Analysis And Design Of Finite Games Based On Algebraic State Space Approach

With the rise of the interdiscipline of game theory and control theory,game theory has attracted extensive attention from control field.The game-based control method has been widely used in cooperative control of multi-agent systems,weapon-target assignment and economic dispatch of power systems.However,the premise of using game theory to solve the control related problem is to have a deep understanding of the properties to the game theory.Therefore it is necessary to investigate structures,properties and evolutionary dynamics of finite games.In this dissertation,orthogonal decomposition,game design,evolutionary dynamics and application in weapon-target assignment problem of finite games are studied based on algebraic state-space method using the semitensor product of matrices.Firstly,dynamic equivalence of harmonic games and orthogonal decomposition of finite games are studied.Necessary and sufficient condition for pure harmonic games being dynamic equivalent with basic pure harmonic games is given by derivation.As for the vector space structure of finite games,orthogonal decompositions of finite games are proposed from the perspectives of symmetric games,zero-sum games and normalized games,and bases of each decomposed subspace are derived,respectively.The function of vector inner product in finite game decomposition is analyzed.It is proved that only when the compatible condition is satisfied,different orthogonal decompositions can be realized.Secondly,verification and design problems of three types of potential games are investigated.For distributed game played on the network,a local information based potential game design method is proposed.A necessary and sufficient condition for designing local information based utility function is presented.For the competitively potential game played on the network,verification and design methods of zero-sum potential games are presented by derivation.For group based game played on the network,verification method of group based potential games is presented by derivation.Group utility function design method is proposed.Thirdly,design method of learning policy for the state based evolutionary game is considered.A two-memory better reply uncoupled learning policy is proposed,and it is proved that the learning policy can converge to the recurrent state equilibrium almostsurely under the reachable condition.To investigate the existence of time efficient algorithm in state based evolutionary games,a counter example is proposed which shows that there is no such time efficient algorithm.Using the designed learning policy,pure Nash equilibria of general finite games can be obtained and consensus of multiagent systems with time-varying topology can be realized.Then,verification and dynamical properties of two classes of hypernetworked evolutionary potential games are investigated.For hypernetworked group based potential games,sufficient conditions for fundamental networked game forming group based potential games are presented.We proved that hypernetworked group based potential games can converge to the Nash equilibrium using group based myopic best response rule.Strategically differentiated myopic best response rule and logit response rule for strategic differentiated games are provided,and convergences of the designed rules are proved.We proved that if the fundamental networked game of networked strategic differentiated games is symmetric coordination game,then the stochastic stable state of the networked strategic differentiated game is consist of risk dominant strategies.Finally,game based method is applied to the weapon-target assignment problem.Game model for weapon-target assignment problem is established.The method of designing local information based potential game to solve the weapon-target assignment problem is proposed for connected communication structure.Effects of myopic best response rule and logit response rule on the convergence rate are compared by simulation.In order to solve the problem of communication interruption,a method of designing group based potential game to solve the weapon-target assignment problem is proposed.Simulation results show that the group-based potential game design method can converge to the suboptimal assignment with a faster speed.For switching communication topology,local information based utility function of each weapon in every state is designed.The optimal allocation is realized using two memory better response learning rule,and validity of this method is verified by simulation.