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Analysis and approximations of terminal-state tracking optimal control problems and controllability problems constrained by linear and semilinear parabolic partial differential equations.

机译：线性和半线性抛物型偏微分方程约束的终端状态跟踪最优控制问题和可控制性问题的分析和逼近。

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摘要

Terminal-state tracking optimal control problems for linear and semilinear parabolic equations are studied. The control objective is to track a desired terminal state and the control is of the distributed type. A distinctive feature of this work is that the controlled state and the target state are allowed to have nonmatching boundary conditions.; In the linear case, analytic solution formulae for the optimal control problems are derived in the form of eigen series. Pointwise-in-time L2 norm estimates for the optimal solutions are obtained and approximate controllability results are established. Exact controllability is shown when the target state and the controlled state have matching boundary conditions. One-dimensional computational results are presented which illustrate the terminal-state tracking properties for the solutions expressed by the series formulae.; In the semilinear case, the existence of an optimal control solution is shown. The dynamics of the optimal control solution is analyzed. Error estimates are obtained for semidiscrete (spatially discrete) approximations of the optimal control problem in two and three space dimensions. A gradient algorithm is discussed and numerical results are presented.
机译：研究了线性和半线性抛物方程的终端状态跟踪最优控制问题。控制目标是跟踪所需的终端状态，控制是分布式的。这项工作的一个显着特点是允许受控状态和目标状态具有不匹配的边界条件。在线性情况下，以本征级数的形式导出最优控制问题的解析解公式。获得了最优解的时间点L2范数估计，并建立了可控的近似结果。当目标状态和受控状态具有匹配的边界条件时，将显示精确的可控制性。给出一维计算结果，该结果说明了级数表达式表示的解的终端状态跟踪特性。在半线性情况下，显示了最优控制解的存在。分析了最优控制解决方案的动力学。在两个和三个空间维度中，针对最佳控制问题的半离散（空间离散）近似值获得了误差估计。讨论了梯度算法并给出了数值结果。

著录项

  • 作者

    Kwon, Hee-Dae.;

  • 作者单位

    Iowa State University.;

  • 授予单位 Iowa State University.;
  • 学科 Mathematics.
  • 学位 Ph.D.
  • 年度 2003
  • 页码 61 p.
  • 总页数 61
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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