Adaptive Dynamic Programming for Control
Adaptive Dynamic Programming for Control
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DOI：
10.1007/978-1-4471-4757-2
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发表时间：
2012-12
期刊：
影响因子：
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通讯作者：
Huaguang Zhang;Derong Liu;Yanhong Luo;Ding Wang
中科院分区：
文献类型：
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作者：
Huaguang Zhang;Derong Liu;Yanhong Luo;Ding Wang
非线性系统的稳定控制器设计方法很多。在寻求超越稳定性的最低要求，离散时间自适应动态规划方法的非线性系统的最优控制具有挑战性的主题，使用自适应动态规划（ADP）的工具。处理系统的范围是广泛的，仿射，切换，奇摄动和时滞非线性系统进行了讨论，是使用神经网络和技术的价值和政策迭代。本文介绍了ADP的三个主要方面，其中提出的用于稳定和跟踪和游戏的方法受益于最优控制方法的结合：·无限时域控制，克服了直接求解偏微分Hamilton-Jacobi-Bellman方程的困难，并证明了迭代值函数更新序列收敛于由容许控制律序列获得的所有值函数的下确界;·有限时域控制，在离散时间非线性系统中实现，向读者展示了如何在固定数量的控制步骤内获得次优控制解决方案，并且结果比通常从无穷大系统中获得的结果更容易应用于真实的系统。水平控制;·非线性博弈，其中一对混合最优策略被导出用于解决当鞍点不存在时的博弈，以及当鞍点存在时，避免鞍点的存在条件。非零和游戏的背景下，一个单一的网络计划，其中获得的政策，保证系统的稳定性和最小化的个人性能函数产生的纳什均衡进行了研究。为了使覆盖面适合学生以及专家读者，离散时间自适应动态规划：·建立了基本理论，明确涉及每一章致力于一个明确可识别的控制范例;·演示了ADP算法的收敛证明，以加深对稳定性和收敛性的推导的理解与使用的迭代计算方法;并展示了ADP方法如何在模拟和真实的应用中使用。这篇文章将是相当感兴趣的研究人员感兴趣的最优控制和它的应用在运筹学，应用数学计算智能和工程。从事控制和运筹学的研究生也会发现这里提出的思想是进一步学习的有力方法的来源。
There are many methods of stable controller design for nonlinear systems. In seeking to go beyond the minimum requirement of stability, Adaptive Dynamic Programming in Discrete Time approaches the challenging topic of optimal control for nonlinear systems using the tools of adaptive dynamic programming (ADP). The range of systems treated is extensive; affine, switched, singularly perturbed and time-delay nonlinear systems are discussed as are the uses of neural networks and techniques of value and policy iteration. The text features three main aspects of ADP in which the methods proposed for stabilization and for tracking and games benefit from the incorporation of optimal control methods:• infinite-horizon control for which the difficulty of solving partial differential Hamilton–Jacobi–Bellman equations directly is overcome, and proof provided that the iterative value function updating sequence converges to the infimum of all the value functions obtained by admissible control law sequences;• finite-horizon control, implemented in discrete-time nonlinear systems showing the reader how to obtain suboptimal control solutions within a fixed number of control steps and with results more easily applied in real systems than those usually gained from infinite-horizon control;• nonlinear games for which a pair of mixed optimal policies are derived for solving games both when the saddle point does not exist, and, when it does, avoiding the existence conditions of the saddle point. Non-zero-sum games are studied in the context of a single network scheme in which policies are obtained guaranteeing system stability and minimizing the individual performance function yielding a Nash equilibrium. In order to make the coverage suitable for the student as well as for the expert reader, Adaptive Dynamic Programming in Discrete Time:• establishes the fundamental theory involved clearly with each chapter devoted to a clearly identifiable control paradigm;• demonstrates convergence proofs of the ADP algorithms to deepen understanding of the derivation of stability and convergence with the iterative computational methods used; and• shows how ADP methods can be put to use both in simulation and in real applications. This text will be of considerable interest to researchers interested in optimal control and its applications in operations research, applied mathematics computational intelligence and engineering. Graduate students working in control and operations research will also find the ideas presented here to be a source of powerful methods for furthering their study.