| 带有交叉项的离散不定随机线性二次控制问题 |
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| 引用本文： | 罗成新,冯恩民. 带有交叉项的离散不定随机线性二次控制问题[J]. 运筹与管理, 2004, 13(5): 18-20 |
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| 作者姓名： | 罗成新 冯恩民 |
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| 作者单位： | 1. 大连理工大学,应用数学系,辽宁,大连,116024;沈阳师范大学,数学系,辽宁,沈阳,110034
2. 大连理工大学,应用数学系,辽宁,大连,116024 |
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| 摘 要： | 研究性能指标带有交叉项的离散时间不定随机线性二次(LQ)控制问题，允许权矩阵是不定的。引入一个广义差分Riccati方程，证明了此方程的可解性是LQ问题存在最优控制的一个充分条件，并用方程的解给出了最优控制。推广了[1]的结果。
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| 关 键 词： | 离散时间 不定随机线性二次控制 广义差分Riccati方程 矩阵广义逆 |
| 文章编号： | 1007-3221(2004)05-0018-03 |
| 修稿时间： | 2004-02-23 |
Discrete-time Indefinite Linear Quadratic Control With Cross Term |
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| LUO Cheng-xin. Discrete-time Indefinite Linear Quadratic Control With Cross Term[J]. Operations Research and Management Science, 2004, 13(5): 18-20 |
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| Authors: | LUO Cheng-xin |
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| Affiliation: | LUO Cheng-xin~ |
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| Abstract: | This paper concerns the discrete-time indefinite stochastic LQ control problem with cross term in the index cost, allowing the weighting matrices in the cost function to be indefinite. A generalized difference Riccati equation (GDRE) is introduced. It shows that the solvability of the GDRE is sufficient for the existence of the optimal control for the LQ problem. Furthermore, it shows that the optimal control is not unique due to the indefiniteness, and the optimal control set is explicitly obtained in terms of the solution of the GDRE. |
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| Keywords: | discrete-time indefinite stochastic LQ control generalized difference Riccati equation Moore-Penrose inverse |
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