The Non-cooperative Differential Game Theory Of Uncertain System And Its Application In Management

The uncertain differential game studies how the participants of the game achieve their respective optimal goals,and their control strategy and stateunderthe constraint ofthe dynamic system described by a differential equation driven by an uncertain Liu process.This dissertation mainly studies the differential game theory of three kinds of uncertain dynamic systems,and mainly studies the problems of the saddle point equilibrium of the zero-sum game,the Nash equilibrium of the non-zero-sum game,and the Stackelberg equilibrium of the master-slave game.The research methods are mainly using the maximum principle of the uncertain optimal control,the construction method and the matching method which are commonly used in the uncertain differential game theory.Firstly,this dissertation studies the saddle point equilibrium,Nash equilibrium and Stackelberg equilibrium problem of three kinds of uncooperative differential game driven by canonical Liu processes,it focuses on the necessary and sufficient conditions for the existence of game equilibrium strategies and the explicit solutions and numerical solution method of equilibrium strategies.Secondly,numerical examples are used to validate and demonstrate the effectiveness of various equilibrium strategy solutions.Finally,the results are applied to the problems of collaborative innovation management of R&D investment in enterprises,as well as the optimal accumulation problem and enterprise investment decision-making.The specific results are as follows:(i)Firstly,the optimal control problem of a pseudo-linear uncertain differential system driven by the canonical Liu process is studied,we get the necessary and sufficient conditions for the existence of the optimal control solution and the explicit expression of the optimal control.Secondly,this dissertation studies the problems of saddle point equilibrium and Nash equilibrium,discusses the necessary and sufficient conditions for the existence of two kinds of equilibrium problem and the explicit expression of the equilibrium strategies.The results show that the equilibrium strategy depends on the solution of a key Riccati equation.In the finite time case,the key Riccati equation is a set of coupled Riccati equations and backward differential equations.The equilibrium strategy of the stationary system in the case of infinite time depends on the states and the coupled algebraic Riccati equation and the solution of the backward differential equation.(ii)This dissertationhave studiedthe principle of maximum value for the problem of uncertain linear system driven by the canonical Liu process and the equilibriumproblem of the Stackeberg game ofgame performance index is quadratic form,get the condition of the existence of Stackebergequilibrium solution,and the conclusion is applied to the problems of collaborative innovation management of R&D investment in enterprises,in this dissertation,the optimal investment strategy and subsidy ratio as well as the optimal interests of the two parties are given.(iii)The equilibrium problem of differential game saddle point and Nash equilibrium problem of uncertain linear time-delay system are studied.First we discuss the control input of uncertain linear time-delay systems with time-delay saddle point equilibrium and Nash equilibrium problems,using the optimality principle and method of formulation.By doing that,we respectively get equilibrium strategies in conditions of Nash equilibrium and saddle point equilibrium which is the corresponding coupled Riccati differential equation solution,and give numerical examples to verify and demonstrate two kinds of method of calculating the equilibrium strategies.Secondly,studied the system state of uncertain linear time-delay systems with time-delay saddle point equilibrium and Nash equilibrium problems,the use of the optimality principle and method of finite time situation saddle points respectively the existence of the equilibrium strategies and Nash equilibrium strategy and policy design rely on the coupled Riccati differential equation form,also give numerical examples to verify and demonstrate the effectiveness of the two methods of equilibrium strategies to solve,as well as discussed the application in capital accumulation.(iv)We studied uncertain linear systems with jump of the saddle point equilibrium and Nash equilibrium problems,using the maximum principle and the method.By doing that,we get saddle points of the equilibrium strategies and Nash equilibrium strategy in the finite time situation and policy design rely on the coupled Riccati differential equation form,and give numerical examples to verify and demonstrate the effectiveness of the two methods of equilibrium strategies to solve,as well as discussed the application in enterprise investment decision-making.