5 research outputs found
Fragility and controllability tradeoff in complex networks
© 2018 AACC. Mathematical theories and empirical evidence suggest that several complex natural and man-made systems are fragile: as their size increases, arbitrarily small and localized alterations of the system parameters may trigger system-wide failures. Examples are abundant, from perturbation of the population densities leading to extinction of species in ecological networks [1], to structural changes in metabolic networks preventing reactions [2], cascading failures in power networks [3], and the onset of epileptic seizures following alterations of structural connectivity among populations of neurons [4]. While fragility of these systems has long been recognized [5], convincing theories of why natural evolution or technological advance has failed, or avoided, to enhance robustness in complex systems are still lacking. In this paper we propose a mechanistic explanation of this phenomenon. We show that a fundamental tradeoff exists between fragility of a complex network and its controllability degree, that is, the control energy needed to drive the network state to a desirable state. We provide analytical and numerical evidence that easily controllable networks are fragile, suggesting that natural and man-made systems can either be resilient to parameters perturbation or efficient to adapt their state in response to external excitations and controls
Functional target controllability of networks: structural properties and efficient algorithms
In this paper we consider the problem of controlling a limited number of
target nodes of a network. Equivalently, we can see this problem as controlling
the target variables of a structured system, where the state variables of the
system are associated to the nodes of the network. We deal with this problem
from a different point of view as compared to most recent literature. Indeed,
instead of considering controllability in the Kalman sense, that is, as the
ability to drive the target states to a desired value, we consider the stronger
requirement of driving the target variables as time functions. The latter
notion is called functional target controllability. We think that restricting
the controllability requirement to a limited set of important variables
justifies using a more accurate notion of controllability for these variables.
Remarkably, the notion of functional controllability allows formulating very
simple graphical conditions for target controllability in the spirit of the
structural approach to controllability. The functional approach enables us,
moreover, to determine the smallest set of steering nodes that need to be
actuated to ensure target controllability, where these steering nodes are
constrained to belong to a given set. We show that such a smallest set can be
found in polynomial time. We are also able to classify the possible actuated
variables in terms of their importance with respect to the functional target
controllability problem.Comment: 10 pages, 4 diagrams; to appear in the IEEE Transactions on Network
Science and Engineerin