Backstepping Synchronization Analysis Of Uncertain Nonlinear Multi - Agent System

As is known to all that the Multi-agent networks have the characteristic such as independent、decentralized、coordination, and also have strong ability of self organization、 learning、and reasoning. In control field, the multi-agent systems are consistent synchronization issues topics and broadly application at the forefront of the current international. In many studies, it was shown that multi-agent systems often exhibit hierarchical organization, where vertexes divide into groups that further subdivide into groups of groups. In many systems such as ecological niches in food webs, genetic regulatory networks and social networks, these groups are found to correspond to known functional units. We called these kinds of systems as hierarchical multi-agent systems (HMSs). However, it is worthy mentioning that seldom mathematical models are given to exhibit the hierarchical organization of Multi-agent systems.In real HMSs, it is necessary to introduce perturbations because of various uncertainties. Considering that time delays unavoidably exist in practice, we also need to introduce time-delay nonlinear perturbations into the designed HMSs. Generally, HMSs may not reach a consensus when uncertain delayed nonlinearities are existed. Hence, effective control schemes have to be designed to force HMSs achieving a consensus.A large number of scientific studies show that the backstepping control method can effectively achieve the control system. In this chapter, various backstepping edesign techniques, including integrator backstepping, backstepping for strict-feedback systems, adaptive backstepping and robust backstepping, will be reviewed. We also introduced the role and design principles about robust controller and adaptive controller.All these topics show that this paper investigates the consensus problem in two-layer hierarchical multi-agent systems with uncertain delayed nonlinearities. The main objective of this paper is to design mathematical models of two-layer hierarchical multi-agent systems (THMSs) with uncertain delayed nonlinearities and discuss the consensus of the designed models. The pinning and backstepping methods are applied to overcome the shortcomings, which include that we knowing the precise time delays and a large number of controllers. By constructing a Lyapunov-Krasovskii functional, it is shown that the THMSs can reach the prescribed consensus by designing appropriate controllers. Finally, in order to illustrate the effectiveness of the developed criteria, we give a simulation result.