On the Minimization of Maximum Transient Energy Growth
On the Minimization of Maximum Transient Energy Growth
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DOI：
10.1109/tac.2007.900854
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发表时间：
2007-09
影响因子：
6.8
通讯作者：
J. Whidborne;J. McKernan
中科院分区：
文献类型：
--
作者：
J. Whidborne;J. McKernan
考虑了最大暂态能量增长最小化问题。该问题在某些流体流动控制问题和其他类型的非线性系统中具有重要意义。静态控制器，确保严格耗散的瞬态能量的存在条件的建立和一个明确的参数化所有这样的控制器提供。它还表明，通过Q-参数化，最小化的最大瞬态能量增长的问题可以构成一个凸优化问题，可以解决的自由参数的里兹近似的装置。通过考虑在适当的离散时间点序列上的暂态能量增长，最小最大暂态能量增长问题可以作为一个半定规划。理论的发展证明了一个数值例子。
The problem of minimizing the maximum transient energy growth is considered. This problem has importance in some fluid flow control problems and other classes of nonlinear systems. Conditions for the existence of static controllers that ensure strict dissipativity of the transient energy are established and an explicit parametrization of all such controllers is provided. It also is shown that by means of a Q-parametrization, the problem of minimizing the maximum transient energy growth can be posed as a convex optimization problem that can be solved by means of a Ritz approximation of the free parameter. By considering the transient energy growth at an appropriate sequence of discrete time points, the minimal maximum transient energy growth problem can be posed as a semidefinite program. The theoretical developments are demonstrated on a numerical example.