Distributed Average Tracking Of Nonlinear Multi-agent Systems

Distributed average tracking(DAT)is a new topic of multi-agent systems.The DAT problem assumes that each agent has a time-varying reference signal.The objec-tive is to design a distributed algorithm such that all agents can track the average of a group of time-varying reference signals by local sole communication.In this thesis,we study the DAT problem of multi-agent systems with nonlinear constraints by employ-ing the knowledge of graph theory,matrix theory,and nonlinear system stability theory.The main contributions of this paper are summarized as follows.First,the DAT problem of a multi-agent system with input saturation is consid-ered.We propose two algorithms based on the techniques of low gain feedback and nonsmooth feedback.The first algorithm considers reference signals without external inputs under the low-gain feedback scheme.We show that if the system matrix of the references is negative semi-definite,then the DAT error will be ultimately upper bounded.The other algorithm considers reference signals with bounded inputs,where the idea of nonsmooth feedback is employed.We show that the DAT can be achieved asymptotically.Second,we study the DAT problem for a multi-agent system with the linear differential inclusions dynamics.Unlike the existing DAT algorithms for multi-agent systems in which all agents are assumed to have certain dynamics,we allow the dynamics to be uncertain for all agents.We propose a distributed algorithm based on nonsmooth feedback.The convergence results rely on the input-to-state stability prop-erties of the underling system and the properties of composite Laplacian quadratics.We show that if the reference signals and their control inputs are bounded,then the DAT can be solved.