Topology Identification of Dynamical Signed Graphs
This work addresses topology identification in signed networks, which is incremental as it builds on existing graph theory and adaptive control methods.
The authors tackled the problem of identifying the topology of dynamical signed networks with cooperative and antagonistic interactions by proposing an adaptive control protocol, achieving simultaneous identification and synchronization with uniform semiglobal practical asymptotic stability of estimation errors.
We propose an adaptive control protocol for identifying the topology of dynamical networks interconnected over undirected graphs with cooperative and antagonistic interactions. The signed network is modeled using a repelling Laplacian. Topology identification relies on an edge-based formulation of the network and adaptive control protocols through the design of a persistently excited auxiliary network. Our approach guarantees the simultaneous identification and synchronization of the unknown signed network and establishes uniform semiglobal practical asymptotic stability of the estimation errors. Numerical simulations validate our theoretical results.