Analysis of Positive Systems Using Copositive Programming
Analysis of Positive Systems Using Copositive Programming
复制标题
使用共正规划分析正系统
DOI：
10.1109/lcsys.2019.2946620
复制
发表时间：
2020
影响因子：
3
通讯作者：
Hagiwara Tomomichi
中科院分区：
文献类型：
--
作者：
Kato Teruki;Ebihara Yoshio;Hagiwara Tomomichi
在控制领域，大量的线性时不变系统的分析和综合问题被简化为半定规划问题。另一方面，在数学规划领域，人们积极研究一类二次规划问题，即协同规划问题（COP）。COP是一个在共积锥上的凸优化问题，而完全正锥、双非负锥、正半定锥与非负锥的Minkowski和也与COP密切相关。当我们处理由非负向量描述的优化问题时，自然会出现这四个锥。在这封信中，我们证明了LTI正系统的稳定性、H∞和H∞性能基本上是由这四个锥上的可行性/优化问题表征的。这些结果可以看作是在正半定锥上基于LMI/ sdp的结果的推广。我们还澄清，在某些性能中，由于共比或完全正锥的固有性质，这种直接推广是不可能的。因此，我们几乎捕捉到了关于我们可以在多大程度上将基于sdp的正系统的结果推广到与COP相关的四个锥上的结果的整个画面。
In the field of control, a wide range of analysis and synthesis problems of linear time-invariant (LTI) systems are reduced to semidefinite programming problems (SDPs). On the other hand, in the field of mathematical programming, a class of conic programming problems, so called the copositive programming problem (COP), is actively studied. COP is a convex optimization problem on the copositive cone, and the completely positive cone, the doubly nonnegative cone, and the Minkowski sum of the positive semidefinite cone and the nonnegative cone are also closely related to COP. These four cones naturally appear when we deal with optimization problems described by nonnegative vectors. In this letter, we show that the stability, the H2and the H∞performances of LTI positive systems are basically characterized by the feasibility/optimization problems over these four cones. These results can be regarded as the generalization of well-known LMI/SDP-based results on the positive semidefinite cone. We also clarify that in some performances such direct generalization is not possible due to inherent properties of the copositive or the completely positive cone. We thus capture almost entire picture about how far we can generalize the SDP-based results for positive systems to those on the four cones related to COP.
正锥体和完全正锥体以及 Z 变换
影响因子：
0.7
作者：
M. Gowda
通讯作者：
M. Gowda