2 research outputs found
Controllability of Heterogeneous Multi-Agent Networks
The existing results on controllability of multi-agents networks are mostly
based on homogeneous nodes. This paper focuses on controllability of
heterogeneous multi-agent networks, where the agents are modeled as two types.
One type is that the agents are of the same high-order dynamics, and the
interconnection topologies of the information flow in different orders are
supposed to be different. It is proved that a heterogeneous-topology network is
controllable if and only if the first-order information topology is
leader-follower connected, and there exists a Laplacian matrix, which is a
linear combination of the Laplacian matrices of each order information, whose
corresponding topology is controllable. The other type is that the agents are
of generic linear dynamics, and the dynamics are supposed to be heterogeneous.
A necessary and sufficient condition for controllability of
heterogeneous-dynamic networks is that each agent contains a controllable
dynamic part, and the interconnection topology of the network is
leader-follower connected. If some dynamics of the agents are not controllable,
the controllability between the agents and the whole network is also studied by
introducing the concept of eigenvector-uncontrollable. Different illustrative
examples are provided to demonstrate the effectiveness of the theoretical
results in this paper
Energy cost for target control of complex networks
To promote the implementation of realistic control over various complex
networks, recent work has been focusing on analyzing energy cost. Indeed, the
energy cost quantifies how much effort is required to drive the system from one
state to another when it is fully controllable. A fully controllable system
means that the system can be driven by external inputs from any initial state
to any final state in finite time. However, it is prohibitively expensive and
unnecessary to confine that the system is fully controllable when we merely
need to accomplish the so-called target control---controlling a subnet of nodes
chosen from the entire network. Yet, when the system is partially controllable,
the associated energy cost remains elusive. Here we present the minimum energy
cost for controlling an arbitrary subset of nodes of a network. Moreover, we
systematically show the scaling behavior of the precise upper and lower bounds
of the minimum energy in term of the time given to accomplish control. For
controlling a given number of target nodes, we further demonstrate that the
associated energy over different configurations can differ by several orders of
magnitude. When the adjacency matrix of the network is nonsingular, we can
simplify the framework by just considering the induced subgraph spanned by
target nodes instead of the entire network. Importantly, we find that, energy
cost could be saved by orders of magnitude as we only need the partial
controllability of the entire network. Our theoretical results are all
corroborated by numerical calculations, and pave the way for estimating the
energy cost to implement realistic target control in various applications