Multi-Agent Systems With Multiplicative Noise:a Two-Time-Scale Consensus Protocol

In recent years,with the rapid development of network technology and sensing technology,multi-agent systems has become a frontier hot topic in control science,and has been widely used in the fields of IoT sensor network adaption,multi-robot arm cooperative assembly,UAV formation,traffic control,production scheduling distribution,etc.In the real world,the process of transferring information between agent through networks is inevitably affected by factors such as environmental noise,and current research on the coherence problem of stochastic multi-agent systems mainly considers the white noise case.However,compared with white noise,multiplicative noise can better portray the time-variability,nonlinear distortion,energy decay,etc.of the real systems.Based on the above discussion,this paper considers the consistency problem of multiagent systems subject to multiplicative noise interference.Based on the optimal MMSE filtering theory,a two-time-scale consensus protocol with alternating estimation and control is proposed for first-order and linear multi-agent systems.The main work of this paper is as follows:1.Consensusability of first-order multi-agent systems disturbed by multiplicative noise is studied.The statistical characteristics of multiplicative noise are more complex.We first model and propose a two-time-scale consensus protocol based on the optimal minimum mean square error(MMSE)filtering theory.On a small time scale,the control input is zero,and a state estimator is designed based on the optimal MMSE filtering theory.The agent estimates the state of itself and neighboring nodes based on this;Design a two-time-scale consensus protocol based on state estimation values and deterministic equivalence criteria on a large time scale for intelligent agents to update their own states.In addition,the relationship between state estimation error and system consistency error was analyzed,and the specific implementation of the algorithm was given.The effectiveness of the designed protocol was verified in simulation.Compared with the previous two-time-scale consensus protocol of Kalman filtering considering the influence of white noise,we selected an appropriate filtering algorithm for the multiplicative noise to achieve effective state estimation,which provides a basis for the design of consensus protocol.2.Consensusability of linear multi-agent systems disturbed by multiplicative noise is studied.The two-time-scale consensus protocol based on optimal MMSE filtering theory is extended to the case of linear multi-agent system.Design appropriate control gains considering the dynamic characteristics and communication topology of the intelligent agent.The boundedness of the system consistency error is analyzed,and the specific implementation of the algorithm is given.The effectiveness of the designed protocol is verified in the simulation.Compared with first-order multi-agent system,the dynamic model of linear multi-agent system is general,and its application scenarios are broader.In this paper,we consider the multi-agent systems consistency problem disturbed by multiplicative noise,and design a two-time-scale consensus protocol with alternating estimation and control when the agent cannot accurately observe the state of its own neighbor nodes and cannot obtain the control input information of the neighbor nodes,and verify the effectiveness,which provides a solution to the multi-agent systems consistency problem disturbed by multiplicative noise in the fields of petroleum seismic exploration,underwater target detection,space target tracking,etc.