Locally Optimal Control of Complex Networks

TL;DR

This paper introduces a method for locally optimal control of complex networks by deriving a time-varying control set, enabling local control trajectories in linearized systems and proposing a series of local control actions for distant targets.

Contribution

It provides a novel approach to control linearized nonlinear systems locally by defining a time-varying control set and sequential re-linearization for distant targets.

Findings

Derived a time-varying control set for linearized systems

Guaranteed local control trajectories within the set

Proposed sequential local control actions for distant states

Abstract

It has recently been shown that the minimum energy solution of the control problem for a linear system produces a control trajectory that is nonlocal. An issue then arises when the dynamics represents a linearization of the underlying nonlinear dynamics of the system where the linearization is only valid in a local region of the state space. Here we provide a solution to the problem of optimally controlling a linearized system by deriving a time-varying set that represents all possible control trajectories parameterized by time and energy. As long as the control action terminus is defined within this set, the control trajectory is guaranteed to be local. If the desired terminus of the control action is far from the initial state, a series of local control actions can be performed in series, re-linearizing the dynamics at each new position.