Controllability Maximization of Large-Scale Systems Using Projected Gradient Method
Controllability Maximization of Large-Scale Systems Using Projected Gradient Method
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DOI：
10.1109/lcsys.2020.2993983
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发表时间：
2020-02
影响因子：
3
通讯作者：
Kazuhiro Sato;A. Takeda
中科院分区：
文献类型：
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作者：
Kazuhiro Sato;A. Takeda
在这封信中，我们制定了两个大规模的网络化动力系统，如脑网络的可控性最大化问题：第一个问题是一个稀疏约束优化问题的框约束。第二个问题是第一个问题的修正问题，其中状态转移矩阵是Metzler。换句话说，第二个问题是一个正系统的实现问题。我们提出了一种投影梯度法来求解该问题，并证明了该方法的全局收敛性和局部线性收敛速度。第一和第二个问题的约束的投影显式地给出。使用该方法进行的数值实验提供了一些理论上难以推导的结果。特别是，观察到的可控性特性的变化与指定稀疏性的参数的增加，和变化率似乎是依赖于网络结构。
In this letter, we formulate two controllability maximization problems for large-scale networked dynamical systems such as brain networks: The first problem is a sparsity constraint optimization problem with a box constraint. The second problem is a modified problem of the first problem, in which the state transition matrix is Metzler. In other words, the second problem is a realization problem for a positive system. We develop a projected gradient method for solving the problems, and prove global convergence to a stationary point with locally linear convergence rate. The projections onto the constraints of the first and second problems are given explicitly. Numerical experiments using the proposed method provide some results that are difficult to deduce theoretically. In particular, the controllability characteristic is observed to change with increase in the parameter specifying sparsity, and the change rate appears to be dependent on the network structure.