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 control… 

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

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

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

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

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

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

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

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

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

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

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.
...

References

SHOWING 1-10 OF 88 REFERENCES

Energy scaling and reduction in controlling complex networks

A physical theory is developed to explain the scaling behaviour through identification of the fundamental structural elements, the longest control chains (LCCs), that dominate the control energy.

Control efficacy of complex networks

A theorem is proved to determine rigorously the control efficacy of the network and to identify the nodes that can be controlled for any given driver nodes, and a picture of diffusion is developed that views the control process as a signal diffused from input signals to the set of controllable nodes.

Controllability of complex networks

Analytical tools are developed to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system’s entire dynamics.

Controllability transition and nonlocality in network control.

The failure of numerical control cannot be overcome in general by merely increasing numerical precision--successful control requires instead increasing the number of control inputs beyond the numerical controllability transition, which reveals a trade-off between nonlocality of the control trajectory in the phase space and nonlocability of the Control inputs in the network itself.

Dominating scale-free networks with variable scaling exponent: heterogeneous networks are not difficult to control

This work addresses complex network controllability from the perspective of the minimum dominating set (MDS) and shows that the more heterogeneous a network degree distribution is, the easier it is to control the entire system.

Pinning control of scale-free dynamical networks

Exact controllability of complex networks

An exact controllability paradigm based on the maximum multiplicity to identify the minimum set of driver nodes required to achieve full control of networks with arbitrary structures and link-weight distributions is introduced.

Controlling complex networks: How much energy is needed?

This work addresses the physically important issue of the energy required for achieving control by deriving and validating scaling laws for the lower and upper energy bounds.

Control Profiles of Complex Networks

The control profile is a network statistic that quantifies the different proportions of control-inducing structures present in a network, and it is found that standard random network models do not reproduce the kinds of control profiles that are observed in real-world networks.

Structural permeability of complex networks to control signals

This work develops a framework to maximize the diffusion of the control signals through a network, while taking into account physical and economic constraints that inevitably arise in applications.
...