引用本文:李振虎,谭述君,吴志刚.LQ终端控制的生成函数法与Riccati变换法的等价性[J].控制理论与应用,2009,26(8):896~898.[点击复制]
lizhenhu,Tan Shu Jun,WU Zhi-gang.Equivalence between generating function method and Riccati transformation method for LQ terminal control[J].Control Theory and Technology,2009,26(8):896~898.[点击复制]
LQ终端控制的生成函数法与Riccati变换法的等价性
Equivalence between generating function method and Riccati transformation method for LQ terminal control
摘要点击 1714  全文点击 1868  投稿时间：2008-01-17  修订日期：2008-11-07
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DOI编号  10.7641/j.issn.1000-8152.2009.8.CCTA080058
  2009,26(8):896-898
中文关键词  LQ软终端控制  LQ硬终端控制  生成函数  Riccati变换法  哈密顿系统
英文关键词  LQ soft terminal control  LQ hard terminal control  generating function  Riccati transformation  Hamiltonian system
基金项目  高校博士点基金资助项目(20070141067); 国家自然科学基金资助项目(10632030); 国家重点基础研究专项经费资助项目(2005CB321704).
作者单位E-mail
李振虎* 大连理工大学 leezhenhu@gmail.com 
谭述君 大连理工大学  
吴志刚 大连理工大学  
中文摘要
      通过定义线性哈密顿系统新形式的第3类生成函数, 建立了求解线性二次终端控制问题的生成函数方法与Riccati变换方法的直接联系, 并证明两种方法导出的最优控制律是等价的. 生成函数方法的优势在于可以灵活地处理边界约束条件. 本文根据Riccati变换方法沿时间逆向求解问题的特点, 定义了适于逆向正则变换的第3类生成函数, 用于求解哈密顿两点边值问题, 可得到用生成函数表示的最优控制律. 并通过验证生成函数方法所得最优控制律的各部分与Riccati变换法所得的结果相对应, 证明了两种方法所得控制律的等价性.
英文摘要
      By defining the third-kind generating function(GF) for a linear Hamiltonian system, this paper relates the generating function approach to the Riccati transformation method for LQ terminal control problems; and proves the equivalence of optimal terminal control laws derived by these two different methods. Since the generating function approach is adaptive to different types of boundary constraints, it provides a substantial advantage over the classical Riccati transformation method. Firstly, considering the backward sweeping character of the Riccati transformation method, we formulate the third-kind generating function in accordance with the backward canonical transform of the linear Hamiltonian system. Next, solving a Hamiltonian two-point-boundary-value problem, we obtain the new optimal control law in term of the generating function. Finally, comparing all terms of each new control law with the conventional control law derived by the Riccati transformation method, we verify the equivalence of these two different solution strategies.