Fixed-time Consensus For Nonlinear Multi-agent Systems With Discontinuous Dynamics

With the evolution of community and the improvement of the field of sciences and technology,collaborative group control is already a topical field of discussion,and multi-agent systems in collaborative group control are generating a considerable amount of awareness.A multi-agent system is a large-scale and multiple complicated system consisting of many autonomous or sub-autonomous subsystems connected by a communication network.As entities,natural or abstract,the amount of state of the agent will be affected by its own structure,control input,external disturbance and other factors.Considering that the research scope of multi-agent system is more and more broad,the paper studies the nonlinear first-order multiagent system with discontinuous dynamics by using auxiliary signals and the second-order multi-agent body systems utilizing the slip mode control and auxiliary signals to lead and follow the fixed time consensus.Firstly,the fixed-time consensus problem for a class of leader-following nonlinear multiagent systems with discontinuous dynamics and bounded disturbances is investigated by us.In order to solve the asymmetric directed topology diagram of the first-order system,an auxiliary signal is designed in the paper.The auxiliary signal is used to observe the state of the leader,and not transmitted in the communication channel,which can effectively reduce the calculation cost of the system.Based on the auxiliary signal,a discontinuous control protocol is designed in this paper,so that the first-order system can reach the consensus in a fixed time.Secondly,the document investigates the problem of achieving leader-following consistency in fixed time for second-order multi-agent systems containing nonlinearities.The second-order nonlinear system has discontinuous dynamics and external disturbances.Based on the designed auxiliary signal,the asymmetry problem of the directed graph of the second order system is solved.A sliding surface is then conceived,on which the control algorithm for the second-order system is devised in reverse.This protocol makes the second-order system more capable of reaching a fixed time consensus.Finally,it is shown using algebraic graph theory,non-smooth analysis,and sliding mode control that multi-agent systems containing directed graphs are capable of achieving fixed-time consensus in an initial state with arbitrary conditions,and that the time to convert is not contingent on the preliminary situation of the system.The reliability of the established protocol is illustrated by MATLAB emulation examples and comparison examples.