Dynamic system methods for solving mixed linear matrix inequalities and linear vector inequalities and equalities
Dynamic system methods for solving mixed linear matrix inequalities and linear vector inequalities and equalities
复制标题
求解混合线性矩阵不等式和线性向量不等式和等式的动态系统方法
DOI：
10.1016/j.amc.2010.02.010
复制
发表时间：
2010-04
影响因子：
4
通讯作者：
Hu, Xiaolin
中科院分区：
文献类型：
--
作者：
Hu, Xiaolin
提出了一种求解混合线性矩阵不等式和线性向量不等式的新思路。首先，将问题转化为具有连续可微凸目标函数的无约束极小化问题。然后，提出了求解该问题的连续时间动态系统和离散时间动态系统。在一些较温和的条件下，证明了所提出的动力系统全局收敛于问题的解。这种方法的优点在于其简单的数值实现和处理非严格线性矩阵不等式的能力。此外，该方法在神经电路实现方面具有广阔的应用前景，因此在许多在线控制问题中具有潜在的应用前景。文中给出了几个数值算例，以说明该方法的性能，并验证理论结果。
A novel idea is proposed for solving a system of mixed linear matrix inequalities and linear vector inequalities and equalities. First, the problem is converted into an unconstrained minimization problem with a continuously differentiable convex objective function. Then, a continuous-time dynamic system and a discrete-time dynamic system are proposed for solving it. Under some mild conditions, the proposed dynamic systems are shown to be globally convergent to a solution of the problem. The merits of the methods refer to their simple numerical implementations and capability for handling nonstrict LMIs easily. In addition, the methods are promising in neural circuits realization, and therefore have potential applications in many online control problems. Several numerical examples are presented to illustrate the performance of the methods and substantiate the theoretical results.
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DOI：
10.1109/tsmcb.2006.886166
发表时间：
2007-06
期刊：
IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)
影响因子：
--
作者：
Xiaolin Hu;Jun Wang
通讯作者：
Xiaolin Hu;Jun Wang
DOI：
10.1016/j.camwa.2006.09.004
发表时间：
2007
期刊：
Comput. Math. Appl.
影响因子：
--
作者：
Yiguang Liu;Zhisheng You;Liping Cao
通讯作者：
Yiguang Liu;Zhisheng You;Liping Cao
影响因子：
8
作者：
Tao Li;Changyin Sun;Xianlin Zhao;Chong Lin
通讯作者：
Tao Li;Changyin Sun;Xianlin Zhao;Chong Lin
影响因子：
--
作者：
Xiaolin Hu;Jun Wang
通讯作者：
Xiaolin Hu;Jun Wang
影响因子：
5.1
作者：
Youshen Xia;Jun Wang;Donald L. Hung
通讯作者：
Youshen Xia;Jun Wang;Donald L. Hung