Consensus Of Stochastic Multi-agent Systems Research Articles

Consensus of stochastic multi-agent systems with time-delay and Markov jump

In this paper, the H ∞ consensus problem of stochastic nonlinear multi-agent systems with time-delay, Markov jump and ( x , u , v ) -dependent noises is studied. Firstly, the H ∞ consensus problem is transformed into a standard H ∞ control problem by model transformation. Then, a dynamic output feedback control protocol is constructed by solving a set of linear matrix inequalities to ensure that the closed-loop system achieves the mean square consensus and meets the specified H ∞ performance level. After that, both delay-independent and delay-dependent stochastic bounded real lemmas are established by taking advantage of the Lyapunov–Krasovskii function method and the generalised It o ^ formula. Finally, we illustrate the validity of the developed method with numerical simulations.

Adaptive Finite-Time Consensus for Stochastic Multiagent Systems With Uncertain Actuator Faults

This paper aims to develop fully distributed adaptive protocols and establish the finite-time consensus criteria for nonlinear stochastic multi-agent systems that are subjected to serious multiple uncertainties not only in the agents' states and inherent nonlinearities but also in their actuators. Firstly, we propose a new continuous fully distributed consensus protocol for leaderless stochastic multi-agent systems by leveraging the adaptive technology, enabling the agents to achieve the finite-time consensus in probability efficiently. Secondly, we develop an adaptive protocol for leader-following multi-agent systems, and remarkably our protocol contains only one dynamic gain, which is adequate to resist serious multiple uncertainties and to ensure the realization of finite-time consensus in probability. Finally, we provide numerical simulations to verify the effectiveness of our protocols.

The mean‐square consensus of stochastic multi‐agent systems under denial‐of‐service and deception attacks via event‐triggered impulsive control

AbstractThe problem of event‐triggered impulsive control (ETIC) for stochastic multi‐agent systems (SMASs) under stochastic cyber attacks is investigated. In a stochastic cyber‐attack model, it is suggested to combine denial‐of‐service (DoS) and deception attacks using two independent Bernoulli random sequences. The event triggering mechanism (ETM) in the ETIC system creates the impulsive control time sequences. It is suggested to use ETMs with waiting times to stop Zeno behavior. Based on the proposed ETMs, sufficient criteria are given for the mean square consensus of SMASs. Two simulation examples are provided to validate our ETIC scheme.

Impulsive consensus of stochastic multi-agent systems under semi-Markovian switching topologies and application

This paper studied the impulsive consensus of stochastic multi-agent systems (MASs) under semi-Markovian switching topologies. The semi-Markovian process is employed to describe the random changes of communication topologies among agents. Applying the impulsive control method, the communication among agents is only needed at impulsive control instants. For the connectivity of communication topologies, we only require that partial communication topologies contain a directed spanning tree, which remove the restriction that every communication topology contains a directed spanning tree in existing works. Using the Lyapunov function method and the stationary distribution of semi-Markovian process, the impulsive control protocol (ICP) is designed to ensure the almost surely exponential consensus of stochastic MASs. As an application, the obtained result is used to solve the secure impulsive consensus of stochastic MASs under random cyber-attacks. We proposed a novel model of random cyber-attacks, in which adversaries can destroy communication links of agents and durations of attack-active interval and attack-free interval are random variables. A simulation example is given to show the effectiveness of obtained results.

Mean Square Average Consensus for Stochastic Multi-agent Systems via an Intermittent Event-triggered Strategy

Mean Square Average Consensus for Stochastic Multi-agent Systems via an Intermittent Event-triggered Strategy

Adaptive fixed-time consensus for stochastic multi-agent systems with uncertain actuator faults

In this paper, we study the adaptive fixed-time consensus control for stochastic multi-agent systems (SMASs) with uncertain actuator faults. Firstly, a fully distributed adaptive consensus protocol and an adaptive fault-tolerant consensus protocol are proposed, respectively, to ensure that the fixed-time consensus of SMASs with actuator faults can be reached. Secondly, an adaptive fault-tolerant containment consensus protocol is further proposed for the SMASs by leveraging the signum function, and this protocol can effectively solve the containment consensus in the unbalanced communication network. Finally, some simulation examples are given to verify the effectiveness of our consensus protocols.

Time Cost for Consensus of Stochastic Multiagent Systems With Pinning Control

In this article, the estimation of time cost for stochastic consensus of second-order nonlinear multiagent systems (MASs) is investigated. Compared with previous studies, the effect of noise and nonlinear inherent dynamics of agents are considered. In order to achieve the finite/fixed-time stochastic consensus while minimizing energy consumption, the pinning protocols are designed, which only need to control a small fraction of agents. Sufficient conditions for the stochastic consensus are established by employing the stability theory of stochastic differential equations and the algebra graph theory. Finally, the proposed protocols are verified through numerical simulation on the consensus of unmanned aerial vehicles (UAVs) system.

