Convexiflcation of Optimal Decentralized Control Without a Stabilizing Controller
Convexiflcation of Optimal Decentralized Control Without a Stabilizing Controller
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无稳定控制器的最优分散控制的凸化
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
S. Lall
中科院分区：
文献类型：
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作者：
M. Rotkowitz;S. Lall
考虑寻找最优分散控制器的问题，其中所考虑的对象和控制器都是理性的。已经表明，如果给定的控制器既稳定又稳定，则称为二次不变性的条件将对象与施加在所需控制器上的约束联系起来，允许将最优分散控制问题转化为凸优化问题。本文展示了即使没有提供这样的控制器，最优分散控制问题仍然可以转化为凸优化问题，尽管是一个更复杂的问题。然后讨论由此产生的凸问题的解决方案。二次不变性给出凸性的结果因此扩展到所有有限维线性问题。特别是，这个结果现在可以用于不能强稳定的设备，或者很难找到稳定控制器的设备。结果在连续时间或离散时间中保持。
The problem of flnding an optimal decentralized controller is considered, where both the plant and the controllers under consideration are rational. It has been shown that a condition called quadratic invariance, which relates the plant and the constraints imposed on the desired controller, allows the optimal decentralized control problem to be cast as a convex optimization problem, provided that a controller is given which is both stable and stabilizing. This paper shows how, even when such a controller is not provided, the optimal decentralized control problem may still be cast as a convex optimization problem, albeit a more complicated one. The solution of the resulting convex problem is then discussed. The result that quadratic invariance gives convexity is thus extended to all flnite-dimensional linear problems. In particular, this result may now be used for plants which are not strongly stabilizable, or for which a stabilizing controller is simply di‐cult to flnd. The results hold in continuous-time or discrete-time.