Game-based Coordination Control Of Multi-agent Systems

The distributed coordination ability of agents is the basis of multi-agent system research and the key to exert its advantages.With the development of coordination control of multi-agent systems,the egoistic behavior of agents has been non-negligible,and it has impacted the coordination control of multi-agent systems.However,the traditional multi-agent system research approach cannot adapt to the new requirements,and more appropriate analysis tools need to be introduced.For coordinating the relationship between the coordination control of multi-agent systems and the competitive behavior among the agents,game-based coordination control of multi-agent systems has received a lot of attention.This dissertation focuses on this subject,investigates how agents with competitive behavior interact with each other in multi-agent systems,and provides the following research:1.Two coordination control problems of distributed consensus and containment control for multi-agent systems with competitive behavior are studied.First,the interaction of agents in the multi-agent system is modeled as a multi-player game.For each agent,the cost function and action set are designed,with the assumption that it tends to minimize its own cost.It can be analyzed that agents select Nash equilibrium of the designed multi-player game as their current states.Then,the unique Nash equilibrium of the multi-player game is proved and calculated.Finally,a necessary and sufficient condition for achieving consensus of the game-based multi-agent system is established using game theory,graph theory and matrix theory.Moreover,the results are extended to the case where there are multiple leaders in the game-based multi-agent system,and a necessary and sufficient condition is provided for the system to solve containment control problem.2.Multi-agent systems with dynamic unknown agents and first-order continuous-time dynamic agents are investigated,and they are constructed as a novel class of game-based hybrid multi-agent systems.The necessary and sufficient conditions for these systems to achieve consensus are considered.The hybrid multi-agent systems consist of agents with unknown dynamics and agents with first-order continuous-time dynamics.The interaction among agents with unknown dynamics is modeled as a multi-player game.According to the frequency of agents with first-order continuous-time dynamics exploit their own states,two different types of distributed control protocols are designed for these agents.Then,in the designed hybrid multi-agent system,some agents update their states based on the multi-player game,and the others update their states based the first-order continuous-time dynamics and the designed distributed control protocols.By game theory,graph theory and matrix theory,necessary and sufficient conditions are established respectively to ensure consensus of the game-based hybrid multi-agent systems with the two proposed protocols.3.Multi-agent systems with dynamic unknown agents and second-order continuous-time dynamic agents are investigated,and they are constructed as a novel class of game-based heterogeneous multi-agent systems.The necessary and sufficient conditions for these systems to achieve consensus are provided.The heterogeneous multi-agent systems based on multi-player games is composed of agents updating states according to Nash equilibrium of multi-player games and second-order continuous-time dynamic agents.The unique Nash equilibrium of the designed multi-player game is calculated,and two kinds of distributed control protocols are designed for second-order continuous-time dynamic agents.Using game theory,graph theory,matrix theory and the system transformation method,necessary and sufficient conditions for the game-based heterogeneous multi-agent systems to reach consensus under two protocols are established,respectively.4.Hybrid multi-agent systems with different preferences and finite set of agent states is investigated,and necessary and sufficient conditions are provided for these systems achieving consensus.The interaction among agents in the hybrid multi-agent systems is modeled as a hybrid graphical coordination game.The action set and decision rule of each agent are provided,and three kinds of payoff matrices are designed for different interaction situations.Based on potential game theory,necessary and sufficient conditions are established for the multi-agent systems based on the hybrid graphical coordination game to achieve consensus.Furthermore,a new 3-action game is constructed by introducing neutral actions into the designed hybrid graphical coordination game.Using game theory and graph theory,necessary and sufficient conditions for the multi-agent system based on the 3-action game are established.By comparing necessary and sufficient conditions for game-based multi-agent systems with or without neutral actions,the impact of neutral actions on the consensus of the multi-agent system based on the hybrid graphical coordination game is analyzed.Based on game theory,graph theory,matrix theory and system transformation method,this dissertation constructs four types of game-based multi-agent systems,and the criteria for solving the coordination control problems of these systems are established respectively.This dissertation better illustrates the intelligence of agents and enrich and develop the relevant theories of swarm intelligence.