Boundary Coupling for Consensus of Nonlinear Leaderless Stochastic Multi-Agent Systems Based on PDE-ODEs

This paper studies the leaderless consensus of the stochastic multi-agent systems based on partial differential equations–ordinary differential equations (PDE-ODEs). Compared with the traditional state coupling, the most significant difference between this paper is that the space state coupling is designed. Two boundary couplings are investigated in this article, respectively, collocated boundary measurement and distributed boundary measurement. Using the Lyapunov directed method, sufficient conditions for the stochastic multi-agent system to achieve consensus can be obtained. Finally, two simulation examples show the feasibility of the proposed spatial boundary couplings.

Fixed-time consensus for stochastic multi-agent systems with discontinuous dynamics via quantized control

In this study, the fixed-time consensus (FDTC) for stochastic multi-agent systems (MASs) with discontinuous inherent dynamics is investigated via quantized control. Firstly, an improved lemma for fixed-time (FDT) stability is derived and several more precise estimations for settling time (SLT) are gained by using certain special functions. Secondly, a more general MAS containing discontinuous inherent dynamics and stochastic perturbations is considered, which is closer to practical life. Thirdly, to overcome the limitation of communication, two kinds of quantized control protocols are designed. Besides, in the light of the graph theory, non-smooth analysis, fixed-time (FDT) stability and stochastic analysis theory, some sufficient conditions are put forward to achieve FDTC of MASs. Finally, the validity of the derived theoretical results is testified by two numerical examples.

Edge-based dynamic event-triggered mean square consensus control for stochastic multi-agent systems under weight-balanced digraph

This paper focuses on the problem of mean square consensus for stochastic multi-agent systems. A new asynchronous edge-based dynamic event-triggered control protocol based on directed edges is designed. Using this event-triggered control protocol can reduce the frequency of event-triggered, save communication resources and avoid Zeno behavior. Since events on different edges occur independently of each other, there is no need for clock synchronization among neighbors. Besides, we relax the constraints on the communication topology of multi-agent systems by limiting it only to a weight-balanced digraph containing a directed spanning tree. In addition, the stochastic multi-agent systems can reach mean square consensus exponentially. Finally, this paper illustrates the effectiveness of the proposed asynchronous edge-based dynamic event-triggered control protocol by a simulation example.

Event-triggered adaptive consensus for stochastic multi-agent systems with saturated input and partial state constraints

This paper is concerned with the consensus tracking problem of stochastic multi-agent systems with both output, partial state constraints, and input saturation via event-triggered strategy. To handle with the saturated control inputs, the saturation function is transformed into a linear form of the control input. By using radial basis function neural network to approximate the unknown nonlinear function, the unmeasurable states are acquired by an adaptive observer. To ensure that the constraints of system outputs and partial states are never violated, an appropriate time-varying barrier Lyapunov function is constructed. The control scheme is event-triggered in order to save communication resources. The proposed distributed controller can guarantee the boundedness of all system signals, the consensus tracking with a small bounded error, and the avoidance of the Zeno behavior by using backstepping techniques. The validity of the theoretical results is verified by computer simulation.

Event-triggered consensus control of continuous-time stochastic multi-agent systems

This paper addresses the event-triggered consensus of stochastic multi-agent systems (MASs), the main breakthroughs are the avoidance of infinitely fast execution and the stochastic stability analysis. Toward this, first, a novel event-triggered mechanism (ETM) based on relative information is proposed to reduce the control effects, and the enforced fixed positive lower bound of the inter-execution times in the ETM can effectively exclude the infinitely fast execution behavior. Moreover, the input-to-state stability (ISS) is analyzed and the execution error is delicately estimated so that the constant control on each inter-execution time possesses enough feedback capability to dominate the effect of execution error. Based on this, the desired consensus is achieved in the almost sure sense. Particularly, the involved stochastic convergence strategy, without using the well-known Lyapunov theorem, is hopeful to provide a potential pattern to achieve an event-triggered consensus for more general stochastic linear/nonlinear MASs. Finally, a simulation example is presented to illustrate the effectiveness of the proposed results.

Cluster-Delay Mean Square Consensus of Stochastic Multi-Agent Systems with Impulse Time Windows.

This paper investigates the cluster-delay mean square consensus problem of a class of first-order nonlinear stochastic multi-agent systems with impulse time windows. Specifically, on the one hand, we have applied a discrete control mechanism (i.e., impulsive control) into the system instead of a continuous one, which has the advantages of low control cost, high convergence speed; on the other hand, we considered the existence of impulse time windows when modeling the system, that is, a single impulse appears randomly within a time window rather than an ideal fixed position. In addition, this paper also considers the influence of stochastic disturbances caused by fluctuations in the external environment. Then, based on algebraic graph theory and Lyapunov stability theory, some sufficiency conditions that the system must meet to reach the consensus state are given. Finally, we designed a simulation example to verify the feasibility of the obtained results.

