Analysis And Control Of A Class Of Random Evolutionary Boolean Games

Evolutionary game theory is an interdisciplinary subject,which is generated by the integration of evolutionary biology theory in the development of classical game theory.Considering the influence of random factors in practical problems,random evolutionary game theory is proposed.At present,random evolutionary game theory has wide applications in many important research fields,such as biology,sociology,finance,engineering and so on.Using algebraic state space representation method,this paper studies the stability,state feedback stabilization,state feedback set sta-bilization and its applications,including output regulation,output tracking and strategy consensus,and optimal control of a class of random evolutionary Boolean games(REBGs).Firstly,the considered REBG and controlled REBG are convert-ed to equivalent stochastic systems,respectively,which is convenient to use the classical control theory to study REBGs.Secondly,the concept of global stability with probability one for considered REBG is given.By defining the state transi-tion probability matrix,a necessary and sufficient condition for judging whether the considered REBG is globally stable with probability one is proposed.By defining a series of probabilistic reachable sets,the necessary and sufficient conditions for stabi-lization and set stabilization with probability one of considered REBG are presented,respectively,and a constructive procedure is proposed to design the corresponding state feedback controllers.The obtained results on stochastic set stabilization are applied to the output regulation,output tracking and strategy consensus problems of considered REBG,and the corresponding necessary and sufficient conditions are presented,respectively.Finally,using the dynamic programming method,an algo-rithm is proposed to solve the finite horizon optimal control problem for considered REBG,which is applied to the Mayer-type optimal control problem.Using the receding horizon control method,the infinite horizon optimal control problem for considered REBG is considered,and an algorithm is established.