| Multi-agent systems(MASs)exist widely in the fields of computers,artificial intelligence,bioecology,communication control,etc.,and provide effective solution ideas for dealing with large-scale complex practical problems.Consensus control generally means to design a distributed protocol such that all agents asymptotically reach an agreement on their states,is the basis of distributed computing.Due to the constraints of real communication conditions,the transmission of information is affected by various factors,especially the noise in the communication process inevitably affects the stability and convergence of the MASs.In order to attenuate the effect of stochastic noises,some scholars have applied certainty equivalence principle to deal with MASs affected by noises.It is worth noting that the protocols all require that the control input information of each agent was sent to its neighbors accurately.It is difficult or even impossible to realize in practical application.Motivated by the above discussions,we will investigate the consensus problem for the discrete-time MASs with communication noises.Without the control inputs of neighbors,we will construct a two-time-scale consensus protocol alternating estimation and control.we will give the stability analysis of the Kalman filter without the initial values of the system and the statistical information of the noises.Then,we will analyze the convergence property for the two-time-scale protocol.The main work of this paper is as follows.1.we investigate the consensus of the first-order MASs with random noises.A twotime-scale alternates between estimation and control is proposed.To select suitable parameters for the Kalman filtering based two-time-scale protocol,we analyze the stability of the Kalman-filter-based estimator without the initial values of the system and the statistical information of the noises.The asymptotic property of the algorithm is analyzed by analyzing the convergence of the explicit closed-loop solution,and the statistical property of the consensus value is given.Finally,a simulation example is presented to verify the correctness of the proposed results.Compared with the classical Kalman filtering based consensus protocol,we relax the conditions on the communication environment,without the assumption that the control input information of each agent was sent to its neighbors.2.We consider the distributed consensus problem of a linear multi-agent systems with random noises,extending the Kalman filtering-based two-time-scale protocol to the linear multi-agent systems.We design a estimator based on the Kalman filtering of linear systems when the control input information is unknown,and a suitable control gain matrix by combining the Riccati equation with the structure of the communication topology under the condition of a suitable network topology and the dynamic model of each agent.A two-time-scale algorithm with alternating estimation and control is used to deal with the problem of not having access to control input information from neighboring nodes.Based on the stability results of the Kalman filter-based estimator,the boundedness of the convergence error of the MASs is verified by theoretical analysis and simulation.Compared to first-order MASs,linear MAss are general and applicable to more complex practical situations.This paper provides solid theoretical support for the Kalman filter-based consensus control method for discrete-time first-order MASs,and provides ideas and preliminary theoretical results for the study of discrete-time linear MASs,addressing the effects of random noise and insufficient information in practical applications. |
