Energy scaling of targeted optimal control of complex networks

Klickstein, Isaac; Shirin, Afroza; Sorrentino, Francesco

doi:10.1038/ncomms15145

Cited by 84 publications

(124 citation statements)

References 57 publications

Supporting

Mentioning

121

Contrasting

Order By: Relevance

“…We call driver nodes, the nodes which directly connect to the external inputs. We call target nodes, the nodes which have prescribed state that must be satisfied at the final time [50].…”

Section: S12 Parametersmentioning

confidence: 99%

Optimal regulation of blood glucose level in Type I diabetes using insulin and glucagon

et al. 2019

Self Cite

View full text Add to dashboard Cite

The Glucose-Insulin-Glucagon nonlinear model accurately describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes. Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon (dual therapy) that can optimally maintain the blood glucose level within desired limits after consumption of a meal and prevent the onset of both hypoglycemia and hyperglycemia. This problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package . Interestingly, in the case of monotherapy, we find the optimal solution is close to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal. We also find that the optimal dual therapy (that uses both insulin and glucagon) is better able to regulate glucose as compared to using insulin alone. We also propose an ad-hoc rule for both the dosage and the time of delivery of insulin and glucagon.

show abstract

“…We call driver nodes, the nodes which directly connect to the external inputs. We call target nodes, the nodes which have prescribed state that must be satisfied at the final time [50].…”

Section: S12 Parametersmentioning

confidence: 99%

Optimal regulation of blood glucose level in Type I diabetes using insulin and glucagon

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…For energy cost of target control, Ref. [19] presented that it exponentially ascends with the number of target nodes. Therefore, it requires much more energy to control the entire network.…”

Section: Introductionmentioning

confidence: 99%

Energy Cost for Target Control of Complex Networks

Duan

Meng

et al. 2019

Advs. Complex Syst.

View full text Add to dashboard Cite

To promote the implementation of realistic control over various complex networks, recent work has been focusing on analyzing energy cost. Indeed, the energy cost quantifies how much effort is required to drive the system from one state to another when it is fully controllable. A fully controllable system means that the system can be driven by external inputs from any initial state to any final state in finite time. However, it is prohibitively expensive and unnecessary to confine that the system is fully controllable when we merely need to accomplish the so-called target control-controlling a subnet of nodes chosen from the entire network. Yet, when the system is partially controllable, the associated energy cost remains elusive. Here we present the minimum energy cost for controlling an arbitrary subset of nodes of a network. Moreover, we systematically show the scaling behavior of the precise upper and lower bounds of the minimum energy in term of the time given to accomplish control. For controlling a given number of target nodes, we further demonstrate that the associated energy over different configurations can differ by several orders of magnitude. When the adjacency matrix of the network is nonsingular, we can simplify the framework by just considering the induced subgraph spanned by target nodes instead of the entire network. Importantly, we find that, energy cost could be saved by orders of magnitude as we only need the partial controllability of the entire network. Our theoretical results are all corroborated by numerical calculations, and pave the way for estimating the energy cost to implement realistic target control in various applications. arXiv:1907.06401v1 [math.OC]

show abstract

“…A key development is the systematic adoption of the linear structural controllability theory to complex networks with directed interactions [4]. Since then, there has been a great deal of effort in investigating the linear controllability of complex networks [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Irrelevance of linear controllability to nonlinear dynamical networks

Jiang

Lai

2019

Nat Commun

View full text Add to dashboard Cite

There has been tremendous development in linear controllability of complex networks. Real-world systems are fundamentally nonlinear. Is linear controllability relevant to nonlinear dynamical networks? We identify a common trait underlying both types of control: the nodal “importance”. For nonlinear and linear control, the importance is determined, respectively, by physical/biological considerations and the probability for a node to be in the minimum driver set. We study empirical mutualistic networks and a gene regulatory network, for which the nonlinear nodal importance can be quantified by the ability of individual nodes to restore the system from the aftermath of a tipping-point transition. We find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former large-degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly the irrelevance of linear controllability to these systems. The recent claim of successful application of linear controllability to Caenorhabditis elegans connectome is examined and discussed.

show abstract

Energy scaling of targeted optimal control of complex networks

Cited by 84 publications

References 57 publications

Optimal regulation of blood glucose level in Type I diabetes using insulin and glucagon

Optimal regulation of blood glucose level in Type I diabetes using insulin and glucagon

Energy Cost for Target Control of Complex Networks

Irrelevance of linear controllability to nonlinear dynamical networks

Contact Info

Product

Resources

About