Distributed Aggregative Games Of Multi-Agent Systems Under Directed Topologies

The distributed aggregative game of multi-agent systems has attracted the attention of scholars in different fields due to its wide application in the fields of system control and engineering practice.Typical applications include demand side management of power systems and congestion control of shared networks.In the research of aggregative game,the Nash equilibrium seeking problem is a key problem.Many works are devoted to solving the Nash equilibrium seeking problem by using distributed strategy,but most of the communication networks in the research works are limited to undirected topologies,and usually study the multi-agent systems in the form of single-integrator.Considering the constraints of communication and physical systems,directed topologies and general decision-making dynamics are of engineering significance.Aiming at the more general directed topologies and multi-agent systems with uncertainties,this dissertation designs a distributed controller to solve the Nash equilibrium seeking problem for aggregative games.Firstly,this dissertation investigates the distributed aggregative game problem of uncertain linear multi-agent systems under directed topologies.This dissertation constructs a distributed output feedback controller based on two-layer framework(i.e.network layer and physical layer)to solve this problem.In the network layer,in order to deal with the asymmetry of the Laplacian matrixes corresponding to directed topologies,a dynamic compensator based on gradient method and average consensus protocol is designed by using the topology balance technology.The dynamic compensator generates an auxiliary signal converging to Nash equilibrium so that the problem can be transformed into a tracking problem.In the physical layer,a linear output feedback tracking controller is constructed by designing a reduced-order observer and an auxiliary dynamics to solve the tracking problem.The effectiveness of the distributed output feedback controller composed of the dynamic compensator and the linear tracking controller is also proved.Secondly,this dissertation investigates the distributed aggregative game problem of uncertain nonlinear multi-agent systems under directed topologies.Based on the two-layer framework,with the help of the dynamic compensator designed in the network layer,the auxiliary signal converging to the Nash equilibrium is generated,and the problem is transformed into the tracking problem of uncertain nonlinear multi-agent systems.In the physical layer,nonlinear terms and uncertainties bring challenges to the stabilization of multi-agent systems,and linear controllers cannot stabilize the nonlinear systems globally.In this dissertation,a nonlinear output feedback tracking controller is designed based on the robust control method,so that the output of the nonlinear multiagent systems can track the auxiliary signal.The effectiveness of the distributed output feedback controller composed of the dynamic compensator and the nonlinear tracking controller is also proved.Finally,this dissertation discusses the application of distributed aggregative game in power system.Aiming at the steam turbine which is an important equipment in thermal power plant,the generation control problem of multi-machine is studied.Firstly,the directed topology is used to describe the information communication between multiple steam turbines,and the problem is modeled as a distributed aggregative game problem.Then,a distributed controller based on two-layer framework is designed,such that the solution of the steam turbine system is bounded and the output power converges to Nash equilibrium.