Consensus For Multi-agent Systems With Complicated Constraints Under Cooperative-antagonistic Topologies

The distributed cooperative control of multi-agent systems can complete complex tasks that are difficult for a single agent through the local information interaction among agents,and is widely used in UAV formation,mobile sensor network,smart grid and other fields.Consensus is the basis of cooperative control of multi-agent systems,which means that the states of all agents tend to be the same.In this thesis,aiming at the consensus control problems for multi-agent systems with multiple constraints over cooperative-antagonistic topologies,the effects of input saturation,unmeasurable velocity,probabilistic time-varying delay,parameter uncertainties and external disturbances on consensus of multi-agent systems are analyzed,and the suitable control protocols are designed to achieve the desired group-bipartite consensus and robust H_∞ bipartite consensus asymptotically for multi-agent systems.The main research contents and contributions of this thesis are as follows:For the group-bipartite consensus problems of linear and nonlinear heterogeneous multi-agent systems with input saturation and unavailable velocity constraints,the hyperbolic tangent saturation function ensures that the inputs of all agents are bounded,and auxiliary variables are introduced to overcome the limitation of unavailable velocities.Under arbitrary grouping scheme,a distributed consensus control algorithm with pinning strategies is proposed.Gauge transformation is used to transform the signed graph into a nonnegative graph.Based on algebraic graph theory and La Salle’s invariance principle,the consensus problem is transformed into the stability problem of the error system.It is analyzed and proved that the desired group-bipartite consensus of heterogeneous multi-agent systems is achieved asymptotically under the undirected,connected and structurally balanced signed graph.That is,each agent converges asymptotically to the state that has the same modulus as the reference trajectory of its group,but the signs may be opposite.For the mean-square group-bipartite consensus control problems of heterogeneous multi-agent systems with probabilistic time-varying delay and unmeasurable velocity constraints,auxiliary variables are introduced to overcome the unmeasurable velocity constraints,and a distributed control algorithm with arbitrary grouping and pinning schemes is developed by utilizing Bernoulli probability distribution characteristics.Under the assumption of bounded time-delay,the appropriate Lyapunov-Krasovskii functional is given to analyze the delay factors.Based on the stochastic analysis theory,sufficient conditions are obtained for heterogeneous multi-agent systems to achieve the desired group-bipartite consensus asymptotically in the mean-square sense.Furthermore,the relationship between the maximum admissible delay and the probability of delay occurrence is obtained with the help of the LMI toolbox of Matlab software.For the robust H_∞ bipartite consensus problems of uncertain nonlinear time-varying multi-agent systems with external disturbances,a distributed static output feedback control law is proposed.Following the approach of robust control theory to deal with uncertainties,the time-varying system can be converted to a time-invariant system with norm-bounded parameter uncertainties.By model transformation,orthogonal transformation,model reduction and diagonalization,the robust consensus problem for multi-agent systems becomes the H_∞ control issue of decoupled subsystems.The sufficient conditions for the robust H_∞ bipartite consensus of multi-agent systems are derived and transformed into the easy to implement linear matrix inequality form by Schur complement lemma,which ensures that the considered system not only achieves the robust bipartite consensus but also satisfies the desired H_∞ performance index.