Finite-time consensus for stochastic multi-agent systems

In this note, we investigate the fixed time consensus in probability for stochastic multi-agent systems under undirected graph. First, a nonlinear consensus protocol with Gaussian white noise is given, and the concept of fixed-time consensus in probability is given. Second, we prove that multi-agent systems can achieve fixed-time consensus in probability under undirected topology by using graph theory, stochastic Lyapunov theory and probability theory. Finally, a simulation example is given to verify the effectiveness of the theory results.

This paper studies the finite-time consensus (FTC) of second-order multi-agent systems (MASs), where the event-triggered strategy is adopted. Firstly, a new protocol is designed to solve the FTC problem for the MASs under consideration. Then, by using Lyapunov theory and graph theory, the sufficient conditions are obtained to guarantee the FTC of the MASs. Meanwhile, a lower-bounded inter-event time is given to exclude the Zeno behavior. Finally, a numerical simulation is presented to demonstrated the effectiveness of the theoretical results.

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.

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.

Finite-time robust consensus of nonlinear disturbed multiagent systems via two-layer event-triggered control

The paper devotes to study fixed‐time stability of stochastic nonlinear systems and fixed‐time consensus of stochastic multi‐agent systems (SMASs). Firstly, a new fixed‐time stability theorem is established and a high‐precise estimation of settling time is provided. Secondly, as an application, the fixed‐time consensus problem of SMASs is discussed in virtue of the established theorem. A new class of fixed‐time nonlinear consensus protocols with stochastic perturbation is designed by employing the neighbour's information. Based on graph theory, matrix theory and fixed‐time stability theorem, we prove that fixed‐time consensus of SMASs is achieved under the designed protocol. Moreover, some sufficient conditions are proposed to guarantee fixed‐time consensus of SMAS. It is shown that the settling time is not only independent of the initial conditions, but also it has higher precise. In the end, three numerical examples are provided to illustrate correctness of our theoretical results.

In this paper, the optimization methods in designing a finite-time average consensus protocol for multi-agent systems or wireless sensor network are taken into account. As we all know, the purpose of the average consensus protocol is that all agents reach the final common value, which is the average of the initial values. In order to run a consensus protocol, there are 2 main steps: self-configuration step, and execution step. In the self-configuration step, the consensus protocol is designed and uploaded to each agent of the system so that the final average value is achieved in the minimal execution time. The proposed optimization method is based on learning and training methods applied for neural network.

Finite-time consensus of second-order leader-following multi-agent systems without velocity measurements

In this article, for second-order multiagent systems with uncertain disturbances, the finite-time leader-follower consensus problem has been investigated. First, by considering that the leader's states are only available to part of the followers, a distributed estimator is constructed to estimate the state tracking errors between the leader and each follower. Then, an estimator-based control scheme is proposed under the event-triggered strategy to achieve finite-time leader-follower consensus. Besides, the event-triggered intervals are with a positive lower bound such that the Zeno behavior can be avoided. Note that the system is discontinuous under the event-triggered mechanism; thus, a nonsmooth analysis is performed. Numerical simulations are presented to demonstrate the effectiveness of our theoretical results.

In this article, the adaptive finite-time consensus problem is discussed for uncertain nonlinear multiagent systems. In contrast with the correlative literature, the systems permit multiple uncertainties (not only in control coefficients but also in inherent nonlinearities), and typically the consensus protocol is pursued in a fully distributed fashion (independent from any global information of network topology). This essentially challenges the realization of the finite-time consensus. To overcome the challenge, a new continuous fully distributed protocol is proposed by combining adaptive techniques such that the finite-time consensus of the systems under investigation is achieved. Remarkably, a dynamic high gain, rather than multiple ones in the related literature, is adequate to resist two kinds of uncertainties and to guarantee the fully distributed fashion of the consensus protocol. Moreover, the adaptive finite-time consensus protocol is specified on the scenario of leader-following multiagent systems. Simulation results of three interaction topologies are acquired to illustrate the validity and the wider applicability of the proposed protocol.

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.

Cloud-based event-triggered leader-follower quasi-bipartite consensus of stochastic multi-agent systems under mixed attacks

With the development of swarm intelligence in last decades, consensus problem of multi-agent systems has been attracting much attention. To reveal the inherent mechanism of leader-following consensus in multi-agent systems with stochastic dynamics, PI control protocols are designed in this paper. Owing to the stochastic analysis techniques, algebraic graph theory, and constructing appropriate Lyapunov function, it is proved that the leader-following consensus of nonlinear stochastic dynamical multi-agent systems can be reached in mean square. Sufficient condition are deduced to select the PI control protocol parameters. Finally, the theoretical results are demonstrated through a simulation example.

The problem of finite-time couple-group consensus for fractional-order multi-agent systems with weakly connected topology is investigated in this paper through pinning control. A new error variable based on cooperative and competitive interactions among agents is introduced to transform the fractional-order multi-agent system into a first-order multi-agent system and a novel group consensus protocol is designed for the transformed system. By applying the Lyapunov approach and matrix theory, several sufficient conditions are obtained to ensure the achievement of finite-time couple-group consensus of the system. In addition, the settling time is upper bounded by a definite value, which is independent of the initial states. Finally, the correctness and validity of our findings are verified through some numerical simulations.

Global leader-following consensus in finite time for fractional-order multi-agent systems with discontinuous inherent dynamics subject to nonlinear growth