| 受控系统为一类紧半群非线性发展方程的最优控制 |
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| 引用本文： | 张鹏,韦维,等.受控系统为一类紧半群非线性发展方程的最优控制[J].贵州科学,2002,20(3):15-23. |
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| 作者姓名： | 张鹏 韦维 |
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| 作者单位： | [1]遵义师范学院数学系，贵州遵义563003 [2]贵州大学数学系，贵州贵阳550025 |
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| 基金项目： | 贵州省自然科学基金资助项目 |
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| 摘 要： | 研究无穷维空间中一类紧半群的非线性积微分方程及其对应的最优控制问题。首先，我们讨论对应的积分算子的紧性，给出此类积微分不等式相应Gronwall不等式。进而，证明了此类积微粉方程的温和解局部和全局存在性。最后，给出了相应的Lagrange型最优控制存在的充分条件。
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| 关 键 词： | 受控系统 一类紧半群 非线性发展方程 积微分方程 Gronwall不等式 先验估计 最优控制 |
Optimal control of systems governed by a class of nonlinear evolation equation with compact semigroup |
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| ZHANG Peng ,YANG Qi ,WEI Wei.Optimal control of systems governed by a class of nonlinear evolation equation with compact semigroup[J].Guizhou Science,2002,20(3):15-23. |
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| Authors: | ZHANG Peng YANG Qi WEI Wei |
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| Institution: | ZHANG Peng 1,YANG Qi 1,WEI Wei 2 |
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| Abstract: | In this paper,a class of nonlinear intrgro_differential equations of infinite dimension spaces with compact semigroup and its optimal control problem is inverstigated.At first,we discuss the compactness of an associated integral.Then,local and golbal existence results of mild solutions for such a class of integro_fifferential equations are presented.Finally,sufficient conditions for existence of optimal control of Largrange problem are obtained. |
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| Keywords: | semigroup integro_differential equations Gronwall lemma a priori estimate optimal control |
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