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Author ORCID Identifier

0000-0002-2670-5864

Abstract

Conventional control theory considers controlling the behavior of a dynamical system toward a desired state by injecting externally designed inputs into the system. Meanwhile, most complex systems exhibit self-organization through local information exchanges among individual dynamical components that are embedded within a complex network of interactions. The self-organizing dynamics of those systems are realized in a highly distributed manner using locally available information only, and therefore, their behaviors have not been discussed much from a control theoretic viewpoint. Meanwhile, adaptive networks, i.e., dynamical networks whose states and topologies coevolve at similar time scales, can offer a promising theoretical framework in which a distributed form of "self-control" can be formulated as adaptive link weight adjustments. Here we propose and study a set of models of self-controlling dynamical networks that can self-organize their own states into a desired one through distributed adaptive link weight adjustments. We demonstrate the feasibility of both a standard first-order adaptive control approach and a second-order approach. Numerical experiments show that the second-order approach works significantly better than the first-order one, achieving a substantially faster and more robust convergence with less transient behaviors. The performance difference is more manifested for systems with faster adaptive network dynamics. However, the second-order approach turns out to be highly sensitive to noise/uncertainty in the system's states, suggesting a non-trivial trade-off between the two self-control approaches.

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