Containment Control Analysis Of Fractional-order Nonlinear Multi-agent Systems With Delays

With the development of science and technology,we are now living in the era of interconnection.Cooperative control of multi-agent systems has become a new research topic in the field of control.Especially,containment control of multi-agent systems with multiple leaders has been received broad interest by scholars.Compared with traditional integer-order model,fractional differential model can be used to describe some complex dynamics more accurately.In addition,delays are often unavoidably in the information interaction between agents,which can have an important impact on the dynamic behavior of systems.Therefore,containment control problems of fractional nonlinear multi-agent systems with delays are studied in this paper:1.By constructing a simple quadratic Lyapunov function,employing matrix analysis theory,graph theory and fractional Razumikhin method,containment control of fractional nonlinear multi-agent systems with both state delays and input delays is considered,and the linear matrix inequality conditions of achieving asymptotic containment control are given.2.By designing the discontinuous communication protocol,utilizing fractional Razumikhin method,the properties of fractional calculus and analytical techniques,finite-time containment control of fractional nonlinear multi-agent systems with delays is considered,and sufficient conditions of achieving finite-time containment control are obtained.The main innovations of this paper are as follows: 1.Innovation of research objects.In this paper,asymptotic containment control and finite-time containment control problems of fractional nonlinear delayed multi-agent systems are studied.2.Innovation of research methods.Our method overcomes the difficulties caused by the invalidity of composition property of fractional operators and delays,the linear matrix inequality conditions of realizing asymptotic and finite-time containment control are obtained by using fractional Razumikhin method,the properties of fractional calculus,graph theory and analytical techniques.