High-performance Computational Differential Game

Artificial intelligence(AI)refers to the intelligence displayed by machines made by people In the era of industrial revolution,we made machines by thinking,while in the era of artificial intelligence,we make machines that think.Before the revolution of artificial intelligence,all the revolutions of human production technology and production mode can be called the process of human learning and discovering,which is the patent of human brain.In the future,artificial intelligence will inherit this characteristic of human.The change of artificial intelligence to the future is the automation of the process of forming our knowledge system,and the automation of the process of replacing human with machine.It has been several centuries since the concept of artificial intelligence technology was put forward.In this process,the theoretical system and practical applications of weak machine consciousness are becoming more and more complete.At the same time,machine behavior has also been developed rapidly.In the development of the next generation of artificial intelligence technology,scientists try to regard machines as individuals who can think independently,so as to study the problem of strong machine consciousness.However,we still do not have enough deep and unified understanding of this problem,and we are facing many directional and technical problems at this stage.So our current research focus is still on the breakthrough of unconscious artificial intelligence technology and basic principles.This work studies the unconscious AI technology from a new dimension,that is,machine intelligence research and mechanism modeling.Machine intelligence uses the mechanism modeling method to describe the internal operation mechanism of a system.At the same time,with the cybernetics and optimization theory as decision-making assistance,it can realize the intelligent decision-making and optimal operation of the machine.Machine intelligence is no longer a simple humanoid intelligence,and no longer depends on the so-called "optimal experience" and massive data samples of human beings.It is an intelligent technology based on the full understanding of the internal characteristics of machine system,which builds a mechanism model and then makes the scientific decision using mathematical and physical methods.Mechanism modeling technology plays an important role in machine intelligence,which is the decision-making basis of machine intelligence.It can describe the nonlinear characteristics of the system in a large range,and also has the good extrapolation ability and strong adaptability.When using the above technology ideas to study the unconscious artificial intelligence technology,assuming that we have a full understanding of the mechanism model,then the relevant control theory and optimization theory of the scientific decision-making of machine intelligence are the most important research contents in this study.In order to deal with the intelligent decision-making and optimal operation of multi-agent system in various interest relations under the current background of interconnection of all things,this study will propose high-performance numerical optimization methods for differential game problems based on differential game theory and numerical optimization technology to research the intelligent decision-making and optimal operation of the system after mechanism modeling.The research contents are as follows1.Introduction of differential game basic theory and the construction and verification of existing algorithms.First of all,this study introduces the basic concept,classification and properties of differential game theory in detail.At the same time,it introduces the existing differential game solving algorithms,such as the analytic method,numerical indirect method and heuristic method On this basis,this study analyzes the solution frameworks of three kinds of typical differential games,namely competitive confrontation differential game,noncooperative differential game and cooperative differential game,gives the actually industrial and military application background of each differential game,builds the mathematical optimization proposition of each differential game,and uses the existing algorithms to solve these differential games.2.Numerical optimization methods for differential game problems.In view of the shortcomings of the above-mentioned differential game algorithms in the optimization process,this study starts with the numerical direct algorithm to overcome the shortcomings of the existing algorithms,so as to ensure the successful solutions of differential game problems in various complex scenarios and various interests.In this study,two numerical direct algorithms are proposes:the simultaneous orthogonal collocation decomposition(SOCD)method and the simultaneous semi direct(SSD)method.The core of the former algorithm is:first,the minimax problem in differential game is decomposed into two general dynamic optimization subproblems which are solved alternately in turn Then,for each subproblem,the orthogonal collocation method is used to discretize it into nonlinear programming(NLP)problem.Finally,the NLP problem is solved until the optimization results converge successfully.The core of the latter algorithm is to obtain the first-order optimality necessary conditions of one player A's dynamic optimization problem by using the indirect method,and then solve the other player B's dynamic optimization problem by using the direct method,and treat the first-order optimality necessary conditions of player A as the constraints of player B's dynamic optimization problem.In this way,we can use the indirect and direct methods to obtain the optimal differential game strategies of player A and player B,respectively.In this study,the details of the above two algorithms are introduced,and the simulation cases in the fields of industry and military are illustrated.In addition,this study also proposes the receding horizon optimization(RHO)algorithm to solve the differential game problem under uncertainty.3.High-performance numerical optimization methods for differential game problems.In the actual differential game numerical optimization process,we also face many challenges from the convergence,real-time and accuracy of optimization.Firstly,to enhance the convergence of numerical optimization algorithm for di fferential game problems,this study proposes the initial value generation strategy based on homotopy-based backtracking method(HBM)and the convergence depth control(CDC)algorithm,respectively,in order to ensure the convergence of optimization and improve the efficiency of convergence process.Secondly,in order to solve the problem of long computation time and convergence difficulty,this study proposes a sensitivity-bsed real-time imeprovement(SRI)algorithm.In this algorithm,the sensitivity information of NLP optimization results is used to predict the approximate optimal solution of differential game in the next optimization cycle on-line.Meanwhile,the accuracy of the approximate optimal solution is further improved by background computation and off-line correction,so as to ensure that the optimal solution of differential game can be obtained quickly and accurately.Finally,in order to improve the accuracy of differential game optimization and ensure the optimality of the results,this study proposes the modified hp-adaptive mesh refinement(mhp-AMR)strategy,which can capture the jump point positions of controls and ensure that the curves used to approximate controls and states are smooth enough by adjusting the number of mesh and the order of interpolation polynomials,respectively,so that the accuracy of optimal solution and the optimality of results are guaranteed.4.Stability of numerical optimization methods for differential game problems.In the practical application scenario,we need to pay attention to how to solve the differential game problem,how to maximize the objective function and how to improve the optimization algorithm performance.We also need to pay attention to whether the differential game system remains stable in the optimization process.We first propose a theoretical analysis tool,input-to-state practical stability(ISpS),for the stability analysis of differential game numerical optimization results.Then,based on ISpS,this study analyzes the stability of optimization results of uncertain differential game,cooperative differential game and noncooperative differential game,and gives the relevant proof at the same time.Finally,this study verifies the validity of the optimization results stability analysis of differential game numerical algorithm through an industrial simulation case.