Research On Distributed Consensus Control Of Multi-Agent Systems With Discontinuous Dynamics

In recent years,the investigation on multi-agent systems(MASs)has drawn much interests in the fields of network science,system science,and engineering due to its extensive applications in intelligent microgrids,networked intelligent communication,and collaborative robots.As a class of typical collective behavior of MASs,the study of consensus has become one of the central issues in related works.Considering the limitations in practical engineering,constructing more generalizable models of MASs and designing effective distributed control strategies to achieve global consensus while ensuring dynamics performance has become a focus for numerous researchers.Hence,the distributed consensus control problems of MASs with discontinuous dynamics was studied in this thesis.The main contents and innovations are as follows:1).The finite-time consensus problem of a class of MASs with discontinuous nonlinear dynamics is studied.Firstly,the generalized Lipschitz condition is proposed via applying the Filippov set-valued map and the measurement selection theorem to linearize discontinuous dynamic function.Then a non-smooth distributed controller is designed based on neighbor state,meanwhile,the traditional saturation strategy is optimized by utilizing the Gaussian error function and the differential mean value theorem.Afterwards,the specific algorithm implementation is given.Sufficient conditions for the finite-time globally consensus on the discontinuous MASs and the settling time are obtained through the Lyapunov stability theorem,the Lie derivative method and the finite-time stability theorem.Finally,the validity and feasibility of the main theories is demonstrated by numerical simulation.2).The exponential consensus issue of a type of discontinuous MASs with hybrid self-delays is investigated due to the existence of channel congestion and transmission limitations.A class of distributed control protocol with time-varying control gain based on state feedback is designed in order to satisfy the complex industrial environment,such that the control flexibility is effectively enhanced while ensuring the dynamic performance.Subsequently,the proposed improved saturation strategy is applied to limit the amplitude of the control signal so that the balance of cost and effect is virtually achieved.Then the generalized Halanay inequality is obtained through using the comparison theorem,and the exponential consensus criteria and the estimation of admissible delay are derived by utilizing the Lyapunov stability theorem.Ultimately,the effectiveness of the proposed distributed control scheme is verified by numerical simulation.3).In view of the changeable communication phenomenon during the state updating of the agent,the constant delay is tentatively extended,and the exponential consensus problem for a kind of MASs with discontinuous dynamic and time-varying delay is fully discussed.A novel aperiodically intermittent control strategy is proposed,the restriction that maintaining the long-term constant or periodic control signal is essentially eliminated,and a substantial promotion in the dynamic performance is exchanged for an appropriate increase in control difficulty.Afterwards,combined with the designed improved saturation strategy,the control cost is further reduced.Sufficient conditions for the exponential consensus and the interval of maximum rest domain is derived based on the Filippov set-valued map,the Halanay inequality and the Lyapunov stability theorem.Finally,the validity of the proposed aperiodically intermittent distributed control protocol is demonstrated via two numerical simulations.