Event-triggered bounded consensus for stochastic multi-agent systems with communication delay

ABSTRACT This paper investigates a problem on event-triggered bounded consensus control for a stochastic multi-agent system with communication delay, process and measurement noises. First, according to Kalman filtering theory, the optimal state estimation of each agent is obtained and sent to its neighbour agents through the undirected network topology. Correspondingly, an event-triggered controller related to the communication delay is proposed to reduce update frequency of the controller effectively. Then, the feedback gain and triggering parameters are co-designed and solved through linear matrix inequality. Relational conclusions for bounded consensus in mean square are established for fixed and time-varying communication delays, respectively. Finally, the effectiveness of the presented results are illustrated through a simulation example.

Digital Implementation of Derivative-Dependent Control by Using Delays for Stochastic Multiagents

In this article, we study the digital implementation of derivative-dependent control for consensus of stochastic multiagent systems. The consensus controllers that depend on the output and its derivatives are approximated as delayed sampled-data controllers. First, we consider the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> th-order stochastic multiagent systems. Second, we consider PID control of the second-order stochastic multiagent systems. For the consensus analysis, we propose novel Lyapunov functionals to derive linear matrix inequalities that allow us to find an admissible sampling period. The efficiency of the presented approach is illustrated by numerical examples.

Stability of nonlinear stochastic Markov jump system with mode-dependent delays and applications

ABSTRACT The pth moment stability of stochastic Markov jump systems (SMJSs) with time-delays and polynomial growth was investigated in this paper. Both the involved time-delays and polynomial growth are mode dependent. By using the new property of the polynomial as well as the relation between the time-delay and the generator of the Markov-chain, sufficient pth moment stability criteria are proposed. Meanwhile, the robustness of the stable SMJSs is also considered, which reveals that how much perturbation the stable SMJSs can tolerate. As an application, the consensus of stochastic multi-agent systems with nonlinear dynamics is investigated. Finally, the effectiveness of our results is illustrated by examples.

Leader-Following Mean Square Consensus of Stochastic Multi-agent Systems via Periodically Intermittent Event-Triggered Control

This paper investigates the leader-following mean square consensus of stochastic multi-agent systems. Firstly, an intermittent event-triggered strategy along with triggering conditions has been presented. Next, a novel Lemma has been established to overcome the difficulty which stems from integrating intermittent strategy into event-triggered strategy. With aid of the established Lemma and some stochastic analysis techniques, two sufficient criteria on consensus of stochastic multi-agent systems via the proposed strategy have been derived. Finally, three numerical examples are presented to demonstrate the effectiveness of theoretical results.

Event-triggered finite-time consensus for stochastic multi-agent systems

This paper studies a consensus problem for a kind of stochastic multi-agent systems (SMAS). First, a reduced-order observer is designed to estimate unknown states in SMASs. Second, an event-triggered adaptive output feedback control method is presented. It can reduce the controller updates and communication burden. Moreover, the radial basis function neural networks are applied to approximate the unknown functions in systems. Finally, it is demonstrated that the proposed control scheme can achieve finite-time practical consensus for SMASs. Simulation results are provided to illustrate the effectiveness of the theoretical analysis.

Leader-Following Mean-Square Consensus of Stochastic Multiagent Systems With ROUs and RONs via Distributed Event-Triggered Impulsive Control.

Based on the distributed event-triggered impulsive mechanism, the leader-following mean-square consensus of stochastic multiagent systems with randomly occurring uncertainties and randomly occurring nonlinearities is investigated for the first time in this article. In order to make better use of the limited communication resources, we proposed some novel communication rules among agents and corresponding control protocol. Moreover, some new triggering functions are designed for different types of agents, which cannot only ensure that the Zeno behavior can be excluded but also make the upper bound of impulsive interval in the total time sequence satisfy a newly proposed constraint condition. When the expected value of the triggering function of the i th agent is non-negative within an event time interval, the impulsive control will be triggered. If the system achieves the consensus, the triggering events of all agents will not occur after some time. The original system is transformed into the delay system by using the input delay approach. Based on the Lyapunov stability theory, several sufficient delay-independent criteria for mean-square consensus are derived by a class of Halanay impulsive differential inequalities. Finally, the effectiveness of theoretical results is illustrated by numerical simulation examples.

Leader-following mean square consensus of stochastic multi-agent systems with ROUs and RONs under periodically variable impulse time windows

In order to bring the theoretical results into harmony or agreement with the reality, this paper copes with the leader-following mean square consensus issue for a class of nonlinear stochastic multi-agent systems with randomly occurring nonlinearities (RONs) and randomly occurring uncertainties (ROUs) under impulse time windows (ITWs). As a majorizing preconfigured mechanism of the windows, the configuration named periodically variable impulse time windows (PVITWs) is put forward. It not only ensures the periodic-based layout of impulse time window (ITW), but also allows the position and width of the window to be arbitrarily adjustable, so that the preset of ITW is more suitable for applications. Based on the Lyapunov stability theory and graph theory, the corresponding sufficient mean square consensus criteria are given. Finally, the feasibility of theoretical analysis is illustrated by numerical simulations.