Consensus Of Multi-agent System Under Imprecise Topology

Coordination control and cooperation of multi-agent systems(MAS)can improve the performance level of individual agent,and even accomplish tasks that cannot be completed individually.In the topology,the connection between agents usually changes when the interference factors are considered in the actual circumstances,such as environment,temperature,bandwidth and other factors,so that the original path may be broken.According to imprecise theory,T-S fuzzy logic systems are used to approximate the communication topology of MAS,and the consensus problems of the MAS are also studied by the iterative learning control(ILC)method under imprecise topology.The main contents are as follows:1.We introduce the consensus problems of single integrator multi-agent systems with a leader under imprecise theory,an appropriate D-type distributed iterative learning control protocol is designed by using the corresponding distributed error of imprecise theory.By combining the graph theory,Schur complementary lemma,fuzzy logic systems and the principle of compression mapping,a sufficient condition is derived for the first-order multi-agent system to achieve the consensus under the imprecise theory.Furthermore,under the same topology for position and velocity,we introduce the double integrator multi-agent systems,a D-type distributed iterative learning protocol is proposed to study the consensus of second-order multi-agent systems according to the corresponding fuzzy distributed error,and the corresponding theory can be obtained.2.The consensus of second-order multi-agent systems with Lipschitz nonlinear function is studied under fuzzy independent topology,in which different topology is discussed for position and velocity.Designing a PD-type distributed iterative learning law.Then,by comparing the position and velocity errors between adjacent iterations,combining the ?-norm and using the principle of compression mapping,a sufficient condition for the consensus of the multi-agent system is derived.The second-order multi-agent consensus problem under independent inaccurate topology is further extended to formation control,and corresponding conclusions are obtained.Finally,numerical simulations are used to verify the validity of the above conclusions.3.The consensus problem of singular multi-agent systems with imprecise theory is investigated,and a distributed iterative learning control law for general singular systems is proposed,meanwhile,we can get a sufficient condition for singular multi-agent systems to achieve consensus in a finite time interval[0,T].We even extend the consequence to formation control for singular multi-agent system.Finally,two simulation examples are used to testify the reliability of the conclusion.