Attainable Subspaces and the Bang-Bang Property of Time Optimal Controls for Heat Equations
Attainable Subspaces and the Bang-Bang Property of Time Optimal Controls for Heat Equations
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DOI：
10.1137/140966022
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发表时间：
2014-04
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影响因子：
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通讯作者：
GengshengBB Wang;Yashan Xu;Yubiao Zhang
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文献类型：
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作者：
GengshengBB Wang;Yashan Xu;Yubiao Zhang
本文研究了具有时变势的内控热方程的两个问题：可达子空间和某些时间最优控制问题的bang-bang性质。给出了可达子空间的一些等价刻画，并给出了保证bang-bang性质的一个充分条件。上述刻画和充分条件都与某些由伴随方程的解组成的函数空间密切相关。对于我们来说，推导具有时不变势的热方程的bang-bang性质的现有方法(例如，参见[H.O.法特蒂尼，无限维线性控制系统：时间最优和范数最优问题，Elsevier，阿姆斯特丹2005]，[F.Gozzi和P.Loreti，SIAM J.Control Opti.，37(1999)，pp.1195-1221]，[V.Mizel and T.Seidman，SIAM J.Control Opti.，35(1997)，pp.1204-1216]，以及[G.Wang，SIAM J.Control Optim.，47(2008)，第1701--1720页])不工作...
In this paper, we study two subjects on internally controlled heat equations with time varying potentials: the attainable subspaces and the bang-bang property for some time optimal control problems. We present some equivalent characterizations on the attainable subspaces and provide a sufficient condition to ensure the bang-bang property. Both the above-mentioned characterizations and the sufficient condition are closely related to some function spaces consisting of some solutions to the adjoint equations. It seems for us that the existing ways to derive the bang-bang property for heat equations with time-invariant potentials (see, for instance, [H. O. Fattorini, Infinite Dimensional Linear Control Systems: The Time Optimal and Norm Optimal Problems, Elsevier, Amsterdam 2005], [F. Gozzi and P. Loreti, SIAM J. Control Optim., 37 (1999), pp. 1195--1221], [V. Mizel and T. Seidman, SIAM J. Control Optim., 35 (1997), pp. 1204--1216], and [G. Wang, SIAM J. Control Optim., 47 (2008), pp. 1701--1720]) do not work...