ABSTRACT

Controlling complex networks is relevant to many areas of science and engineering, and has the potential to generate technological breakthroughs. The aim of the talk is to discuss recent results from AFOSR sponsored research on complex networks at Arizona State University: (1) optimization of network controllability and (2) energy required for controlling complex networks.

For the first problem, optimal control is referred to as the situation where a large, complex networked dynamical system is driven toward some desired state using as few external control signals as possible. In the past year, we proposed a general approach to optimizing the network controllability by judiciously perturbing the structure of the network. The principle of our perturbation method was validated theoretically and demonstrated numerically for homogeneous and heterogeneous random networks and for different types of real networks as well. The applicability of the method was addressed with respect to the relative costs of establishing links and imposing external controllers. The implementation of our method elucidates, interestingly, some intricate relationship between certain structural properties of the network and its controllability.

For the second problem, we addressed the physically important issue of the energy required for achieving control by deriving and validating scaling laws for the lower and upper energy bounds. These bounds represent a reasonable estimate of the energy cost associated with control, and provide a step forward from the current research on controllability toward ultimate control of complex networked systems.

References:

1. W.-X. Wang, X. Ni, Y.-C. Lai, and C. Grebogi, “Optimizing controllability of complex networks by small structural perturbations,” Physical Review E 85, 026115 (2012).

2. G. Yan, J. Ren, Y.-C. Lai, C. H. Lai, and B. Li, “Controlling complex networks - how much energy is needed?” Physical Review Letters 108, 218703 (2012).