论文标题
使用投影梯度方法对大型系统的最大化性最大化
Controllability maximization of large-scale systems using projected gradient method
论文作者
论文摘要
在这项工作中，我们为大型网络动力学系统（例如大脑网络）制定了两个可控性最大化问题：第一个问题是带有盒子约束的稀疏约束优化问题。第二个问题是第一个问题的修改问题，其中状态过渡矩阵是Metzler。换句话说，第二个问题是正面系统的实现问题。我们开发了一种预测的梯度方法来解决问题，并证明了具有局部线性收敛速率的固定点的全局收敛。明确给出了第一和第二个问题约束的投影。使用所提出的方法的数值实验提供了非平凡的结果。特别是，观察到可控性特征会随着参数指定稀疏性的增加而变化，并且变化率似乎取决于网络结构。
In this work, 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 non-trivial results. 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.
