| With the development of fractional calculus and the further research on the consensus control of integer-order multi-agent systems,the consensus control of fractional-order multi-agent systems(FOMASs)has become a hot research issue in the control field.Because of the effects of environmental noise,the parameters of FOMASs,such as the adjacency weights of communication graph and the fractional orders of agents,are likely to be disturbed and locate over a finite interval.Thus,it is practically significant to investigate the consensus control problem of FOMASs in the presence of interval uncertainties.This thesis investigates the consensus control of FOMASs with the interval uncertainties,and its main research contents are as follows:(1)The iterative learning control for the consensus of the nonlinear FOMASs with the interval uncertain topologies is investigated.A fractional-order iterative learning consensus protocol is proposed,and by analyzing the convergence of the learning process,a consensus condition,which includes unknown eigenvalues of graphs and an undetermined learning coefficient,is derived.A min-max optimization problem is formulated based on the fast convergence of the λ-norm of consensus tracking errors,then the optimal learning coefficient can be obtained by solving the min-max optimization problem,and the difficulties of leaning coefficient design caused by the unknown eigenvalues are dealt with.Thereby,for the undirected and directed interval uncertain graphs,two algorithms about the optimal learning coefficients are proposed,respectively.(2)The iterative learning control for the consensus of the fractional-order interval uncertain nonlinear multi-agent systems is investigated,in which the system matrix and the input matrix are perturbed simultaneously,and there exist the linear coupling relationships among the fractional order and the perturbations of system matrix and input matrix.An observer-type fractional-order iterative learning consensus protocol is proposed.Based on the definition of fractional integral,a performance index,which can exhibit the monotonic convergence of the input errors,is constructed.A Lyapunov-like method is applied to analyze the stability of the closed-loop system,and thereby the sufficient conditions in terms of linear matrix inequalities are derived to guarantee the consensus tracking and the monotonic convergence of the input errors.(3)The output feedback control for the consensus of the fractional-order interval uncertain linear multi-agent systems(FOIULMASs)is investigated,in which the fractional order,the system matrix and the input matrix are perturbed simultaneously,and there exist the linear coupling relationships among them.An output feedback protocol is designed by using the information of agents’ neighbors.By analyzing the stability of closed-loop fractional-order multi-agent system,a sufficient condition guaranteeing the robust output consensus of FOIULMASs is derived in terms of2(N-1)(N denotes the number of agents)nonlinear matrix inequalities.By the matrix transformation,the singular value decomposition and the properties of convex function,the consensus condition is further simplified into four linear matrix inequalities,and then by solving four linear matrix inequalities the output feedback gain matrix is obtained.(4)The iterative learning control for a class of non-identical fractional-order multi-agent systems is investigated,in which the different agents have different fractional orders and dynamic functions.By designing the event-triggered mechanism along an iteration axis and introducing it into the iterative learning controller,an event-triggered iterative learning consensus protocol is proposed.By analyzing the convergence of learning process,the sufficient conditions are derived to guarantee that the output consensus tracking can be achieved over the finite time interval as the iteration step goes to infinity.Meanwhile,under the proposed protocol,the number of controller update is tremendously reduced and the communication resource is obviously saved. |
