【作者】 朱强；

【导师】 邵之江； Lorenz T.Biegler；

【作者基本信息】 浙江大学 ， 控制科学与工程， 2020， 博士

【副题名】一种机器智能方法

【摘要】 人工智能,是指由人制造的机器所表现出的智能。在工业革命时代,我们通过思考制造机器;而到了人工智能时代,我们制造会思考的机器。在人工智能革命前,所有人类生产技术和生产方式的革命均可称为人类学习和发现的过程,是人类大脑的专利。而放眼未来,人工智能终将继承人类的这一特质。人工智能对未来的改变,是对我们一点一滴形成知识体系过程本身的自动化,是用机器取代人类过程本身的自动化。人工智能技术从概念提出到今日蓬勃发展已历经几个世纪,在此过程中弱机器意识问题的理论体系以及实际应用日趋完备,同时机器行为学也得到了迅猛发展。而在下一代人工智能技术发展中,科学家们试图把机器视为可以独立思考的个体,从而研究强机器意识问题。但目前我们对此问题仍没有足够深刻而统一的认识,且现阶段面临着诸多方向性和技术性的难题,所以我们当下的研究重点仍然放在无意识的人工智能领域技术和基本原理的突破上。本文将从机器智能研究和机理建模的角度来研究无意识人工智能技术。机器智能是利用机理建模的方法描述一个系统内部运作的机制,同时配以控制论和优化理论作为决策辅助,从而实现机器的智能决策和最优操作。机器智能不再是一种简单的仿人智能,也不再依赖于人类所谓的“最优经验”和海量的数据样本,而是基于对机器系统内部特征的充分认识构建机理模型,之后利用数学物理方法进行科学决策的一种智能技术。机理建模技术在机器智能中充当着重要角色,是机器智能的决策基础,其可以在大范围内描述系统的非线性特征,具有较好的外推能力,适应性强。在使用上述技术思路研究无意识人工智能技术时,假设我们对机理模型已经有了充分认识,则机器智能科学决策中的相关控制理论和最优化理论就是本文最重要的研究内容。为处理当前万物互联背景下各种利益关系中多智能体系统的智能决策和最优操作问题,本文基于微分博弈理论和数值优化技术构建了一套高性能微分博弈数值优化算法,来对机理建模后的系统进行智能决策和最优操作分析,从而建立了一种机器智能方法来支撑人工智能研究。本文主要研究内容概括如下:1.微分博弈基本理论的介绍及已有求解算法的构造及验证。首先,本文针对微分博弈理论的基本概念、分类及性质做了详实的介绍,同时还介绍了目前较为成熟的微分博弈求解算法,如解析法、数值间接法及启发式算法等。在此基础上,本文针对三类典型的微分博弈,即竞争对抗微分博弈、非合作微分博弈及合作微分博弈进行求解框架分析,赋予每种微分博弈实际的工业、军事应用背景,构建每种微分博弈的数学优化命题,并利用成熟的计算方法进行仿真求解。2.微分博弈问题数值优化求解算法。针对传统微分博弈求解算法存在的缺陷,本文从数值直接求解算法入手,用以克服已有算法的不足,从而保证各种复杂场景、各种利益关系下的微分博弈问题成功求解。本文提出了两种数值直接求解算法:联立迭代分解正交配置法(SOCD,Simultaneous Orthogonal Collocation Decomposition)和联立直接间接混合法(SSD,Simultaneous Semi Direct)。前者的算法核心是:先将微分博弈中的极大极小化问题分解为两个轮流交替求解的普通动态优化子问题,之后针对每个子问题采用正交配置法将其离散化为非线性规划(NLP,NonLinear Programming)问题,最后求解该NLP问题,直到优化结果成功收敛为止。后者的算法核心是:先使用间接法得到某一位玩家A动态优化问题的一阶最优性必要条件,之后使用直接法求解另一位玩家B的动态优化问题,同时把玩家A的一阶最优性必要条件当作是玩家B动态优化问题中的约束来看待。这样就可以分别使用间接法和直接法来获得玩家A和B的微分博弈最优策略。本文对上述两种算法的细节进行了详细描述,同时配以工业、军事等领域仿真案例加以解释说明。此外,本文还提出了滚动时域优化算法(RHO,Receding Horizon Optimization),用于求解不确定性微分博弈问题。3.微分博弈问题高性能数值优化求解算法。在实际的微分博弈数值优化求解过程中,我们还面临着来自优化求解收敛性、实时性及准确性方面带来的诸多挑战。首先,对于增强微分博弈问题数值优化求解算法的收敛性,本文分别提出了基于回溯同伦法(HBM,Homotopy-based Backtracking Method)的初值化生成策略以及收敛深度控制算法(CDC,Con-vergence Depth Control),用以保证优化求解的收敛性并提高收敛过程的计算效率。其次,为了解决微分博弈动态优化问题在线求解计算耗时长,优化收敛难的问题,本文提出了一种基于灵敏度信息的微分博弈优化求解实时性提升算法(SRI,Sensitivity-based Real-time Im-provement)。该算法利用当前 NLP 问题优化结果的灵敏度信息实现在线预估未来优化周期内的微分博弈近似最优解,同时通过背景计算和离线矫正等手段进一步提升预估解的精度,从而保证既快又准地获得微分博弈动态优化问题的最优解。最后,为了提高微分博弈优化求解的精度并保证求解结果的最优性,本文提出了改进的hp自适应网格精细化策略(mhp-AMR,modified hp-Adaptive Mesh Refinement),该策略分别通过自适应调整网格个数以及插值多项式的阶次来精准捕捉控制变量的跳变点位置以及保证用来近似控制变量和状态变量的曲线足够光滑,从而提高微分博弈优化求解的准确性并保证求解结果的最优性。4.微分博弈问题数值优化求解算法结果稳定性分析。在实际应用场景中,除需要关注微分博弈问题如何求解、如何极大化目标函数以及如何提升优化算法的性能外,我们还需要关注微分博弈系统在优化求解过程中是否一直保持稳定。我们首先提出了一种针对微分博弈数值求解算法优化结果稳定性分析的理论分析工具——输入状态实际稳定性(IS p S,Input-to-State practical Stability)。之后,本文基于ISpS对不确定性微分博弈、合作微分博弈以及非合作微分博弈问题进行了优化结果稳定性分析并给出了相关证明。最后,本文通过工业仿真案例对微分博弈数值求解算法优化结果稳定性分析进行了有效性验证。更多还原

【Abstract】 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.更多还原