictive formation control strategy for cyber-physical multi-agent systems under communication constraints

This paper focuses on the formation control problem under communication constraints for leader-follower cyber-physical multi-agent systems (CPMASs). The introduction of a leader-follower structure motivates the design of a distributed predictive formation control (DPFC) protocol for CPMASs, which features active compensation for constraints in the network with the aim of achieving formation consensus and stability. The cost functions are designed separately for leader and followers, enabling the output coordination of the leader and followers under the consideration of the formation configuration. The necessary and sufficient condition for stability and consensus is derived through the detailed analysis of closed-loop CPMASs with DPFC scheme. The control performance of the designed DPFC scheme is validated by the presented numerical simulations, which is extended to a formation control experiment of three-degree-of-freedom air-bearing-simulator (ABS) systems.

Dynamic Event-Triggered Consensus Control for Markovian Switched Multi-Agent Systems: A Hybrid Neuroadaptive Method

This paper presents a solution to the consensus problem for a particular category of uncertain switched multi-agent systems (MASs). In these systems, the communication topologies between agents and the system dynamics are governed by a time-homogeneous Markovian chain in a stochastic manner. To address this issue, we propose a novel neuroadaptive distributed dynamic event-triggered control (DETC) strategy. By leveraging stochastic Lyapunov theory and matrix inequality methodology, we establish sufficient conditions for practical ultimate mean square consensus (UMSBC) of MASs using a combination of neural networks (NNs) adaptive control strategy and DETC method. Our approach employs a distributed adaptive NNs DETC mechanism in MASs with unknown nonlinear dynamics and upgrades it at the moment of event sampling in an aperiodic manner, resulting in significant savings in computation and resources. We also exclude the Zeno phenomenon. Finally, we provide numerical examples to demonstrate the feasibility of our proposed approach, which outperforms existing approaches.

Periodic event‐triggered consensus based on triggered communication states for multi‐agent systems with packet losses

AbstractIn this paper, periodic event‐triggered leaderless and leader‐following consensus problems are studied for linear multi‐agent systems with deterministic packet losses under the generic directed communication topology. Specially, an event‐triggered mechanism is proposed, which only needs to communicate the event‐triggered states of the agent and verify the event‐triggered condition at the periodic sampling instants. A switched system with stable and unstable subsystems is used to describe packet dropouts in a deterministic way. The incidence matrix of a directed spanning tree in the directed communication topology is utilized to construct a linear transformation so that the consensus problems are equivalently transformed into the asymptotic stability problems of reduced‐order systems. Then, some sufficient consensus conditions are derived and the consensus protocol gains are designed. Finally, simulation examples are given to show the effectiveness of the proposed results.

An output formation consensus control for leader–follower networked multi‐agent systems under communication constraints and switching topologies

AbstractIn this paper, the formation consensus problem for a class of leader–follower networked multi‐agent systems under communication constraints and switching topologies is investigated. A networked predictive control scheme is proposed to achieve stability and output formation consensus with the switching topology, capable of compensating for data loss and time delays in the network. By equating the whole closed‐loop networked multi‐agent system with the proposed control scheme to the corresponding switched system, the sufficient and necessary condition of output formation consensus and stability for agents is given. Finally, using three‐degree‐of‐freedom air‐bearing spacecraft simulators as the control objects, the proposed scheme is demonstrated to be able to actively compensate for the communication constraints through numerical simulations, and it is also verified to have a good control performance by further realizing the formation task of the simulators through practical experiments.

Consensus of interconnected systems via event‐triggered control with different cyber‐physical topologies

AbstractIn this paper, the consensus problem for a class of interconnected systems with different cyber‐physical topologies is investigated. A two‐layer control framework is proposed where two different connections exist among the systems in physical and cyber layers, respectively. The former directly reflects the physical coupling among systems, while the latter uses the states' information transferred by communication channels to generate control. The physical and cyber topologies are undirected and not required to be connected. An event‐triggered protocol based on cyber local sampled information is designed with no need to solve any matrix equation or inequality. Theoretical sufficient conditions for consensus are derived in terms of algebraic inequality and Zeno behavior is excluded. A novel expandable construction scheme is proposed to construct switching topologies for cyber layer. Numerical simulation and comparison show the effectiveness of the proposed control method and the advantage on saving communication network constructions.

Bipartite consensus for networked Euler–Lagrange systems with cooperative–competitive interactions and time delays

AbstractThis paper investigates the coordinated behaviour of the multiple Euler–Lagrange systems under diverse interactions with time delays. Specially, in the case of undirected interconnection, the proportional plus damping control strategy is proposed and the sufficient conditions of bipartite consensus are derived via energy function based approach. Subsequently, a velocity‐free controller is further developed by introducing a novel second‐order auxiliary system to each agent. In the case of directed network, by fully investigating the property of the Laplacian matrix associated with the cooperative–competitive interactions, a bipartite consensus controller is devised and the input–output property analysis of the system transfer function in frequency domain is presented. Simulation results are provided to demonstrate the effectiveness of the presented algorithms.