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This type of mitigating intervention is expected to involve the control of fewer nodes than full controllability and thus it should be more practical.
For example, the authors show that in a mobile phone network, one needs to control about 20% of the nodes in order to achieve full controllability of the system.
It is concluded that there is no full controllability and only a two-dimensional subspace of the three-dimensional solution space can be explored.
On the other hand, the proof of the exactness of the proposed relaxation requires unrealistic assumptions and, in particular, (i) full controllability of loads and generation in the network and (ii) no upper-bound on the controllable loads.
These include the possibility of multi-pole design with a gearless construction that offers slow speed operation and reduced maintenance since no brushes are used, elimination of the excitation system, full controllability for maximum wind power extraction and grid interface, and easiness in accomplishing fault-ride through and grid support.
We illustrate that full controllability for a fermionic system can be achieved with quadratic Hamiltonians and a single fourth-order interaction term.
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By contrast, results for controllability in infinite dimensions have been mostly negative, stating that full control cannot be achieved with a finite-dimensional control Lie algebra.
Further development of this type of analysis could provide a tool for distribution-based control similar to those developed for full state controllability, allowing predictions to be made regarding the potential for effective control within a system.
Based on different impacts on the robustness of controllability caused by links absence, the links have been classified into three categories [ 16]: "critical" if its absence causes the minimum number of driver nodes increased so as to maintain full control; "redundant" if it can be removed without affecting the current set of driver nodes; "ordinary" if it is neither critical nor redundant.
This paper introduced the problem of distribution-based control as an alternative to existing approaches to complex network control which typically addresses the problem of full state controllability.
Another criticism of work relating to full state controllability analysis is that, in many scenarios, the requirement of full state controllability is unnecessarily strong.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com