# Energy scaling of targeted optimal control of complex networks

@article{Klickstein2017EnergySO, title={Energy scaling of targeted optimal control of complex networks}, author={Isaac S. Klickstein and Afroza Shirin and Francesco Sorrentino}, journal={Nature Communications}, year={2017}, volume={8} }

Recently it has been shown that the control energy required to control a dynamical complex network is prohibitively large when there are only a few control inputs. Most methods to reduce the control energy have focused on where, in the network, to place additional control inputs. Here, in contrast, we show that by controlling the states of a subset of the nodes of a network, rather than the state of every node, while holding the number of control signals constant, the required energy to controlâ€¦Â

## 63 Citations

### Optimal control of complex networks: Balancing accuracy and energy of the control action.

- Computer ScienceChaos
- 2017

A new control strategy called balanced control is introduced for which the requiredEnergy for the optimal balanced control problem approximates the required energy for the ideal target control problem when the coefficient of the second term is very small.

### Control Distance and Energy Scaling of Complex Networks

- Computer ScienceIEEE Transactions on Network Science and Engineering
- 2020

This work provides an upper bound of the control energy as a function of path length between driver node and target node along an infinite path graph for a single target node and refines the upper bound, by an order of magnitude or more, taking into account not only the length of the path, but also the redundancy of paths.

### Upper bound of the minimum energy cost for controlling complex networks

- Computer Science2019 Chinese Control Conference (CCC)
- 2019

The upper bound of the minimum control energy over all possible control directions within a certain control distance between the initial and final states is focused on, paving the way to implement realistic control over various complex networks with the minimum energy cost.

### Controlling network ensembles

- Computer ScienceNature communications
- 2021

This work investigates the minimum energy control of network ensembles, which may take one of a number of possible realizations, and characterizes the solution of the optimal control problem in the limit in which the systems are drawn from a continuous distribution.

### Energy Scaling with Control Distance in Complex Networks

- Computer Science2018 IEEE International Symposium on Circuits and Systems (ISCAS)
- 2018

This work finds that the energy scaling law can be written to include information about the distance between driver nodes and target nodes to more accurately predict control energy.

### Data-driven control of complex networks

- Computer Science, MathematicsNature communications
- 2021

This paper develops a data-driven framework to control a complex network optimally and without any knowledge of the network dynamics, and proves its controls are provably correct for networks with linear dynamics.

### Control energy scaling in temporal networks

- Computer Science
- 2017

This work systematically analyze the scaling behavior of a key control cost for temporal networks--the control energy, and finds that this scaling is largely dictated by the first and the last network snapshot in the temporal sequence, independent of the number of intervening snapshots, the initial and final states, and thenumber of driver nodes.

### Prevalence and scalable control of localized networks

- Computer ScienceProceedings of the National Academy of Sciences of the United States of America
- 2022

It is shown that network locality is captured by an information metric and is almost universally observed across real and model networks, and established that large networks can be controlled with computation and communication costs comparable to those for small networks.

### Optimizing target node set for the control energy of directed complex networks

- Computer Science
- 2019

This work derived the matrix derivative gradient needed for the search algorithm in a general way, and searched for target nodes which result in reduced control energy, given that driver nodes placement is fixed, and revealed that when the path distances from driver nodes to target nodes are minimised, control energy is optimal.

### Optimizing target nodes selection for the control energy of directed complex networks

- Computer ScienceScientific reports
- 2020

An iterative method based on Stiefel manifold optimization of selectable target node matrix to reduce control energy is proposed, which derives the matrix derivative gradient needed for the search algorithm in a general way, and search for target nodes which result in reduced control energy, assuming that driver nodes placement is fixed.

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