Analysis, synchronization and control of complex networks

i) Synchronization and consensus in network of dynamical systems. The topological properties of complex networks and their effect on emerging collective dynamics, such as consensus and synchronization, have been studied. Different analytical tools have been employed, such as Lyapunov-based ones, contraction theory, and extensions of the Master Stability Function approach.

ii) Adaptive synchronization of complex networks. Novel adaptive strategies for synchronization have been devised, and their effectiveness tested both numerically and analytically. The theoretical developments have been then further widened through a collaboration with Professors Guanrong Chen (City University of Hong Kong), Jurgen Kurths, (Research Domain IV, Institute for Climate Impact Research, Potsdam, Germania) and Wenwu Yu (Southeast University, Nanjing, China).

iii) Pinning control of networks of dynamical systems. Decentralized techniques for adapting coupling and control gains have been devised to control networks by directly accessing (pinning) only a limited fraction of nodes. Moreover, pinning control techniques have been extended to the case where it is not feasible to control the network at every time instant and/or node dynamics are uncertain. The feasibility of the devised pinning control strategies has been experimentally validated through a setup composed by 8 Chua’s circuits, built in the Electrical Laboratory of the Department of Electrical Engineering and Information Technology.

Selected publications

• L. F. R. Turci, P. De Lellis, E. E. Macau, M. Di Bernardo, M. M. R. Simoes, Adaptive pinning control: A review of the fully decentralized strategy and its extensions, The European Physical Journal Special Topics, 223(13), 2649-2664, 2014

• V. Mwaffo, P. DeLellis, M. Porfiri, “Criteria for stochastic pinning control of networks of chaotic maps”, Chaos, 24(1), 013101, 2014.

• W. Yu, P. DeLellis, G. Chen, M. di Bernardo, J. Kurths, “Distributed adaptive control of synchronization in complex networks”, IEEE Transactions on Automatic Control, 57(8), 2153-2158, 2012.

• P. DeLellis, M. diBernardo, F. Garofalo, D. Liuzza, “Analysis and Stability of Consensus in Networked Control Systems”, Applied Mathematics and Computation, Special Issue in Honor of George Leitmann, 217(3), 988-1000, 2010.

• P. DeLellis, M. diBernardo, F. Garofalo, “Novel decentralized adaptive strategies for the synchronization of complex networks”, Automatica, 45(5), 1312-1318, 2009.