Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations
Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations
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DOI：
10.1007/978-0-8176-4755-1
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发表时间：
1997-12
期刊：
影响因子：
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通讯作者：
M. Bardi;I. Capuzzo-Dolcetta
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文献类型：
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作者：
M. Bardi;I. Capuzzo-Dolcetta
本书的目的是提供一个最新的帐户理论的粘性解决方案的一阶偏微分方程的哈密尔顿-雅可比型及其应用最优确定性控制和微分游戏。80年代初，由MG Crandall和PL Lions [CL 81，CL 83]，MG Crandall，LC Evans和PL Lions [CEL 84]以及PL Lions的有影响的专著[L 82]所提出的粘性解理论，为处理动态优化问题中出现的值函数缺乏光滑性提供了非常方便的偏微分方程框架。这本书的主要主题是一个实施的粘性解决方案的方法，以一些显着的模型问题，在op-real确定性控制和微分游戏的描述。我们试图强调这种方法在建立C-响应的Hamilton-Jacobi方程的适定性方面所提供的优势，并指出它在反馈综合这一重要问题中的作用（当与最优控制理论和非光滑分析的各种技术相结合时）。
The purpose of the present book is to offer an up-to-date account of the theory of viscosity solutions of first order partial differential equations of Hamilton-Jacobi type and its applications to optimal deterministic control and differential games. The theory of viscosity solutions, initiated in the early 80's by the papers of MG Crandall and PL Lions [CL81, CL83], MG Crandall, LC Evans and PL Lions [CEL84] and PL Lions' influential monograph [L82], provides an-tremely convenient PDE framework for dealing with the lack of smoothness of the value functions arising in dynamic optimization problems. The leading theme of this book is a description of the implementation of the viscosity solutions approach to a number of significant model problems in op-real deterministic control and differential games. We have tried to emphasize the advantages offered by this approach in establishing the well-posedness of the c-responding Hamilton-Jacobi equations and to point out its role (when combined with various techniques from optimal control theory and nonsmooth analysis) in the important issue of feedback synthesis.