5 research outputs found
Neural Ordinary Differential Equation Control of Dynamics on Graphs
We study the ability of neural networks to calculate feedback control signals
that steer trajectories of continuous time non-linear dynamical systems on
graphs, which we represent with neural ordinary differential equations (neural
ODEs). To do so, we present a neural-ODE control (NODEC) framework and find
that it can learn feedback control signals that drive graph dynamical systems
into desired target states. While we use loss functions that do not constrain
the control energy, our results show, in accordance with related work, that
NODEC produces low energy control signals. Finally, we evaluate the performance
and versatility of NODEC against well-known feedback controllers and deep
reinforcement learning. We use NODEC to generate feedback controls for systems
of more than one thousand coupled, non-linear ODEs that represent epidemic
processes and coupled oscillators.Comment: Fifth version improves and clears notatio
Actuator Placement for Optimizing Network Performance under Controllability Constraints
With the rising importance of large-scale network control, the problem of
actuator placement has received increasing attention. Our goal in this paper is
to find a set of actuators minimizing the metric that measures the average
energy consumption of the control inputs while ensuring structural
controllability of the network. As this problem is intractable, greedy
algorithm can be used to obtain an approximate solution. To provide a
performance guarantee for this approach, we first define the submodularity
ratio for the metric under consideration and then reformulate the structural
controllability constraint as a matroid constraint. This shows that the problem
under study can be characterized by a matroid optimization involving a weakly
submodular objective function. Then, we derive a novel performance guarantee
for the greedy algorithm applied to this class of optimization problems.
Finally, we show that the matroid feasibility check for the greedy algorithm
can be cast as a maximum matching problem in a certain auxiliary bipartite
graph related to the network graph