引用本文:唐功友,刘毅敏,张勇.非线性离散系统的近似最优跟踪控制[J].控制理论与应用,2010,27(3):400~405.[点击复制]
TANG Gong-you,LIU Yi-min,ZHANG Yong.Approximate optimal output tracking control for nonlinear discrete-time systems[J].Control Theory and Technology,2010,27(3):400~405.[点击复制]
非线性离散系统的近似最优跟踪控制
Approximate optimal output tracking control for nonlinear discrete-time systems
摘要点击 2087  全文点击 1387  投稿时间：2007-12-09  修订日期：2009-11-17
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DOI编号  10.7641/j.issn.1000-8152.2010.3.021
  2010,27(3):400-405
中文关键词  非线性系统  离散系统  最优控制  跟踪控制  连续槽式搅拌器
英文关键词  nonlinear systems  discrete-time systems  optimal control  tracking control  CSTR
基金项目  国家自然科学基金资助项目(60574023, 40776051); 山东省自然科学基金重点资助项目(Z2005G01).
作者单位E-mail
唐功友 中国海洋大学 信息科学与工程学院, 山东 青岛 266100 gtang@ouc.edu.cn 
刘毅敏 中国电波传播研究所, 山东 青岛 266107 dongbaren@hotmail.com 
张勇 中国石油大学 信息与控制工程学院, 山东 东营 257061 paul_zhangyong@163.com 
中文摘要
      研究非线性离散系统的最优跟踪控制问题. 通过在由最优控制问题所导致的非线性两点边值问题中引入灵敏度参数, 并对它进行Maclaurin级数展开, 将原最优跟踪控制问题转化为一族非齐次线性两点边值问题. 得到的最优跟踪控制由解析的前馈反馈项和级数形式的补偿项组成. 解析的前馈反馈项可以由求解一个Riccati差分方程和一个矩阵差分方程得到. 级数补偿项可以由一个求解伴随向量的迭代算法近似求得. 以连续槽式反应器为例进行仿真验证了该方法的有效性．
英文摘要
      The optimal output tracking control(OOTC) problem is considered for discrete-time nonlinear systems. By introducing a sensitivity parameter in the nonlinear two-point boundary value(TPBV) problem which is obtained from the optimal control problems and expanding Maclaurin series around it, the original nonlinear OOTC problem is transformed into a series of nonhomogeneous linear TPBV problems. The OOTC law consists of analytic feedback and feedforward terms and a compensation term in an infinite series form. The analytic terms can be obtained by solving a Riccati difference equation and a matrix difference equation. The series compensation term can be approximately obtained by an iterative algorithm of adjoint vector equations. A simulation example from continuously stirred tank reactor(CSTR) is employed to test the validity of the presented algorithm.