Research On Consensus For Fractional-order Multi-a Gent Systems With Time-delays

FOSs(Fractional-Order Systems)are the systems in which the dynamics are characterized by fractional differential equations,and they are extensions of the traditional integer-order systems.FOMASs(Fractional-Order Multi-Agent Systems)are the multi-agent systems in which the dynamic model of each agent is characterized by fractional differential equations or the control protocols contain fractional derivatives,and they are extensions of the traditional integer-order multi-agent systems.The distributed coordinated control of FOMASs can make agents achieve a remarkable overall effect by the interaction among the agents,which can not be achieved by the simple collection of individual functions of agents,and it is a research hotspot and frontier in the field of distributed coordinated control of multi-agent systems.Consensus problem of FOMASs is a basic problem in the distributed coordinated control of FOMASs.In this thesis,an effective method for solving consensus control problems of FOMASs with time-delays is proposed and theory system of consensus control for FOMASs with timedelays is perfected.The main contents and contributions of this thesis are as follows:For the effects of time-delays on consensus of FOMASs,an effective method for solving consensus control problems of FOMASs with time-delays is proposed,and the delay margins for consensus control of FOMASs with time-delays are derived.The models of FOMASs with time-delays are transformed by using the Laplace transform tool,consensus control problems of FOMASs with time-delays are converted into stability problems of FOMASs with time-delays,and based on matrix theory and system stability theory,the delay margins for consensus control of FOMASs with time-delays are obtained.For the effects of fractional orders on consensus of FOMASs with time-delays,distributed consensus control protocols based on local state information feedback of fractional-order agents are designed,the dynamic models of FOMASs with time-delays and different fractional orders(single integral,double integral,multiple integral)are established,consensus conditions for FOMASs with time-delays and different fractional orders are derived,consensus control problems of FOMASs with time-delays and different fractional orders are solved,and theory system of consensus control for FOMASs with time-delays is perfected.For consensus problems of single-integral and double-integral FOMASs with stateless derivative feedback and time-delays,state derivative feedback is introduced into the control protocols to improve the consensus performance of single-integral and doubleintegral FOMASs with stateless derivative feedback and time-delays.Based on the theoretical results of consensus control for single-integral and doubleintegral FOMASs with non-uniform time-delays in this thesis,the delay margins for formation control of single-integral and double-integral FOMASs with relative damping and non-uniform time-delays are respectively derived.Firstly,distributed control protocols based on local state information feedback of agents are designed;Secondly,formation control problems of single-integral and double-integral FOMASs with relative damping and non-uniform time-delays are transformed into consensus control problems of single-integral and double-integral FOMASs with relative damping and non-uniform time-delays by variable substitution;Finally,based on the theoretical results of consensus control for single-integral and double-integral FOMASs with non-uniform time-delays,the delay margins for formation control of single-integral and double-integral FOMASs with relative damping and non-uniform time-delays are respectively obtained.