| 耦合Riccati不等式组解的局部优化算法及其在微分对策中的应用 |
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| 引用本文： | 年晓红,杨胜跃,郭丽梅.耦合Riccati不等式组解的局部优化算法及其在微分对策中的应用[J].系统工程,2005,23(6):105-109. |
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| 作者姓名： | 年晓红 杨胜跃 郭丽梅 |
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| 作者单位： | 中南大学,信息科学与工程学院,湖南,长沙,410075 |
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| 基金项目： | 国家自然科学基金资助项目（60474029）;湖南省自然科学基金重点资助项目（00JJY1009） |
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| 摘 要： | 研究与线性二次微分对策的Nash次优均衡对策相联系的一组耦合Riccati矩阵不等式组的解的算法问题。将耦合Riccati矩阵不等式组的求解问题化为具有非线性约束的非凸优化问题，用双线性矩阵不等式（BMI）方法给出了Riccati矩阵不等式组解的局部优化算法，这种算法可以用MATLAB中的线性矩阵不等式工具箱（LMI Toolbox）求解，并给出了这种算法在微分对策中的一个应用实例。
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| 关 键 词： | 微分对策 Riccati不等式 双线性矩阵不等式 线性矩阵不等式 |
| 文章编号： | 1001-4098（2005）06-0105-05 |
| 收稿时间： | 2005-03-17 |
| 修稿时间： | 2005-03-17 |
Partial Optimization Algorithm for Coupled Riccati Inequalities and Its Application in Differential Games |
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| NIAN Xiao-Hong,YANG Sheng-yue,GUO Limei.Partial Optimization Algorithm for Coupled Riccati Inequalities and Its Application in Differential Games[J].Systems Engineering,2005,23(6):105-109. |
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| Authors: | NIAN Xiao-Hong YANG Sheng-yue GUO Limei |
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| Abstract: | In this paper, the problem of algorithm for the solution of coupled matrix Riccati inequalities which associated with the sub-optimal strategies of non-zero sum linear quadratic differential games is considered. The problem for solving coupled matrix Riccati inequalities is formulated as a non-convex optimization problem with nonlinear constraints. A partial optimization algorithm via bilinear matrix inequalities (BMI) technique which can be solved by using LMI Toolbox of (MATLAB) is introduced to solve the coupled Riccati inequalities. A numerical example is presented to show the efficiency of the presented algorithm. |
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| Keywords: | Differential Game Riccati Inequalities Bilinear Inequalities Linear Matrix Inequalities |
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