On Stochastic Seeking Of Nash Equilibria

Game theory is on optimal decisions based on rigorous mathematical models,mainly consisting of Players,Strategies,Information,Payoff Function,Equilibria,etc.With the widespread use of game theory in natural science,social science,military science,etc,various research results are shared by scholars in different areas.Especially for the Nash Equilibrium in noncooperative game,the most traditional methods solve this problem relying on the some information of the game,i.e.,the expression of payoff function,the strategies adopted by the other players,etc.The challenges occur when model information can not be obtained.In this thesis,we primarily utilizes stochastic extremum seeking method to develop the Nash equilibrium seeking algorithm and study the optimal control of wind power generation unit.The main work includes:We provide the discrete-time extremum seeking algorithm to solve Nash equilib-rium seeking problem in N-players non-cooperative game.The strategies are unable to be shared while the payoffs can be obtained in time.And the payoffs are gen-eral(not necessary quadratic)with unknown specific form.Based on the stochastic extremum seeking method,the Nash equilibrium seeking algorithm is produced and then the convergence of this algorithm is proved through stochastic averaging the-orem.Finally,the simulation of game in three players cases are researched,which well prove the validity of our algorithm.We study the control principle of wind turbines and employ the extremum seeking method to track the maximum power point of wind generation unit based on the single extremum relation between the utilization rate of power function and the tip speed ratio.The wind speed is handled by a bounded and periodic function,which is considered as the dither signal to detect the gradient of utilization rate of power function.Then we determine the direction of search of tip speed ratio,and obtain the referenced value and corresponding rotate speed reference.Finally,we utilize the vector control technology to adjust current rotate speed to achieve the optimal control of the wind power generation unit.