Containment Control Analysis Of Fractional Multiple Agent Systems With Mixed Delays

In recent years,consensus control of multiple agent systems has attracted much attention due to its wide applications on software systems,traffic control and neural networks.In particular,consensus control of multiple agent systems with multiple leaders is called containment control.Compared with traditional integer-order systems,fractional-order differential models may accurately describe certain biological phenomenons and complex systems.In addition,time delays are usually unavoidable among communication of agents and have vital impact on dynamical behavior of the system.This paper deals with containment control of fractional multiple agent systems in Caputo and Riemann-Liouville sense,respectively,and mainly investigates the following works:1.The containment control for Caputo fractional multiple agent systems with discrete and distributed delays is analyzed.Utilizing graph theory and fractional Razumikhin technique,several linear matrix inequality conditions are proposed to ensure containment control by adopting non-delayed and delayed control protocols,respectively.The examples and simulations are given to further verify reliability and validity of the conclusions.2.The containment control for nonlinear delayed Riemann-Liouville fractional multiple agent systems as well as Riemann-Liouville fractional multi-agent systems with discrete and distributed delays is considered.Under non-delayed and delayed control protocols,a reliable and simple method is addressed to deal with containment control,some sufficient conditions are proposed by utilizing traditional Lyapunov direct method,properties of fractional calculus and analytical technique.The method overcomes the difficulties caused by fractional derivatives and time delays.The validity of the conclusions is further verified by numerical simulations.The main contributions of this paper are listed as follows:(1)Innovation of research objects.This article focuses on research fractional multiple agent systems with mixed delays,which makes the systems we studied can more accurately describe a number of concrete models in engineering practice,and has strong representativeness and good application prospects.(2)Innovation of research methods.By constructing a simple quadratic Lyapunov function,using algebraic graph theory and fractional Razumikhin method,an effective method is proposed to analyze containment control of Caputo fractional delayed multiple agent systems.A simple method is addressed to realize containment control for Riemann-Liouville fractional delayed multiple agent systems by employing traditional Lyapunov direct method,properties of fractional calculus and analytical techniques,which may make our method overcome well the troubles brought from fractional derivatives and delays.